Exam 7: Factoring, Solving Equations and Problem Solving

Suppose that the width of a certain rectangle is 6 inches less than its length. The area is numerically 9 less than twice the perimeter. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

(Short Answer)

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Question 41

Solve the equation. $z ^ { 2 } - 13 z = 0$

(Multiple Choice)

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Question 42

The sum of the areas of two circles is $65 \pi$ square inches. The length of a radius of the smaller circle is 3 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle. __________ inches

(Short Answer)

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Question 43

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$ Enter none if the trinomial is not factorable.

(Short Answer)

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Question 44

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 x ^ { 2 } - 23 x + 7$

(Multiple Choice)

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Question 45

Solve the equation. $9 x - x ^ { 2 } = 0$

(Multiple Choice)

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Question 46

Solve the equation. $n ^ { 2 } - 2 n - 80 = 0$

(Multiple Choice)

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Question 47

Solve the equation. $81 a ^ { 2 } - 180 a + 100 = 0$

(Multiple Choice)

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Question 48

Solve the equation. $612 x ^ { 3 } = 17 x$

(Multiple Choice)

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Question 49

Factor the following trinomial completely. $y ^ { 2 } - y - 30$

(Multiple Choice)

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Question 50

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number. Enter your answer as ordered pairs separated by commas.

(Short Answer)

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Question 51

Solve the equation. $4 x ^ { 2 } - 8 x = 0$

(Multiple Choice)

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Question 52

One positive number is 5 larger than another number. The sum of their squares is 53. Find the numbers. Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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Question 53

Find which of the following trinomials is not factorable using integers.

(Multiple Choice)

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Question 54

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 6 z - 3$

(Short Answer)

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Question 55

Set up an equation and solve the problem. The area of a triangle is 50 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length. __________ feet

(Short Answer)

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Question 56

Solve the equation. $x ( x - 9 ) = - 20$

(Multiple Choice)

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Question 57

Use the process of factoring by grouping to factor the polynomial. $y ^ { 2 } - 4 y - 2 y + 8$

(Multiple Choice)

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Question 58

Solve the equation. $3 a ^ { 2 } - 18 a = 0$ Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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Question 59

Factor the following perfect square trinomial. $9 p ^ { 2 } - 30 p y + 25 y ^ { 2 }$

(Multiple Choice)

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Question 60

Suppose that the width of a certain rectangle is 6 inches less than its length. The area is numerically 9 less than twice the perimeter. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

Solve the equation. $z ^ { 2 } - 13 z = 0$

The sum of the areas of two circles is $65 \pi$ square inches. The length of a radius of the smaller circle is 3 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle. __________ inches

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$ Enter none if the trinomial is not factorable.

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 x ^ { 2 } - 23 x + 7$

Solve the equation. $9 x - x ^ { 2 } = 0$

Solve the equation. $n ^ { 2 } - 2 n - 80 = 0$

Solve the equation. $81 a ^ { 2 } - 180 a + 100 = 0$

Solve the equation. $612 x ^ { 3 } = 17 x$

Factor the following trinomial completely. $y ^ { 2 } - y - 30$

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number. Enter your answer as ordered pairs separated by commas.

Solve the equation. $4 x ^ { 2 } - 8 x = 0$

One positive number is 5 larger than another number. The sum of their squares is 53. Find the numbers. Please enter your answer as two numbers, separated by a comma.

Find which of the following trinomials is not factorable using integers.

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 6 z - 3$

Set up an equation and solve the problem. The area of a triangle is 50 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length. __________ feet

Solve the equation. $x ( x - 9 ) = - 20$

Use the process of factoring by grouping to factor the polynomial. $y ^ { 2 } - 4 y - 2 y + 8$

Solve the equation. $3 a ^ { 2 } - 18 a = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the following perfect square trinomial. $9 p ^ { 2 } - 30 p y + 25 y ^ { 2 }$

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 7: Factoring, Solving Equations and Problem Solving

Suppose that the width of a certain rectangle is 6 inches less than its length. The area is numerically 9 less than twice the perimeter. Find the length and width of the rectangle. Please enter your answer as two numbers without the units, separated by a comma.

Solve the equation. z2−13z=0z ^ { 2 } - 13 z = 0z2−13z=0

The sum of the areas of two circles is 65π65 \pi65π square inches. The length of a radius of the smaller circle is 3 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle. __________ inches

Factor the trinomial completely. 12y2+12y+312 y ^ { 2 } + 12 y + 312y2+12y+3 Enter none if the trinomial is not factorable.

Factor the trinomial completely. Indicate if it is not factorable using integers. 6x2−23x+76 x ^ { 2 } - 23 x + 76x2−23x+7

Solve the equation. 9x−x2=09 x - x ^ { 2 } = 09x−x2=0

Solve the equation. n2−2n−80=0n ^ { 2 } - 2 n - 80 = 0n2−2n−80=0

Solve the equation. 81a2−180a+100=081 a ^ { 2 } - 180 a + 100 = 081a2−180a+100=0

Solve the equation. 612x3=17x612 x ^ { 3 } = 17 x612x3=17x

Factor the following trinomial completely. y2−y−30y ^ { 2 } - y - 30y2−y−30

Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number. Enter your answer as ordered pairs separated by commas.

Solve the equation. 4x2−8x=04 x ^ { 2 } - 8 x = 04x2−8x=0

One positive number is 5 larger than another number. The sum of their squares is 53. Find the numbers. Please enter your answer as two numbers, separated by a comma.

Find which of the following trinomials is not factorable using integers.

Use the process of factoring by grouping to factor the polynomial. 2z2+z−6z−32 z ^ { 2 } + z - 6 z - 32z2+z−6z−3

Set up an equation and solve the problem. The area of a triangle is 50 square feet. If one side of the triangle and the altitude to that side are of equal length, find the length. __________ feet

Solve the equation. x(x−9)=−20x ( x - 9 ) = - 20x(x−9)=−20

Use the process of factoring by grouping to factor the polynomial. y2−4y−2y+8y ^ { 2 } - 4 y - 2 y + 8y2−4y−2y+8

Solve the equation. 3a2−18a=03 a ^ { 2 } - 18 a = 03a2−18a=0 Please enter your answer as two numbers, separated by a comma.

Factor the following perfect square trinomial. 9p2−30py+25y29 p ^ { 2 } - 30 p y + 25 y ^ { 2 }9p2−30py+25y2

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Solve the equation. $z ^ { 2 } - 13 z = 0$

The sum of the areas of two circles is $65 \pi$ square inches. The length of a radius of the smaller circle is 3 inches less than the length of a radius of the larger circle. Find the length of a radius of the larger circle. __________ inches

Factor the trinomial completely. $12 y ^ { 2 } + 12 y + 3$ Enter none if the trinomial is not factorable.

Factor the trinomial completely. Indicate if it is not factorable using integers. $6 x ^ { 2 } - 23 x + 7$

Solve the equation. $9 x - x ^ { 2 } = 0$

Solve the equation. $n ^ { 2 } - 2 n - 80 = 0$

Solve the equation. $81 a ^ { 2 } - 180 a + 100 = 0$

Solve the equation. $612 x ^ { 3 } = 17 x$

Factor the following trinomial completely. $y ^ { 2 } - y - 30$

Solve the equation. $4 x ^ { 2 } - 8 x = 0$

Use the process of factoring by grouping to factor the polynomial. $2 z ^ { 2 } + z - 6 z - 3$

Solve the equation. $x ( x - 9 ) = - 20$

Use the process of factoring by grouping to factor the polynomial. $y ^ { 2 } - 4 y - 2 y + 8$

Solve the equation. $3 a ^ { 2 } - 18 a = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the following perfect square trinomial. $9 p ^ { 2 } - 30 p y + 25 y ^ { 2 }$