Exam 7: Factoring, Solving Equations and Problem Solving

The area of a rectangle is 2 times the area of a square. If the rectangle is 10 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

(Multiple Choice)

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Question 281

The length of one leg of a right triangle is 7 centimeters more than the length of the other leg. The length of the hypotenuse is 17 centimeters. Find the lengths of the two legs.

(Multiple Choice)

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Question 282

Solve the equation. $m ^ { 2 } - 4 m - 5 = 0$

(Multiple Choice)

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Question 283

Find two numbers whose product is 40 such that one of the numbers is 2 more than two times the other number. Enter your answer as ordered pairs separated by commas.

(Short Answer)

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Question 284

Factor the following trinomial completely. $x ^ { 2 } + 4 x - 5$

(Short Answer)

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Question 285

Solve the equation. $10 ( p - 8 ) - p ( p - 8 ) = 0$ Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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Question 286

The area of a triangle is 35 square inches. One side of the triangle is 11 inches less than three times the length of the altitude to that side. Find the length of that side. __________ inches

(Short Answer)

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Question 287

As a general guideline when factoring, always look for a common monomial factor first.

(True/False)

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Question 288

Factor the polynomial completely. $7 z ^ { 6 } + 7 z ^ { 7 } + 7 z ^ { 4 }$

(Multiple Choice)

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Question 289

Find the greatest common factor of the given expressions. $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$

(Multiple Choice)

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Question 290

If n represents an even integer, then n + 2 represents the next consecutive even integer.

(True/False)

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Question 291

Solve the equation. $7 p ^ { 2 } = - 28 p$

(Multiple Choice)

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Question 292

Factor the following trinomial completely. $x ^ { 2 } + 7 x - 18$

(Multiple Choice)

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Question 293

Factor the following perfect square trinomial. $y ^ { 2 } + 4 y + 4$

(Multiple Choice)

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Question 294

One positive number is 4 larger than another number. The sum of their squares is 106. Find the numbers.

(Multiple Choice)

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Question 295

Solve the equation. $x ^ { 2 } - 196 = 0$ Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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Question 296

Suppose that the width of a certain rectangle is 4 inches less than its length. The area is numerically 11 less than twice the perimeter. Find the length and width of the rectangle.

(Multiple Choice)

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Question 297

Factor the polynomial completely. $18 x ^ { 2 } + 108$

(Short Answer)

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Question 298

Solve the equation. $x ( 24 x - 72 ) - 10 ( 24 x - 72 ) = 0$

(Multiple Choice)

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Question 299

Solve the equation. $( 11 p - 1 ) ( 7 p - 6 ) = 0$

(Short Answer)

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Question 300

The area of a rectangle is 2 times the area of a square. If the rectangle is 10 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

The length of one leg of a right triangle is 7 centimeters more than the length of the other leg. The length of the hypotenuse is 17 centimeters. Find the lengths of the two legs.

Solve the equation. $m ^ { 2 } - 4 m - 5 = 0$

Find two numbers whose product is 40 such that one of the numbers is 2 more than two times the other number. Enter your answer as ordered pairs separated by commas.

Factor the following trinomial completely. $x ^ { 2 } + 4 x - 5$

Solve the equation. $10 ( p - 8 ) - p ( p - 8 ) = 0$ Please enter your answer as two numbers, separated by a comma.

The area of a triangle is 35 square inches. One side of the triangle is 11 inches less than three times the length of the altitude to that side. Find the length of that side. __________ inches

As a general guideline when factoring, always look for a common monomial factor first.

Factor the polynomial completely. $7 z ^ { 6 } + 7 z ^ { 7 } + 7 z ^ { 4 }$

Find the greatest common factor of the given expressions. $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$

If n represents an even integer, then n + 2 represents the next consecutive even integer.

Solve the equation. $7 p ^ { 2 } = - 28 p$

Factor the following trinomial completely. $x ^ { 2 } + 7 x - 18$

Factor the following perfect square trinomial. $y ^ { 2 } + 4 y + 4$

One positive number is 4 larger than another number. The sum of their squares is 106. Find the numbers.

Solve the equation. $x ^ { 2 } - 196 = 0$ Please enter your answer as two numbers, separated by a comma.

Suppose that the width of a certain rectangle is 4 inches less than its length. The area is numerically 11 less than twice the perimeter. Find the length and width of the rectangle.

Factor the polynomial completely. $18 x ^ { 2 } + 108$

Solve the equation. $x ( 24 x - 72 ) - 10 ( 24 x - 72 ) = 0$

Solve the equation. $( 11 p - 1 ) ( 7 p - 6 ) = 0$

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

The area of a rectangle is 2 times the area of a square. If the rectangle is 10 inches long and the width of the rectangle is the same as the length of a side of the square, find the length of a side of the square.

The length of one leg of a right triangle is 7 centimeters more than the length of the other leg. The length of the hypotenuse is 17 centimeters. Find the lengths of the two legs.

Solve the equation. m2−4m−5=0m ^ { 2 } - 4 m - 5 = 0m2−4m−5=0

Find two numbers whose product is 40 such that one of the numbers is 2 more than two times the other number. Enter your answer as ordered pairs separated by commas.

Factor the following trinomial completely. x2+4x−5x ^ { 2 } + 4 x - 5x2+4x−5

Solve the equation. 10(p−8)−p(p−8)=010 ( p - 8 ) - p ( p - 8 ) = 010(p−8)−p(p−8)=0 Please enter your answer as two numbers, separated by a comma.

The area of a triangle is 35 square inches. One side of the triangle is 11 inches less than three times the length of the altitude to that side. Find the length of that side. __________ inches

As a general guideline when factoring, always look for a common monomial factor first.

Factor the polynomial completely. 7z6+7z7+7z47 z ^ { 6 } + 7 z ^ { 7 } + 7 z ^ { 4 }7z6+7z7+7z4

Find the greatest common factor of the given expressions. 45zd,40zd5 and 65z2d45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d45zd,40zd5 and 65z2d

If n represents an even integer, then n + 2 represents the next consecutive even integer.

Solve the equation. 7p2=−28p7 p ^ { 2 } = - 28 p7p2=−28p

Factor the following trinomial completely. x2+7x−18x ^ { 2 } + 7 x - 18x2+7x−18

Factor the following perfect square trinomial. y2+4y+4y ^ { 2 } + 4 y + 4y2+4y+4

One positive number is 4 larger than another number. The sum of their squares is 106. Find the numbers.

Solve the equation. x2−196=0x ^ { 2 } - 196 = 0x2−196=0 Please enter your answer as two numbers, separated by a comma.

Suppose that the width of a certain rectangle is 4 inches less than its length. The area is numerically 11 less than twice the perimeter. Find the length and width of the rectangle.

Factor the polynomial completely. 18x2+10818 x ^ { 2 } + 10818x2+108

Solve the equation. x(24x−72)−10(24x−72)=0x ( 24 x - 72 ) - 10 ( 24 x - 72 ) = 0x(24x−72)−10(24x−72)=0

Solve the equation. (11p−1)(7p−6)=0( 11 p - 1 ) ( 7 p - 6 ) = 0(11p−1)(7p−6)=0

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. $m ^ { 2 } - 4 m - 5 = 0$

Factor the following trinomial completely. $x ^ { 2 } + 4 x - 5$

Solve the equation. $10 ( p - 8 ) - p ( p - 8 ) = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. $7 z ^ { 6 } + 7 z ^ { 7 } + 7 z ^ { 4 }$

Find the greatest common factor of the given expressions. $45 z d , 40 z d ^ { 5 } \text { and } 65 z ^ { 2 } d$

Solve the equation. $7 p ^ { 2 } = - 28 p$

Factor the following trinomial completely. $x ^ { 2 } + 7 x - 18$

Factor the following perfect square trinomial. $y ^ { 2 } + 4 y + 4$

Solve the equation. $x ^ { 2 } - 196 = 0$ Please enter your answer as two numbers, separated by a comma.

Factor the polynomial completely. $18 x ^ { 2 } + 108$

Solve the equation. $x ( 24 x - 72 ) - 10 ( 24 x - 72 ) = 0$

Solve the equation. $( 11 p - 1 ) ( 7 p - 6 ) = 0$