Exam 6: Factoring and Quadratic Equations

The longer leg of a right triangle is 2 centimeters longer than twice its shorter leg. The hypotenuse is 1 centimeter longer than longer leg. Find the dimensions of the lengths of the triangle.

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Question 1

Correct Answer:

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D

Factor the trinomial completely. $2 x ^ { 2 } + 9 x + 4$

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Question 2

Correct Answer:

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A

Factor the trinomial. Factor out the GCF first. $2 x ^ { 2 } + 8 x - 64$

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(Multiple Choice)

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Question 3

Correct Answer:

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C

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $5 - x ^ { 2 } - 4 x$

(Multiple Choice)

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Question 4

The equation $7 x ^ { 2 } - 5 x - 1 = 0$ is written in $a x ^ { 2 } + b x + c = 0$ form. What are a, b and c ?

(Multiple Choice)

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Question 5

Factor the following perfect square trinomial. $25 a ^ { 2 } - 60 a y + 36 y ^ { 2 }$

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Question 6

The distance (in feet)that an object will fall in t seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

(Multiple Choice)

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Question 7

Factor by grouping. $13 x ^ { 2 } + 91 x - 3 x - 21$

(Multiple Choice)

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Question 8

Factor the trinomial. Factor out $-$ 1 first. $- a ^ { 2 } + 11 a - 30$

(Multiple Choice)

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Question 9

Factor the trinomial. Factor out any common monomials first (including $-$ 1 if necessary). $- 7 u ^ { 2 } + 42 u - 63$

(Multiple Choice)

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Question 10

The longer leg of a right triangle is 3 units longer than the shorter leg and 3 units less than hypotenuse. Find the length of the shorter leg of the triangle.

(Multiple Choice)

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Question 11

Paul is elder than his brother Bryan. Their ages are consecutive integers whose product is 552. How old are Bryan and Paul?

(Multiple Choice)

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Question 12

The length of the rectangular desk is twice its width. Its area is 0.98 square meters. Find the dimensions of the desk.

(Multiple Choice)

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Question 13

Factor by grouping. $a x ^ { 4 } - x ^ { 4 } + 2 a - 2$

(Multiple Choice)

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Question 14

Factor the trinomial. $x ^ { 2 } - 18 x + 77$

(Multiple Choice)

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Question 15

Use the factoring method to solve the equation. $6 x ^ { 2 } + 13 x + 5 = 0$

(Multiple Choice)

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Question 16

Factor the expression. $y ^ { 3 } + 64$

(Multiple Choice)

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Question 17

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

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Question 18

Factor the expression. $( a - m ) c + ( a - m ) f$

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Question 19

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

(Multiple Choice)

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Question 20

The longer leg of a right triangle is 2 centimeters longer than twice its shorter leg. The hypotenuse is 1 centimeter longer than longer leg. Find the dimensions of the lengths of the triangle.

Factor the trinomial completely. $2 x ^ { 2 } + 9 x + 4$

Factor the trinomial. Factor out the GCF first. $2 x ^ { 2 } + 8 x - 64$

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $5 - x ^ { 2 } - 4 x$

The equation $7 x ^ { 2 } - 5 x - 1 = 0$ is written in $a x ^ { 2 } + b x + c = 0$ form. What are a, b and c ?

Factor the following perfect square trinomial. $25 a ^ { 2 } - 60 a y + 36 y ^ { 2 }$

The distance (in feet)that an object will fall in t seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

Factor by grouping. $13 x ^ { 2 } + 91 x - 3 x - 21$

Factor the trinomial. Factor out $-$ 1 first. $- a ^ { 2 } + 11 a - 30$

Factor the trinomial. Factor out any common monomials first (including $-$ 1 if necessary). $- 7 u ^ { 2 } + 42 u - 63$

The longer leg of a right triangle is 3 units longer than the shorter leg and 3 units less than hypotenuse. Find the length of the shorter leg of the triangle.

Paul is elder than his brother Bryan. Their ages are consecutive integers whose product is 552. How old are Bryan and Paul?

The length of the rectangular desk is twice its width. Its area is 0.98 square meters. Find the dimensions of the desk.

Factor by grouping. $a x ^ { 4 } - x ^ { 4 } + 2 a - 2$

Factor the trinomial. $x ^ { 2 } - 18 x + 77$

Use the factoring method to solve the equation. $6 x ^ { 2 } + 13 x + 5 = 0$

Factor the expression. $y ^ { 3 } + 64$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Factor the expression. $( a - m ) c + ( a - m ) f$

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 6: Factoring and Quadratic Equations

The longer leg of a right triangle is 2 centimeters longer than twice its shorter leg. The hypotenuse is 1 centimeter longer than longer leg. Find the dimensions of the lengths of the triangle.

Factor the trinomial completely. 2x2+9x+42 x ^ { 2 } + 9 x + 42x2+9x+4

Factor the trinomial. Factor out the GCF first. 2x2+8x−642 x ^ { 2 } + 8 x - 642x2+8x−64

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). 5−x2−4x5 - x ^ { 2 } - 4 x5−x2−4x

The equation 7x2−5x−1=07 x ^ { 2 } - 5 x - 1 = 07x2−5x−1=0 is written in ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 form. What are a, b and c ?

Factor the following perfect square trinomial. 25a2−60ay+36y225 a ^ { 2 } - 60 a y + 36 y ^ { 2 }25a2−60ay+36y2

The distance (in feet)that an object will fall in t seconds is given by the formula s=16t2s = 16 t ^ { 2 }s=16t2 . How long will it take an object to fall 576 feet?

Factor by grouping. 13x2+91x−3x−2113 x ^ { 2 } + 91 x - 3 x - 2113x2+91x−3x−21

Factor the trinomial. Factor out −-− 1 first. −a2+11a−30- a ^ { 2 } + 11 a - 30−a2+11a−30

Factor the trinomial. Factor out any common monomials first (including −-− 1 if necessary). −7u2+42u−63- 7 u ^ { 2 } + 42 u - 63−7u2+42u−63

The longer leg of a right triangle is 3 units longer than the shorter leg and 3 units less than hypotenuse. Find the length of the shorter leg of the triangle.

Paul is elder than his brother Bryan. Their ages are consecutive integers whose product is 552. How old are Bryan and Paul?

The length of the rectangular desk is twice its width. Its area is 0.98 square meters. Find the dimensions of the desk.

Factor by grouping. ax4−x4+2a−2a x ^ { 4 } - x ^ { 4 } + 2 a - 2ax4−x4+2a−2

Factor the trinomial. x2−18x+77x ^ { 2 } - 18 x + 77x2−18x+77

Use the factoring method to solve the equation. 6x2+13x+5=06 x ^ { 2 } + 13 x + 5 = 06x2+13x+5=0

Factor the expression. y3+64y ^ { 3 } + 64y3+64

Factor the trinomial square and use the square root method to solve the equation. 3x2+7x+1=23 x ^ { 2 } + 7 x + 1 = 23x2+7x+1=2

Factor the expression. (a−m)c+(a−m)f( a - m ) c + ( a - m ) f(a−m)c+(a−m)f

The height in feet h of a rocket in flight is given by the formula h=−16t2+224th = - 16 t ^ { 2 } + 224 th=−16t2+224t , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Factor the trinomial completely. $2 x ^ { 2 } + 9 x + 4$

Factor the trinomial. Factor out the GCF first. $2 x ^ { 2 } + 8 x - 64$

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $5 - x ^ { 2 } - 4 x$

The equation $7 x ^ { 2 } - 5 x - 1 = 0$ is written in $a x ^ { 2 } + b x + c = 0$ form. What are a, b and c ?

Factor the following perfect square trinomial. $25 a ^ { 2 } - 60 a y + 36 y ^ { 2 }$

The distance (in feet)that an object will fall in t seconds is given by the formula $s = 16 t ^ { 2 }$ . How long will it take an object to fall 576 feet?

Factor by grouping. $13 x ^ { 2 } + 91 x - 3 x - 21$

Factor the trinomial. Factor out $-$ 1 first. $- a ^ { 2 } + 11 a - 30$

Factor the trinomial. Factor out any common monomials first (including $-$ 1 if necessary). $- 7 u ^ { 2 } + 42 u - 63$

Factor by grouping. $a x ^ { 4 } - x ^ { 4 } + 2 a - 2$

Factor the trinomial. $x ^ { 2 } - 18 x + 77$

Use the factoring method to solve the equation. $6 x ^ { 2 } + 13 x + 5 = 0$

Factor the expression. $y ^ { 3 } + 64$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Factor the expression. $( a - m ) c + ( a - m ) f$

The height in feet h of a rocket in flight is given by the formula $h = - 16 t ^ { 2 } + 224 t$ , where t is the time of the flight in seconds. How long will it take for the rocket to hit the ground?