Solving Quadratic Equations: Factoring Answers

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Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?

A
x2 + 5 = 176
B
x(x + 5) = 176
C
x(x – 5) = 176
D
x2 – 5 = 176
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The function h(t) = –16t2 + 96t + 6 represents an object projected into the air from a cannon. The maximum height reached by the object is 150 feet.

A
2 seconds
B
3 seconds
C
6 seconds
D
9 seconds
3

Two negative integers are 8 units apart on the number line and have a product of 308.Which equation could be used to determine x, the smaller negative integer?

A
x2 + 8x – 308 = 0
B
x2 – 8x + 308 = 0
C
x2 + 8x + 308 = 0
D
x2 − 8x − 308 = 0
5

John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.

A
w(w – 2) = 48
B
w(w + 2) = 48
C
2w(w – 2) = 48
D
2w(w + 2) = 48
6

Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.

A
–19
B
–13
C
13
D
16
7

Which is a solution to the equation?(x −2)(x + 5) = 18

A
x = −10
B
x = −7
C
x = −4
D
x = −2
9

Two positive integers are 3 units apart on a number line. Their product is 108.

A
m(m – 3) = 108
B
m(m + 3) = 108
C
(m + 3)(m – 3) = 108
D
(m – 12)(m – 9) = 108
10

For what values of x is x2 + 2x = 24 true?

A
–6 and –4
B
–4 and 6
C
4 and –6
D
6 and 4
11

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.

A
x2 + 4x – 81 = 0
B
x2 + 4x – 65 = 0
C
x2 + 8x – 65 = 0
D
x2 + 8x – 81 = 0
12

Which is a solution to (x – 3)(x + 9) = –27?

A
x = –9
B
x = –3
C
x = 0
D
x = 6
13

Which equations can be used to solve for y, the length of the room? Select three options.

A
y(y + 5) = 750
B
y2 – 5y = 750
C
750 – y(y – 5) = 0
D
y(y – 5) + 750 = 0
E
(y + 25)(y – 30) = 0
14

The product of two consecutive negative integers is 600. What is the value of the lesser integer?

A
–60
B
–30
C
–25
D
–15
15

Which is a solution to (x − 2)(x + 10) = 13?

A
x = 3
B
x = 8
C
x = 10
D
x = 11
16

For what values of x is x2-36=5x true?

A
-9 and -4
B
-4 and 9
C
4 and -9
D
9 and 4

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