AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYSolving Quadratic Equations: Factoring

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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
x squared plus 5 is equal to 176
B
x times open paren x plus 5 close paren is equal to 176
C
x squared minus 5 is equal to 176
D
x times open paren x minus 5 close paren is equal to 176
2
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y , the length of the room? Choose three correct answers.

A
y times open paren y minus 5 close paren plus 750 is equal to 0
B
y squared minus 5 y is equal to 750
C
open paren y plus 25 close paren times open paren y minus 30 close paren is equal to 0
D
750 minus y times open paren y minus 5 close paren is equal to 0
E
y times open paren y plus 5 close paren is equal to 750
4

For what values of x is x squared plus 2 x is equal to 24 true?

A
4 and negative 6
B
negative 4 and 6
C
negative 6 and negative 4
D
6 and 4
5

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
x squared minus 8 x plus 308 is equal to 0
B
x squared minus 8 x minus 308 is equal to 0
C
x squared plus 8 x minus 308 is equal to 0
D
x squared plus 8 x plus 308 is equal to 0
6

For what values of x is x squared minus 36 is equal to 5 x true?

A
negative 4 and 9
B
negative 9 and negative 4
C
9 and 4
D
4 and negative 9
8

A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches. Which equation can be used to solve for x , the increase in side length of the square in inches?

A
x squared plus 8 x minus 65 is equal to 0
B
x squared plus 4 x minus 65 is equal to 0
C
x squared plus 8 x minus 81 is equal to 0
D
x squared plus 4 x minus 81 is equal to 0
10

Two positive integers are 3 units apart on a number line. Their product is 108. Which equation can be used to solve for m , the greater integer?

A
open paren m plus 3 close paren times open paren m minus 3 close paren is equal to 108
B
m times open paren m plus 3 close paren is equal to 108
C
open paren m minus 12 close paren times open paren m minus 9 close paren is equal to 108
D
m times open paren m minus 3 close paren is equal to 108

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