1. factor the following quadratic equation.
x^2+10x+21
a. (x+21)(x+1)
b.(x+5)(x+2)
c.(x+3)(x+7)
d.(x-3)(x-7)
2. factor the following quadratic expression.
x^2-11x+24
a.(x+6)(x+4)
b.(x-2)(x-12)
c.(x-1)(x-24)
d.(x-3)(x-8)
3. factor the following quadratic expression.
x^2+2x-8
a.(x+2)(x+4)
b.(x-2)(x-4)
c.(x-2)(x+4)
d.(x+2)(x-4)
4. factor the following quadratic expression.
a.(x+6)(x+6)
b.(x-6)(x-6)
c.(x-4)(x-9)
d.(x+9)(x+9)
5. factor the following quadratic expression.
x^2-81
a.(x+9)(x+9)
b.(x-9)(x+9)
c.(x-81)(x-1)
d.(x+81)(x-1)

1) C. (x+3)(x+7)

2) D. (x-3)(x-8)

3) C. (x-2)(x+4)

5) B. (x+9)(x-9)

Step-by-step explanation:

1)

x2 + 10x + 21

(we look for 2 numbers whose product gives 21 and whose sum gives 10, then replace 10x by those two numbers)

x2 + 7x + 3x +21

x(x+7) + 3(x+7)

(x+3)(x+7)

2)

x2 - 11x + 24

(we look for 2 numbers whose product gives 24 and whose sum gives -11, then replace -11x by those two numbers)

x2 -3x-8x +24

x(x-3) -8(x-3)

(x-3)(x-8)

3)

x2 + 2x - 8

(we look for 2 numbers whose product gives -8 and whose sum gives 2, then replace 2x by those two numbers)

x2 + 2x - 8

x2 + 4x - 2x - 8

x(x+4) -2(x+4)

(x+4)(x-2)

5)

x2 - 81

Its a difference of two squares

(x-9)(x+9)

27

step-by-step explanation: