Question

Please Help

Factor the expression. Then solve using the zero product property.
x² - 18x + 45

A {-18, 45}
B {-45, 18}
C {3, 15}
D {-15, -3}

Answer 1

C

Explanation:

Given

x² - 18x + 45

Consider the factors of the constant term (+ 45) which sum to give the coefficient of the x- term (- 18)

The factors are - 15 and - 3, since

- 15 × - 3 = + 45 and - 15 - 3 = - 18, thus

(x - 15)(x - 3) ← in factored form

To solve equate to zero, that is

(x - 15)(x - 3) = 0

Equate each factor to zero and solve for x

x - 15 = 0 ⇒ x = 15

x - 3 = 0 ⇒ x = 3

Solutions are { 3, 15 } → C

Answer 2

C {3, 15}

Explanation:

x² - 18x + 45

Factor

What 2 numbers multiply to 45 and add to -18

-15*-3 = 45

-15+-3 = -18

(x-15) (x-3) =0

Using the zero product property

x-15 =0 x-3=0

x-15+15=0+15 x-3+3=0+3

x=15 x=3