Question

Monica is attempting to factor the expression 18x2 + 27x – 5. In her first step, she rewrites the expression as 18x2 + 32x – 5x – 5. Which of the following statements is true about Monica's work?

Answer 1

B

Explanation:

For quadratic expression in this form, the first step is to multiply the number in front of
`x^2` with the last term, the constant (with the sign in front as well). This is the "multiplied number".

Step 2 is to come up with 2 numbers which when multiplied is equal to the "multiplied number" in step 1 above and also add to the number in front of
`x`.

For this problem, we would need 2 numbers that

• Add up to 27, and
• When multiplied, comes to -90 (18 * -5 = -90)

They already found the 2 numbers as expressed in the form shown
`18x^2+32x-5x-5`. The 2 numbers are +32 and -5.

Do they add up to 27, as required?

Yes, 32-5=27

Do they come to -90 when multiplied?

No, 32 * -5 = -160

Hence, they add up, BUT NOT multiplied.

So the answer choice B is right.