Question

factor using the ac - method.
$10x^2 + 17x + 3$
a. 1 and 30
b. 5 and 6
c. 2 and 15
d. none of the pairs of factors sum to 17.
what is the next best step in factoring the given expression using the ac - method?
a. factor by grouping.
b. divide the expression by the leading coefficient.
c. examine the signs of coefficients to determine the signs of the factors.
d. split the middle term, writing it as the sum of two factors of 30.

Explanation:

Step1: Calculate $ac$ value

For $10x^2+17x+3$, $a=10$, $c=3$, so $ac=10\times3=30$.

Step2: Find factors of $ac$ summing to $b$

We need factors of 30 that add to $b=17$. Check pairs:

• $1+30=31

eq17$

• $5+6=11

eq17$

• $2+15=17$, which matches.

Step3: Identify next ac-method step

After finding the correct factor pair, the next step is to split the middle term using these factors, then factor by grouping. The direct next step after finding the pair is splitting the middle term.

Answer:

First question: C. 2 and 15
Second question: D. Split the middle term, writing it as the sum of two factors of 30.