Question

factor using the ac - method.\\(10x^{2}+17x + 3\\)\\(\circ\\) a. look for a pair of factors of 17 whose sum is 30.\\(\circ\\) b. look for a pair of factors of 17 whose sum is 3.\\(\circ\\) c. look for a pair of factors of 3 whose sum is 17.\\(\circ\\) d. look for a pair of factors of 30 whose sum is 17.\\(\\)\\(\\)which pair of factors of 30 below has a sum of 17?\\(\circ\\) a. 1 and 30\\(\circ\\) b. 5 and 6\\(\circ\\) c. 2 and 15\\(\circ\\) d. none of the pairs of factors sum to 17.

Explanation:

Step1: Recall ac-method first step

For quadratic $ax^2+bx+c$, calculate $ac$.
Here $a=10$, $c=3$, so $ac=10\times3=30$. We need factors of $ac$ that sum to $b=17$.

Step2: Evaluate first question options

Only option D matches the ac-method requirement: factors of 30 summing to 17.

Step3: Check factor pairs of 30

• A: $1+30=31

eq17$

• B: $5+6=11

eq17$

• C: $2+15=17$

Step4: Confirm second question answer

Pair 2 and 15 sums to 17, so option C is correct.

Answer:

First question: D. Look for a pair of factors of 30 whose sum is 17.
Second question: C. 2 and 15