Question

factor using the ac - method.\\(10x^{2}+17x + 3\\)\\(17x=2x + 15x\\)\\(\text{now factor by grouping.}\\)\\(10x^{2}+17x + 3=10x^{2}+2x + 15x + 3\\)\\(=2x(5x + 1)+3(5x + 1)\\)\\(=(5x + 1)(2x + 3)\\)\\((\text{factor completely.})\\)\\(\text{check the factorization by multiplying.}\\)\\((5x + 1)(2x + 3)=\square\\)

Explanation:

Step1: Apply FOIL multiplication

Multiply first terms: $5x \times 2x = 10x^2$
Multiply outer terms: $5x \times 3 = 15x$
Multiply inner terms: $1 \times 2x = 2x$
Multiply last terms: $1 \times 3 = 3$

Step2: Combine like terms

$10x^2 + 15x + 2x + 3 = 10x^2 + 17x + 3$

Answer:

$10x^2 + 17x + 3$