Question

question
factor completely.
5x² + 46x + 9
answer
attempt 1 out of 2

Explanation:

Step1: Find pair for AC method

For $ax^2+bx+c$, compute $a \times c = 5 \times 9 = 45$. Find two numbers that multiply to 45 and add to 46: 1 and 45.

Step2: Split middle term

Rewrite $46x$ as $x + 45x$:
$5x^2 + x + 45x + 9$

Step3: Group and factor pairs

Group first/second and third/fourth terms:
$(5x^2 + x) + (45x + 9)$
Factor GCF from each group:
$x(5x + 1) + 9(5x + 1)$

Step4: Factor common binomial

Factor out $(5x + 1)$:
$(5x + 1)(x + 9)$

Answer:

$(5x + 1)(x + 9)$