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Factor the trinomial completely.
x^(2)+12 x+35
Select the correct choice below and, if neces
A. x^(2)+12 x+35= ◻
B. The polynomial is prime.

$4$ . Factor the trinomial completely. $\newline$ $x^{2}+12 x+35$ $\newline$ Select the correct choice below and, if neces $\newline$ A. $x^{2}+12 x+35=$ $\square$ $\newline$ B. The polynomial is prime.

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Factor out a monomial

Full solution

Q.

4

. Factor the trinomial completely.

\newline

x^{2}+12 x+35

\newline

Select the correct choice below and, if neces

\newline

A.

x^{2}+12 x+35=

\square

\newline

B. The polynomial is prime.

List Factors of $35$ : We list the pairs of factors of $35$ : $(1, 35)$ and $(5, 7)$ . We need to find which pair adds up to $12$ .
Find Pair Adding to $12$ : Checking the pairs, we see that $5 + 7$ equals $12$ . Therefore, the numbers we are looking for are $5$ and $7$ .
Write Trinomial as Product: Now we can write the trinomial as a product of two binomials using the numbers $5$ and $7$ . The factored form is $(x + 5)(x + 7)$ .
Check Factored Form: To ensure there are no mistakes, we can check our factored form by expanding $(x + 5)(x + 7)$ to see if we get the original trinomial $x^2 + 12x + 35$ .
Expand and Simplify: Expanding $(x + 5)(x + 7)$ gives us $x^2 + 7x + 5x + 35$ , which simplifies to $x^2 + 12x + 35$ . This matches the original trinomial, confirming that our factored form is correct.

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