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.

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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Algebra 1

Factor out a monomial

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4

. Factor the trinomial completely.

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x^{2}+12 x+35

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Select the correct choice below and, if neces

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x^{2}+12 x+35=

\square

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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.