QuestionAugust 25, 2025

Factor the trinomial. x^2+10x-39 square

Factor the trinomial. x^2+10x-39 square
Factor the trinomial. x^2+10x-39 square

Solution
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Answer

(x - 3)(x + 13) Explanation 1. Identify the coefficients The trinomial is x^2 + 10x - 39. Coefficients are a = 1, b = 10, and c = -39. 2. Find two numbers that multiply to ac and add to b We need two numbers that multiply to 1 \times (-39) = -39 and add to 10. These numbers are 13 and -3. 3. Rewrite the middle term using these numbers Rewrite 10x as 13x - 3x: x^2 + 13x - 3x - 39. 4. Factor by grouping Group terms: (x^2 + 13x) + (-3x - 39). Factor each group: x(x + 13) - 3(x + 13). 5. Factor out the common binomial Factor out (x + 13): (x - 3)(x + 13).

Explanation

1. Identify the coefficients<br /> The trinomial is $x^2 + 10x - 39$. Coefficients are $a = 1$, $b = 10$, and $c = -39$.<br />2. Find two numbers that multiply to $ac$ and add to $b$<br /> We need two numbers that multiply to $1 \times (-39) = -39$ and add to $10$. These numbers are $13$ and $-3$.<br />3. Rewrite the middle term using these numbers<br /> Rewrite $10x$ as $13x - 3x$: $x^2 + 13x - 3x - 39$.<br />4. Factor by grouping<br /> Group terms: $(x^2 + 13x) + (-3x - 39)$.<br /> Factor each group: $x(x + 13) - 3(x + 13)$.<br />5. Factor out the common binomial<br /> Factor out $(x + 13)$: $(x - 3)(x + 13)$.
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