QuestionAugust 24, 2025

Factor the trinomial. 7. 5x^2+26x+5

Factor the trinomial. 7. 5x^2+26x+5
Factor the trinomial.
7. 5x^2+26x+5

Solution
4.7(212 votes)

Answer

(5x + 1)(x + 5) Explanation 1. Identify the product and sum Find two numbers that multiply to 5 \times 5 = 25 and add to 26. 2. Determine the numbers The numbers are 25 and 1 since 25 \times 1 = 25 and 25 + 1 = 26. 3. Rewrite the middle term Rewrite 26x as 25x + x: 5x^2 + 25x + x + 5. 4. Factor by grouping Group terms: (5x^2 + 25x) + (x + 5). Factor out common factors: 5x(x + 5) + 1(x + 5). 5. Factor out the common binomial Factor out (x + 5): (5x + 1)(x + 5).

Explanation

1. Identify the product and sum<br /> Find two numbers that multiply to $5 \times 5 = 25$ and add to $26$.<br /><br />2. Determine the numbers<br /> The numbers are $25$ and $1$ since $25 \times 1 = 25$ and $25 + 1 = 26$.<br /><br />3. Rewrite the middle term<br /> Rewrite $26x$ as $25x + x$: $5x^2 + 25x + x + 5$.<br /><br />4. Factor by grouping<br /> Group terms: $(5x^2 + 25x) + (x + 5)$.<br /> Factor out common factors: $5x(x + 5) + 1(x + 5)$.<br /><br />5. Factor out the common binomial<br /> Factor out $(x + 5)$: $(5x + 1)(x + 5)$.
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