Factor the trinomial: 5x^(2)+12 x+7 Answer:

Identify a, b, c: Identify a, b, and c in the trinomial 5x^2 + 12x + 7. Compare 5x^2 + 12x + 7 with ax^2 + bx + c. a = 5 b = 12 c = 7Find two numbers: Find two numbers whose product is a*c (5*7=35) and whose sum is b (12). We need to find two numbers that multiply to 35 and add up to 12. After checking possible factors of 35, we find that: 5 * 7 = 35 5 + 7 = 12 Two numbers: 5, 7Rewrite middle term: Rewrite the middle term 12x using the two numbers found in Step 2. 5x^2 + 12x + 7 becomes 5x^2 + 5x + 7x + 7Factor by grouping: Factor by grouping. Group the terms: (5x^2 + 5x) + (7x + 7) Factor out the common factors from each group: 5x(x + 1) + 7(x + 1)Factor out common binomial: Factor out the common binomial factor (x + 1). (5x + 7)(x + 1)

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factor the trinomial:

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5 x^{2}+12 x+7

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the trinomial $5x^2 + 12x + 7$ . Compare $5x^2 + 12x + 7$ with $ax^2 + bx + c$ . $a = 5$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $5*7=35$ ) and whose sum is $b$ ( $12$ ). $\newline$ We need to find two numbers that multiply to $35$ and add up to $12$ . $\newline$ After checking possible factors of $35$ , we find that: $\newline$ $5 * 7 = 35$ $\newline$ $5 + 7 = 12$ $\newline$ Two numbers: $5$ , $5*7=35$ $0$
Rewrite middle term: Rewrite the middle term $12x$ using the two numbers found in Step $2$ . $5x^2 + 12x + 7$ becomes $5x^2 + 5x + 7x + 7$
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(5x^2 + 5x) + (7x + 7)$ $\newline$ Factor out the common factors from each group: $\newline$ $5x(x + 1) + 7(x + 1)$
Factor out common binomial: Factor out the common binomial factor $(x + 1)$ . $\newline$ $(5x + 7)(x + 1)$