Why is the factorization of $2 x^{2} + 7 x + 6 = (2 x + 3) (x + 2) ?$ $2x^2+7x+6=(2x+3)(x+2)?$

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Why is the factorization of $2 x^{2} + 7 x + 6 = (2 x + 3) (x + 2) ?$ $2x^2+7x+6=(2x+3)(x+2)?$

If you factor quadratics with $a > 1$ $a gt 1$ then you have to find factors of $a c$ $ac$ that add to give $b$ $b$ . So why is the answer $2$ $2$ and $3$ $3$ if they don't add to give $7$ $7$ ?

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Answer 1 · 2018-06-04T17:14:54

$see explanation$ $"see explanation"$

Explanation:

$given a a quadratic in standard form; a x^{2} + b x + c$ $"given a a quadratic in "color(blue)"standard form ";ax^2+bx+c$

$to factor consider the factors of ac which sum to b as$ $"to factor consider the factors of ac which sum to b as"$
$you have stated above$ $"you have stated above"$

$2 x^{2} + 7 x + 6 is in standard form$ $2x^2+7x+6" is in standard form"$

$with a = 2, b = 7 and c = 6$ $"with "a=2,b=7" and "c=6$

$the factors of the product 2 \times 6 = 12$ $"the factors of the product "2xx6=12$

$which sum to + 7 are + 4 and + 3$ $"which sum to + 7 are + 4 and + 3"$

$split the middle term using these factors$ $"split the middle term using these factors"$

$2 x^{2} + 4 x + 3 x + 6 \leftarrow factor by grouping$ $2x^2+4x+3x+6larrcolor(blue)"factor by grouping"$

$= 2 x (x + 2) + 3 (x + 2)$ $=color(red)(2x)(x+2)color(red)(+3)(x+2)$

$take out the common factor (x + 2)$ $"take out the "color(blue)"common factor "(x+2)$

$= (x + 2) (2 x + 3)$ $=(x+2)(color(red)(2x+3))$

$2 x^{2} + 7 x + 6 = (x + 2) (2 x + 3)$ $2x^2+7x+6=(x+2)(2x+3)$

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Why is the factorization of $2 x^{2} + 7 x + 6 = (2 x + 3) (x + 2) ?$ $2x^2+7x+6=(2x+3)(x+2)?$

If you factor quadratics with $a > 1$ $a gt 1$ then you have to find factors of $a c$ $ac$ that add to give $b$ $b$ . So why is the answer $2$ $2$ and $3$ $3$ if they don't add to give $7$ $7$ ?

1 Answer

Explanation:

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Why is the factorization of 2x2+7x+6=(2x+3)(x+2)?2x^2+7x+6=(2x+3)(x+2)?

If you factor quadratics with a>1a gt 1 then you have to find factors of acac that add to give bb. So why is the answer 22 and 33 if they don't add to give 77?

1 Answer

Explanation:

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Impact of this question

Why is the factorization of $2 x^{2} + 7 x + 6 = (2 x + 3) (x + 2) ?$ $2x^2+7x+6=(2x+3)(x+2)?$

If you factor quadratics with $a > 1$ $a gt 1$ then you have to find factors of $a c$ $ac$ that add to give $b$ $b$ . So why is the answer $2$ $2$ and $3$ $3$ if they don't add to give $7$ $7$ ?