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2x^(2)-6x+3-8x^(2)-12 x+5

$2 x^{2}-6 x+3-8 x^{2}-12 x+5$

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Factor by grouping

Full solution

Q.

2 x^{2}-6 x+3-8 x^{2}-12 x+5

Combine Like Terms: Combine like terms in the expression $2x^{2}-6x+3-8x^{2}-12x+5$ . We need to add or subtract the coefficients of the terms with the same variable and exponent. $2x^{2} - 8x^{2} = -6x^{2}$ $-6x - 12x = -18x$ $3 + 5 = 8$ So, the combined expression is $-6x^{2} - 18x + 8$ .
Factor Out GCF: Factor out the greatest common factor (GCF) from the expression $-6x^{2} - 18x + 8$ . $\newline$ The GCF of $-6x^{2}$ , $-18x$ , and $8$ is $-2$ . $\newline$ So, we factor out $-2$ from each term. $\newline$ $-6x^{2} / -2 = 3x^{2}$ $\newline$ $-18x / -2 = 9x$ $\newline$ $8 / -2 = -4$ $\newline$ The factored expression is $-2(3x^{2} + 9x - 4)$ .
Factor Quadratic Expression: Factor the quadratic expression $3x^{2} + 9x - 4$ . We look for two numbers that multiply to $(3)(-4) = -12$ and add to $9$ . The numbers $12$ and $-1$ work because $12 \times -1 = -12$ and $12 + (-1) = 11$ , which is not $9$ . This is a mistake.

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