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Factor completely.

2x^(4)+4x^(3)-30x^(2)=

Factor completely. $\newline$ $2 x^{4}+4 x^{3}-30 x^{2}=$

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Powers with negative bases

Full solution

Q. Factor completely.

\newline

2 x^{4}+4 x^{3}-30 x^{2}=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the polynomial. $\newline$ The terms $2x^4$ , $4x^3$ , and $-30x^2$ all have a common factor of $2x^2$ . $\newline$ GCF: $2x^2$
Factor out GCF: Factor out the GCF from the polynomial. $\newline$ $2x^4 + 4x^3 - 30x^2 = 2x^2(x^2 + 2x - 15)$
Factor quadratic expression: Factor the quadratic expression inside the parentheses. $\newline$ The quadratic $x^2 + 2x - 15$ can be factored into two binomials. $\newline$ We look for two numbers that multiply to $-15$ and add to $2$ . These numbers are $5$ and $-3$ . $\newline$ So, $x^2 + 2x - 15 = (x + 5)(x - 3)$
Write completely factored form: Write the completely factored form of the original polynomial. $2x^4 + 4x^3 - 30x^2 = 2x^2(x + 5)(x - 3)$

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