Factor completely. 4x^(3)-56x^(2)+180 x Answer:

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the polynomial 4x^3 - 56x^2 + 180x. The GCF of 4x^3, 56x^2, and 180x is 4x, since 4x is the largest factor that divides evenly into all three terms.Factor out GCF: Factor out the GCF from each term in the polynomial. 4x^3 ÷ 4x = x^2 56x^2 ÷ 4x = 14x 180x ÷ 4x = 45 So, factoring out 4x gives us 4x(x^2 - 14x + 45).Factor quadratic expression: Factor the quadratic expression x^2 - 14x + 45. We need to find two numbers that multiply to 45 and add up to -14. The numbers that satisfy these conditions are -9 and -5. So, x^2 - 14x + 45 can be factored as (x - 9)(x - 5).Write fully factored form: Write the fully factored form of the original polynomial. Since we factored out 4x in Step 2 and factored the quadratic in Step 3, the fully factored form of the polynomial is 4x(x - 9)(x - 5).

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Q. Factor completely.

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4 x^{3}-56 x^{2}+180 x

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Answer:

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms in the polynomial $4x^3 - 56x^2 + 180x$ . The GCF of $4x^3$ , $56x^2$ , and $180x$ is $4x$ , since $4x$ is the largest factor that divides evenly into all three terms.
Factor out GCF: Factor out the GCF from each term in the polynomial. $\newline$ $4x^3 \div 4x = x^2$ $\newline$ $56x^2 \div 4x = 14x$ $\newline$ $180x \div 4x = 45$ $\newline$ So, factoring out $4x$ gives us $4x(x^2 - 14x + 45)$ .
Factor quadratic expression: Factor the quadratic expression $x^2 - 14x + 45$ . We need to find two numbers that multiply to $45$ and add up to $-14$ . The numbers that satisfy these conditions are $-9$ and $-5$ . So, $x^2 - 14x + 45$ can be factored as $(x - 9)(x - 5)$ .
Write fully factored form: Write the fully factored form of the original polynomial. $\newline$ Since we factored out $4x$ in Step $2$ and factored the quadratic in Step $3$ , the fully factored form of the polynomial is $4x(x - 9)(x - 5)$ .