Factor completely. 4x^(4)-48x^(3)+128x^(2) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial 4x^(4)-48x^(3)+128x^(2). The GCF is the largest polynomial that divides each term of the polynomial, which in this case is 4x^(2).Factor out GCF: Factor out the GCF from each term of the polynomial. 4x^(4)-48x^(3)+128x^(2) = 4x^(2)(x^(4)/x^(2) - 48x^(3)/x^(2) + 128x^(2)/x^(2)) Simplify the terms inside the parentheses. 4x^(2)(x^(2) - 12x + 32)Simplify terms: Now, factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to 32 and add up to -12. The numbers that satisfy these conditions are -8 and -4. So, we can write the quadratic as (x - 8)(x - 4).Factor quadratic: Write the completely factored form of the original polynomial by combining the GCF and the factored quadratic. 4x^(2)(x - 8)(x - 4) This is the completely factored form of the polynomial.

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Factor completely.

\newline

4 x^{4}-48 x^{3}+128 x^{2}

\newline

Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial $4x^{4}-48x^{3}+128x^{2}$ . The GCF is the largest polynomial that divides each term of the polynomial, which in this case is $4x^{2}$ .
Factor out GCF: Factor out the GCF from each term of the polynomial. $\newline$ $4x^{4}-48x^{3}+128x^{2} = 4x^{2}(\frac{x^{4}}{x^{2}} - \frac{48x^{3}}{x^{2}} + \frac{128x^{2}}{x^{2}})$ $\newline$ Simplify the terms inside the parentheses. $\newline$ $4x^{2}(x^{2} - 12x + 32)$
Simplify terms: Now, factor the quadratic expression inside the parentheses. $\newline$ We are looking for two numbers that multiply to $32$ and add up to $-12$ . $\newline$ The numbers that satisfy these conditions are $-8$ and $-4$ . $\newline$ So, we can write the quadratic as $(x - 8)(x - 4)$ .
Factor quadratic: Write the completely factored form of the original polynomial by combining the GCF and the factored quadratic. $\newline$ $4x^{2}(x - 8)(x - 4)$ $\newline$ This is the completely factored form of the polynomial.