Factor completely: 11x^(2)-10 x-x^(3) Answer:

Rewrite in standard form: Rewrite the polynomial in standard form by ordering the terms from highest to lowest degree. Rearrange the terms: -x^3 + 11x^2 - 10xFactor out GCF: Factor out the greatest common factor (GCF) from the polynomial. In this case, the GCF is x. Factor out x: x(-x^2 + 11x - 10)Factor quadratic expression: Factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to -10 and add up to 11. These numbers are 10 and -1. Factor the quadratic: x(-x + 10)(x - 1)Check factored form: Check the factored form by expanding it to ensure it matches the original polynomial. Expand: x * (-x + 10) * (x - 1) = x(-x^2 + x + 10x - 10) = -x^3 + 11x^2 - 10x The expanded form matches the original polynomial.

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Factor completely:

\newline

11 x^{2}-10 x-x^{3}

\newline

Answer:

Rewrite in standard form: Rewrite the polynomial in standard form by ordering the terms from highest to lowest degree. $\newline$ Rearrange the terms: $-x^3 + 11x^2 - 10x$
Factor out GCF: Factor out the greatest common factor (GCF) from the polynomial. In this case, the GCF is $x$ . $\newline$ Factor out $x$ : $x(-x^2 + 11x - 10)$
Factor quadratic expression: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $-10$ and add up to $11$ . These numbers are $10$ and $-1$ . $\newline$ Factor the quadratic: $x(-x + 10)(x - 1)$
Check factored form: Check the factored form by expanding it to ensure it matches the original polynomial. $\newline$ Expand: $x \cdot (-x + 10) \cdot (x - 1) = x(-x^2 + x + 10x - 10) = -x^3 + 11x^2 - 10x$ $\newline$ The expanded form matches the original polynomial.