Factor completely. -2x^(2)+20 x-48= +=^(x)

Identify the quadratic expression: Identify the quadratic expression to be factored. The given expression is -2x^2 + 20x - 48.Look for a common factor: Look for a common factor in all terms of the quadratic expression. The common factor in -2x^2, 20x, and -48 is -2.Factor out the common factor: Factor out the common factor from the quadratic expression. -2(x^2 - 10x + 24)Factor the quadratic expression: Factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to 24 and add up to -10. These numbers are -4 and -6.Write the factored form: Write the factored form using the two numbers found in Step 4. -2(x - 4)(x - 6)Check the factored form: Check the factored form by expanding it to ensure it equals the original expression. -2(x - 4)(x - 6) = -2(x^2 - 6x - 4x + 24) = -2(x^2 - 10x + 24) = -2x^2 + 20x - 48 The expanded form matches the original expression.

Home

Math Problems

Algebra 2

Factor quadratics

Full solution

Q. Factor completely.

\newline

-2 x^{2}+20 x-48=

Identify the quadratic expression: Identify the quadratic expression to be factored. $\newline$ The given expression is $-2x^2 + 20x - 48$ .
Look for a common factor: Look for a common factor in all terms of the quadratic expression. $\newline$ The common factor in $-2x^2$ , $20x$ , and $-48$ is $-2$ .
Factor out the common factor: Factor out the common factor from the quadratic expression. $\newline$ $-2(x^2 - 10x + 24)$
Factor the quadratic expression: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $24$ and add up to $-10$ . These numbers are $-4$ and $-6$ .
Write the factored form: Write the factored form using the two numbers found in Step $4$ . $\newline$ $-2(x - 4)(x - 6)$
Check the factored form: Check the factored form by expanding it to ensure it equals the original expression. $\newline$ $-2(x - 4)(x - 6) = -2(x^2 - 6x - 4x + 24) = -2(x^2 - 10x + 24) = -2x^2 + 20x - 48$ $\newline$ The expanded form matches the original expression.