Factor completely: x^(2)(5x^(2)-6)-9x(5x^(2)-6)-10(5x^(2)-6) Answer:

Identify Common Factor: Identify the common factor in all three terms of the expression x^(2)(5x^(2)-6)-9x(5x^(2)-6)-10(5x^(2)-6). The common factor is (5x^(2)-6).Factor Out Common Factor: Factor out the common factor (5x^(2)-6) from each term. The expression becomes (5x^(2)-6)(x^(2)-9x-10).Factor Quadratic Expression: Now, factor the quadratic expression x^(2)-9x-10. This is a simple trinomial factoring problem. We look for two numbers that multiply to -10 and add up to -9. These numbers are -10 and +1. The factored form of x^(2)-9x-10 is (x-10)(x+1).Combine Factored Expressions: Combine the factored quadratic with the common factor that was factored out earlier. The completely factored form of the original expression is (5x^(2)-6)(x-10)(x+1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor completely:

x^(2)(5x^(2)-6)-9x(5x^(2)-6)-10(5x^(2)-6)
Answer:

Factor completely: $\newline$ $x^{2}\left(5 x^{2}-6\right)-9 x\left(5 x^{2}-6\right)-10\left(5 x^{2}-6\right)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Factor completely:

\newline

x^{2}\left(5 x^{2}-6\right)-9 x\left(5 x^{2}-6\right)-10\left(5 x^{2}-6\right)

\newline

Answer:

Identify Common Factor: Identify the common factor in all three terms of the expression $x^{2}(5x^{2}-6)-9x(5x^{2}-6)-10(5x^{2}-6)$ . The common factor is $(5x^{2}-6)$ .
Factor Out Common Factor: Factor out the common factor $(5x^{2}-6)$ from each term. $\newline$ The expression becomes $(5x^{2}-6)(x^{2}-9x-10)$ .
Factor Quadratic Expression: Now, factor the quadratic expression $x^{2}-9x-10$ . This is a simple trinomial factoring problem. We look for two numbers that multiply to $-10$ and add up to $-9$ . These numbers are $-10$ and $+1$ . The factored form of $x^{2}-9x-10$ is $(x-10)(x+1)$ .
Combine Factored Expressions: Combine the factored quadratic with the common factor that was factored out earlier. $\newline$ The completely factored form of the original expression is $(5x^{2}-6)(x-10)(x+1)$ .