Factor completely: 33x^(2)-72 x-3x^(3) Answer:

Factor out GCF: First, we can factor out the greatest common factor (GCF) from each term of the polynomial. The GCF of 33x^(2), -72x, and -3x^(3) is 3x. So we factor out 3x from each term. 3x(11x - 24 - x^2)Rearrange terms in standard order: Next, we need to rearrange the terms inside the parentheses in standard polynomial order, which is from the highest power to the lowest power of x. 3x(-x^2 + 11x - 24)Factor quadratic expression: Now, we need to factor the quadratic expression inside the parentheses. We are looking for two numbers that multiply to -24 and add up to 11. These numbers are 12 and -2. So we can write the quadratic as: 3x(-x^2 + 12x - 2x - 24)Group terms for factoring: We can now group the terms inside the parentheses to factor by grouping. 3x[(-x^2 + 12x) - (2x + 24)]Correct factorization: Factor out the common factor from each group. 3x[-x(x - 12) - 2(x + 12)]We notice that (x - 12) and (x + 12) are not common factors, so we made a mistake in the previous step. We need to find the correct factors that will give us the middle term of 11x when multiplied out. Let's go back and try to factor the quadratic expression again.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor completely:

33x^(2)-72 x-3x^(3)
Answer:

Factor completely: $\newline$ $33 x^{2}-72 x-3 x^{3}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Solve complex trigonomentric equations

Full solution

Q. Factor completely:

\newline

33 x^{2}-72 x-3 x^{3}

\newline

Answer:

Factor out GCF: First, we can factor out the greatest common factor (GCF) from each term of the polynomial. The GCF of $33x^{2}$ , $-72x$ , and $-3x^{3}$ is $3x$ . So we factor out $3x$ from each term. $3x(11x - 24 - x^2)$
Rearrange terms in standard order: Next, we need to rearrange the terms inside the parentheses in standard polynomial order, which is from the highest power to the lowest power of $x$ . $3x(-x^2 + 11x - 24)$
Factor quadratic expression: Now, we need to factor the quadratic expression inside the parentheses. $\newline$ We are looking for two numbers that multiply to $-24$ and add up to $11$ . $\newline$ These numbers are $12$ and $-2$ . $\newline$ So we can write the quadratic as: $\newline$ $3x(-x^2 + 12x - 2x - 24)$
Group terms for factoring: We can now group the terms inside the parentheses to factor by grouping. $3x[(-x^2 + 12x) - (2x + 24)]$
Correct factorization: Factor out the common factor from each group. $3x[-x(x - 12) - 2(x + 12)]$
Correct factorization: Factor out the common factor from each group. $\newline$ $3x[-x(x - 12) - 2(x + 12)]$ We notice that $(x - 12)$ and $(x + 12)$ are not common factors, so we made a mistake in the previous step. We need to find the correct factors that will give us the middle term of $11x$ when multiplied out. $\newline$ Let's go back and try to factor the quadratic expression again.