Factor completely. -7x^(4)y^(3)z^(4)+41x^(6)y^(5)z^(7) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. The GCF is the highest power of each variable that divides both terms and the largest number that divides both coefficients. For the coefficients, the GCF is 1 since 7 and 41 are both prime and do not share any common factors. For the variables, the GCF is x^(4)y^(3)z^(4) since that is the highest power of each variable that appears in both terms.Factor out GCF: Factor out the GCF from each term. The expression becomes: 1 * (-7x^(4)y^(3)z^(4) + 41x^(6)y^(5)z^(7)) / (x^(4)y^(3)z^(4)) This simplifies to: -7 + 41x^(2)y^(2)z^(3)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Factor completely.

-7x^(4)y^(3)z^(4)+41x^(6)y^(5)z^(7)
Answer:

Factor completely. $\newline$ $-7 x^{4} y^{3} z^{4}+41 x^{6} y^{5} z^{7}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Factor completely.

\newline

-7 x^{4} y^{3} z^{4}+41 x^{6} y^{5} z^{7}

\newline

Answer:

Identify GCF: Identify the greatest common factor (GCF) of the two terms. $\newline$ The GCF is the highest power of each variable that divides both terms and the largest number that divides both coefficients. $\newline$ For the coefficients, the GCF is $1$ since $7$ and $41$ are both prime and do not share any common factors. $\newline$ For the variables, the GCF is $x^{4}y^{3}z^{4}$ since that is the highest power of each variable that appears in both terms.
Factor out GCF: Factor out the GCF from each term. $\newline$ The expression becomes: $\newline$ $1 \times (-7x^{4}y^{3}z^{4} + 41x^{6}y^{5}z^{7}) / (x^{4}y^{3}z^{4})$ $\newline$ This simplifies to: $\newline$ $-7 + 41x^{2}y^{2}z^{3}$