Question

4a^2x^5-6a^5x^2+2a^2x^2

how to factor

Answer 1

\[4a^2x^5-6a^5x^2+2a^2x^2\]
You want to look at each factor separately. So starting with the constants, what's the greatest common factor of 4, 6, and 2?

Answer 2

2

Answer 3

Let's simplify step-by-step.
4a2x5−6a5x2+2a2x2
=4a2x5+−6a5x2+2a2x2
Answer:
=−6a5x2+4a2x5+2a2x2

Answer 4

Right - so we can factor that out of each term:

\[2(2a^2x^5-3a^5x^2+a^2x^2)\]
Now look at the a's. What's the greatest common factor of a^2, a^5, and a^2?

Answer 5

a^2

Answer 6

Right! Now take that out of the 3 terms:

\[2a^2(2x^5-3a^3x^2+x^2)\]
Now do the same for the x's - greatest common factor of x^5, x^2, and x^2?

Answer 7

x^2

Answer 8

Yup...so last step is to take that out to:

\[2a^2x^2(2x^3-3a^3+1)\]
And you're done!

Answer 9

why do the 2x and -3a turn to ^3?

Answer 10

Because:
\[a^5 \div a^2=a^3\]
Remember your exponent laws: when dividing numbers with the same base (in this case a) but different exponents, you keep the base and subtract the exponents. Same applies for the x's!

Answer 11

When you factor out a number, you divide the terms you're factoring by that number.

Answer 12

ok thanks!