Question

Use the grouping method to factor the polynomial below completely

Answer 1

(5x²+3)(2x-7)

Explanation:

As stated, this is a factor by grouping question: a(x+y)+b(x+y)=(x+y)(a+b)

10x³-35x²+6x-21

first, look for common factors.

-35x² and -21 have the common factor of -7

10x³and 6x have the common factor of 2x

now, rearrange the polynomial

10x³+6x-35x²-21

factor 2x out of 10x³+6x

2x(5x²+3)

factor -7 out of -35x² and -21

-7(5x²+3)

Now, the polynomial is 2x(5x²+3)-7(5x²+3)

(5x²+3) is common in both parts, so factor that out, 2x-7 would be another expression as that is left.

now, the expression is

(5x²+3)(2x-7)

Hope this helps!