How do you factor #6 + 7x - 20x^2#?

Question

Julia Adams · Accepted Answer

#6-7x-20x^2 = (3-4x)(2+5x)#

Find factors of #6 and 20# which differ by #7#

#" "6" "20# #" "darr" "darr#

#" "3" "4" "rarr 2 xx 4 = 8# #" "2" "5" " rarr 3xx5 =ul15# #color(white)(xxxxxxxxxxxxxxxxx)7#

We have the correct factors, now add in the signs.

We need #-20# and #+7#

#" "3" "-4" "rarr 2 xx -4 = -8# #" "2" "+5" " rarr 3xx+5 =+ul15# #color(white)(xxxxxxxxxxxxxxxxxxxxx)+7#

#6-7x-20x^2 = (3-4x)(2+5x)#

Abigail Allen · Answer

undefined To factor 6 + 7x - 20x^2, you can use the factoring by grouping method:

First, multiply the leading coefficient (a) and the constant term (c):
a * c = 6 * (-20) = -120

Now, find two numbers that multiply to -120 and add up to the coefficient of the linear term (b), which is 7:
The numbers are 15 and -8, since 15 * (-8) = -120 and 15 + (-8) = 7.

Now, rewrite the middle term using these two numbers:
6 + 15x - 8x - 20x^2

Now, group the terms:
(6 + 15x) + (-8x - 20x^2)

Factor out the greatest common factor from each group:
3(2 + 5x) - 4x(2 + 5x)

Now, you can see that (2 + 5x) is common to both terms, so factor it out:
(2 + 5x)(3 - 4x)

So, the factored form of 6 + 7x - 20x^2 is (2 + 5x)(3 - 4x).