Question 60355: Factor completely
a. 4b^2 +3b - 10
b. -5g^2 + 2g + 16
Answer by mystic1306(20)  (Show Source):
You can put this solution on YOUR website! 4b^2 + 3b - 10
First you want to multiply 10 and 4
That equals 40
now find multiples of 40 that will equal 3 (for the 3b)
Multiples of 40:
1, 40 1+40 1-40 does not =3
2, 20 2+20 2-20 doesn't =3
4, 10 same thing
5, 8 8-5 equals 3
SO..write the equation
4b^2 + 8b - 5b - 10
take out the greatest commom factor 4b^2 +8 and -5b -10
4b is the GCF of 4b^2 + 8b, then divide the 4b out
-5 is the GCF of 5b - 10, then divide -5 out
SO write
4b(b+2)-5(b+2)
-5 divided by -10 makes positive 2
VERY IMPORTANT: the numbers in the () must match
Now finish it the (b+2) and the other (b+2) are combined into a single expression and 4b and -5 are put in () (4b-5)
Put them together and your answer is:
(b+2)(4b-5)
-5g^2 + 2g + 16
multiply 16 and 5 =80
multiples of 80
1, 80 1+ 80 1-80 doesn't =2 (for the 2g)
2,40
4, 20
5, 10
8,10 10-8=2
-5g^2 +10g -8g + 16 pull out GCF of -5g^2 +10g and -8g + 16 and divide
-5g(g-2) -8(g-2) combine (g-2) and (-5g-8)
(g-2)(-5g-8)
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