factorise the following expression 7m-6m2+20
Answers
7m-6m²+20
-6m²+7m+20
6m²-7m-20
6m²-(15m-8m)-20
6m²-15m+8m-20
3m(2m-5)+4(2m-5)
(2m-5) (3m+4) answer
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Step-by-step explanation:
7x−6x
2
+20
Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.
−6x
2
+7x+20
Factor the expression by grouping. First, the expression needs to be rewritten as −6x
2
+ax+bx+20. To find a and b, set up a system to be solved.
a+b=7
ab=−6×20=−120
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −120.
−1,120
−2,60
−3,40
−4,30
−5,24
−6,20
−8,15
−10,12
Calculate the sum for each pair.
−1+120=119
−2+60=58
−3+40=37
−4+30=26
−5+24=19
−6+20=14
−8+15=7
−10+12=2
The solution is the pair that gives sum 7.
a=15
b=−8
Rewrite −6x
2
+7x+20 as (−6x
2
+15x)+(−8x+20).
(−6x
2
+15x)+(−8x+20)
Factor out −3x in the first and −4 in the second group.
−3x(2x−5)−4(2x−5)
Factor out common term 2x−5 by using distributive property.
(2x−5)(−3x−4)