Factorise the following polynomials 28c2d2 – 21c2d
Answers
Answer:
Let the given polynomial be p(x)=2x
3
−9x
2
+7x+6.
We will now substitute various values of x until we get p(x)=0 as follows:
Forx=0
p(0)=2(0)
3
−9(0)
2
+(7×0)+6=0−0+0+6=6
=0
∴p(0)
=0
Forx=1
p(1)=2(1)
3
−9(1)
2
+(7×1)+6=2−9+7+6=15−9=6
=0
∴p(1)
=0
Forx=2
p(2)=2(2)
3
−9(2)
2
+(7×2)+6=(2×8)−(9×4)+14+6=16−36+14+6=36−36=0
∴p(2)=0
Thus, (x−2) is a factor of p(x).
Now,
p(x)=(x−2)⋅g(x).....(1)
⇒g(x)=
(x−2)
p(x)
Therefore, g(x) is obtained by after dividing p(x) by (x−2) as shown in the above image:
From the division, we get the quotient g(x)=2x
2
−5x−3 and now we factorize it as follows:
2x
2
−5x−3
=2x
2
−6x+x−3
=2x(x−3)+1(x−3)
=(x−3)(2x+1)
From equation 1, we get p(x)=(x−2)(x−3)(2x+1).
Hence, 2x
3
−9x
2
+7x+6=(x−2)(x−3)(2x+1).
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