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Factorise the following polynomials 6b a(f+g)+b(f+g) |
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Answer» 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=0p(0)=2(0) 3 −9(0) 2 +(7×0)+6=0−0+0+6=6=0∴p(0)=0 Forx=1p(1)=2(1) 3 −9(1) 2 +(7×1)+6=2−9+7+6=15−9=6=0∴p(1)=0Forx=2p(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)=0Thus, (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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