CBSE Class 9 Answered
Factorize the following polynomials-
a)6x cube-x square-5x+2
b)x4+x3-7x2-x+6
Asked by raghavrattan | 10 Jul, 2010, 08:38: PM
Expert Answer
Hello,
Factorization of the above polynomials can be done as follows:
a)
f(x) = 6x3-x2-5x+2
Putting -1 in place of x gives f (x) = 0
hence one root of f(x) becomes -1.
and hence we can write :
f (x) = (x+1)(6x2-7x+2)
= (x+1)(6x2-4x-3x+2)
= (x+1)(2x(3x-2)-(3x-2)
= (x+1)(3x-2)(2x-1)
b) f(x) = x4+x3-7x2-x+6
f(1) = 0;
this implies x = 1 is a root of f (x)
and hence we can write:
f(x) = (x-1)(x3+2x2-5x-6)
= (x-1)g(x)
x = -1 is a root of g(x)
therefore we can write:
f(x) = (x-1)(x+1)(x2+x-6)
= (x-1)(x+1)(x2+3x-2x-6)
= (x-1)(x+1)(x+3)(x-2)
Regards,
Topperlearning
Answered by | 13 Jul, 2010, 03:02: PM
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