InterviewSolution
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InterviewSolution
| 1. |
Factorisex^3+13x^2+32x+20 |
| Answer» Let p(x) = x3\xa0+ 13x2\xa0+ 32x + 20p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0Therefore (x + 1) is a factor of p(x).On dividing p(x) by (x + 1) we getp(x)\xa0\xa0(x + 1) = x2\xa0+ 12x + 20Thus,x3\xa0+ 13x2\xa0+ 32x + 20 = (x + 1)(x2\xa0+ 12x + 20)= (x + 1) (x2\xa0+ 10x + 2x + 20)= (x + 1)[x(x + 10) + 2(x + 10)]= (x + 1) (x +2) (x + 10)Hence, x3\xa0+ 13x2\xa0+ 32x + 20 = (x + 1) (x +2) (x + 10). | |