Factorize each of the following polynomials:
(i) x³+13x²+31x-45 given that x+9 is a factor
(ii) 4x³+20x²+33x+18 given that 2x+3 is a factor.
Answers
(i) x³+13x²+31x-45 given that x+9 is a factor (x-1) (x+5)
(ii) 4x³+20x²+33x+18 given that 2x+3 is a factor. (x+3/2) ( x+2)
(i) x³+13x²+31x-45 given that x+9 is a factor
x+9 )x^3+13x^2+31x-45( x^2+4x-5
x^3+9x^2
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4x^2+31x
4x^2+36x
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-5x-45
-5x-45
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0
x^2+4x-5 = x^2-x+5x-5 = x(x-1)+5(x-1) = (x-1)(x+5)
(ii) 4x³+20x²+33x+18 given that 2x+3 is a factor.
2x+3 )4x^3+20x^2+33x+18( 2x^2+7x+6
4x^3+6x^2
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14x^2+33x
14x^2+21x
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12x+18
12x+18
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0
2x^2+7x+6 = (x+3/2) ( x+2)