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Question
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
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Solution
Let ` f(x) = 4x^3 + 20x^2 + 33x+ 18` be the given polynomial.
Therefore (2x + 3)is a factor of the polynomial f(x).
Now,
`f(x)= 2x^2 (2x + 3)+7x(2x + 3) + 6(2x + 3)`
`=(2x + 3){2x^2 + 4x 3x + 6}`
`= (2x + 3){2x^2 + 4x + 3x + 6}`
` = (2x + 3)(2x + 3)(x + 2)`
Hence (x +2),(2x+3) and (2x + 3 ) are the factors of polynomial f(x).
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