Factorization Of Polynomials — Maths STD 9 — Question
Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Polynomials4 Marks
Question
Using factor theorem, factorize the following polynomials:
$x^3 - 10x^2 - 53x - 42$
✓
Answer
Let $f(x)=x^3-10 x^2-53 x-42$ be the given polynomial.
Now, putting $x=-1$, we get
$f(-1)=(-1)^3-10(-1)^2-53(-1)-42$
$=-1-10+53-42$
$=-53+53=0$
Therefore, $(x+1)$ is a factor of polynomial $f(x)$.
Now,
$f(x)=x^2(x+1)-11 x(x+1)-42(x+1)$
$=(x+1)\left(x^2-11 x-42\right)$
$=(x+1)\left(x^2-14 x+3 x-42\right)$
$=(x+1)(x+3)(x-14)$
Hence $(x+1),(x+3)$ and $(x-14)$ are the factors of polynomial $f(x)$.
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