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HCF

Find the HCF ...

Question

Find the HCF of $p (x) = x^{2} - x - 12$ and $q (x) = x^{2} - 9$ .

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Solution

We have
$p (x) = x^{2} - x - 12 = (x - 4) (x + 3)$ , $q (x) = x^{2} - 9 = (x - 3) (x + 3)$
Here, the common factor is $x + 3$ and the lowest power of $x + 3$ in $p (x)$ and $q (x)$ is $x + 3$ itself. Hence $x + 3$ is the HCF of $p (x)$ and $q (x)$ .

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Similar questions

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

p (x)

q (x)

(x^{2} - 9)

2 (x + 1)^{2}

p (x) = 12 (x + 1) (x - 3)

q (x)

p (x) = (x^{3} - 27) (x^{2} - 3 x + 2)

q (x) = (x^{2} + 3 x + 9) (x^{2} - 5 x + 6)

P (x) + q (x) = x^{2} - 4 x + 1 a n d P (x) - q (x) = x^{2} + 5 x - 2

p (x) = x^{3} - 1

q (x) = x^{3} + 1

r (x) = {(x^{2} + 1)}^{2} - x^{2}

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