# Class 9 Math Algebric Manipulation

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$6. For what value of k is (x+4) the H.C.F. of x^{2}+x-(2 k+2) and 2 x^{2}+k x-12 ?$

$2. Fill in the blanks.(iii) HCF of y^{2}-5 y and y+6 and y-2 is$

$2. Find the square root of the following algebraic expressions by division method.(viii) x^{6}+\frac{1}{x^{6}}-4\left(x^{3}+\frac{1}{x^{3}}\right)+6 x \neq 0$

$Example 01 Simplify: \frac{x^{2}-x-6}{2 x^{2}-5 x-3}+\frac{1}{4 x^{2}-1}$

Simplify the following\[\text { (x) } 2\left(\frac{x^{2}+7 x+12}{x^{2}-16}+\frac{x^{2}+x-2}{x^{2}+4 x+4}\right) \times \frac{x^{2}-2 x-8}{2 x+8 x^{2}+4} .\]

$9. Let p(x)=10\left(x^{2}-9\right)\left(x^{2}-3 x+2\right) and q(x)=10 x(x+3)(x-1)^{2} . If the H.C.F. of p(x) q(x) is 10(x+3)(x-1) find their L.C.M.$