91Ó°ÊÓ

The product of HCF and LCM of two polynomials is \(\left(x^{2}-1\right)\left(x^{4}-1\right)\), then the product of the polynomials is (1) \(\left(x^{2}-1\right)\left(x^{2}+1\right)\) (2) \(\left(x^{2}-1\right)\left(x^{2}+1\right)^{2}\) (3) \(\left(x^{2}-1\right)^{2}\left(x^{2}+1\right)\) (4) None of these

Find the LCM of \(x^{3}-x^{2}+x-1\) and \(x^{3}-2 x^{2}+x-2\). \((1)(x+1)(x-1)\) (2) \(x-1\) (3) \(\left(x^{2}+1\right)(x-1)(x-2)\) (4) None of these

The product of additive inverses of \(\frac{x^{2}-1}{2 x}\) and \(\frac{x^{2}-4}{3-x}\) is (1) \(x^{2}+5 x+6\) (2) \(\mathrm{x}^{2}+\mathrm{x}-6\) (3) \(x^{2}-x-6\) (4) \(x^{2}-5 x+6\)

The HCF of two polynomials \(\mathrm{p}(\mathrm{x})\) and \(\mathrm{q}(\mathrm{x})\) using long division method was found to be \(\mathrm{x}+5\), If their first three quotients obtained are \(x, 2 x+5\), and \(x+3\) respectively. Find \(p(x)\) and \(q(x)\). (The degree of \(\mathrm{P}(\mathrm{x})>\) the degree of \(\mathrm{q}(\mathrm{x}))\) \(\begin{array}{rlrl}\text { (1) } \mathrm{p}(\mathrm{x})=2 \mathrm{x}^{4}+21 \mathrm{x}^{3}+72 \mathrm{x}^{2}+88 \mathrm{x}+15 & \text { (2) } \mathrm{p}(\mathrm{x}) & =2 \mathrm{x}^{4}-21 \mathrm{x}^{3}-72 \mathrm{x}^{2}-88 \mathrm{x}+15 \\ \mathrm{q}(\mathrm{x}) & =2 \mathrm{x}^{3}+21 \mathrm{x}^{2}+71 \mathrm{x}+80 & \mathrm{q}(\mathrm{x}) & =2 \mathrm{x}^{3}+21 \mathrm{x}^{2}-71 \mathrm{x}+80 \\ \text { (3) } \mathrm{p}(\mathrm{x}) & =2 \mathrm{x}^{4}+21 \mathrm{x}^{3}+88 \mathrm{x}+15 & \text { (4) } \mathrm{p}(\mathrm{x}) & =2 \mathrm{x}^{4}-21 \mathrm{x}^{2}-72 \mathrm{x}^{2}+80 \mathrm{x}+15 \\ \mathrm{q}(\mathrm{x}) & =2 \mathrm{x}^{3}+71 \mathrm{x}+80 & \mathrm{q}(\mathrm{x}) & =2 \mathrm{x}^{3}-21 \mathrm{x}^{2}+71 \mathrm{x}+80\end{array}\)

Find the HCF of \(6 x^{4} y\) and \(12 x y\). (1) \(6 \mathrm{x}^{2} \mathrm{y}\) (2) \(6 x\) (3) \(6 \mathrm{y}\) (4) \(6 \mathrm{xy}\)

The HCF of two polynomials \(p(x)\) and \(q(x)\) using long division method was found in two steps to be \(3 \mathrm{x}-2\), and the first two quotients obtained are \(\mathrm{x}+2\) and \(2 \mathrm{x}+1\). Find \(\mathrm{p}(\mathrm{x})\) and \(\mathrm{q}(\mathrm{x})\). (The degree of \(\mathrm{P}(\mathrm{x})>\) the degree of \(\mathrm{q}(\mathrm{x}))\). (1) \(\mathrm{p}(\mathrm{x})=6 \mathrm{x}^{3}+11 \mathrm{x}^{2}+\mathrm{x}+6, \mathrm{q}(\mathrm{x})=6 \mathrm{x}^{2}+\mathrm{x}+2\) (2) \(\mathrm{P}(\mathrm{x})=6 \mathrm{x}^{3}+11 \mathrm{x}^{2}-\mathrm{x}+6, \mathrm{q}(\mathrm{x})=6 \mathrm{x}^{2}-\mathrm{x}+2\) (3) \(\mathrm{P}(\mathrm{x})=6 \mathrm{x}^{3}-11 \mathrm{x}^{2}+\mathrm{x}-6, \mathrm{q}(\mathrm{x})=6 \mathrm{x}^{2}-\mathrm{x}-2\) (4) \(\mathrm{p}(\mathrm{x})=6 \mathrm{x}^{3}+11 \mathrm{x}^{2}-\mathrm{x}-6, \mathrm{q}(\mathrm{x})=6 \mathrm{x}^{2}-\mathrm{x}-2\)

If \(f(x)=x^{2}+6 x+a, g(x)=x^{2}+4 x+b, h(x)=x^{2}+14 x+c\) and the \(L C M\) of \(f(x), g(x)\) and \(h(x)\) is \((x+8)(x-2)(x+6)\), then find \(a+b+c .(a, b\) and \(c\) are constants \()\) (1) 20 (2) 16 (3) 32 (4) 10

If the LCM of the polynomials \(f(x)=(x+1)^{5}(x+2)^{4}\) and \(g(x)=(x+1)^{b}(x+2)^{4}\) is \((x+1)^{2}\) \((x+2)^{b}\), then find the minimum value of \(a+b\). (1) is 10 (2) is 14 (3) is 15 (4) Cannot say