Question

$2x^2+7x-1$ completely divides $10x^4+17x^3-62x^2+30x-3$ .

• A. True
• B. False

Answer 1

The correct option is A

True

On dividing, we get

$\begin{array}{cc}& 5x^2-9x+3\\ 2x^2+7x-1& 10x^4+17x^3-62x^2+30x-3\\ & 10x^4+35x^3-5x^2\\ & --+\\ & -18x^3-57x^2+30x-3\\ & -18x^3-63x^2+9x\\ & ++-\\ & 6x^2+21x-3\\ & 6x^2+21x-3\\ & --+\\ & 0\end{array}$

The remainder hence obtained is zero. Therefore $2x^2+7x-1$ divides $10x^4+17x^3-62x^2+30x-3$ completely.