Question

Using Division Algorithm, match the following polynomials with their respective q(x) when divided by $x$.

• A. 5x
• B. 2x + 1
• C. 3x + 2
• D. 2x${}^2$ + 3

Answer 1

Factor of a polynomial divides the polynomial completely, i.e., remainder = 0

Dividend = Divisor × Quotient + Remainder

$\therefore$ By division algorithm,

5x${}^2$ = $x$ $\times$ 5x + 0

2x${}^2$ + x = $x$ $\times$ (2x + 1) + 0

3x${}^2$ + 2x = $x$ $\times$ (3x + 2) + 0

2x${}^3$ + 3x = $x$ $\times$ (2x${}^2$ + 3) + 0