what should be added to 6x^5+4x^4-27x^3-7x^2-27x-6 so that the resulting polynomial is exactly divisible by 2x^2-3 - Maths - Algebraic Expressions and Identities

Question

what should be added to 6x^5+4x^4-27x^3-7x^2-27x-6 so that the
resulting polynomial is exactly divisible by 2x^2-3

Ajanta Trivedi · Accepted Answer

the given polynomial be $p (x) = 6 x^{5} + 4 x^{4} - 27 x^{3} - 7 x^{2} - 27 x - 6$

let us divide p(x) by $2 x^{2} - 3$ .

$2 x^{2} - 3 \begin{matrix} 3 x^{3} + 2 x^{2} - 9 x - \frac{1}{2} \\ 6 x^{5} + 4 x^{4} - 27 x^{3} - 7 x^{2} - 27 x - 6 \end{matrix}$

$\underset{̲}{6 x^{5} - 9 x^{3}} \times 4 x^{4} - 18 x^{3} - 7 x^{2} - 27 x - 6 \underset{̲}{4 x^{4} - 6 x^{2}} \times - 18 x^{3} - x^{2} - 27 x - 6 \underset{̲}{- 18 x^{3} + 27 x} \times - x^{2} - 54 x - 6 \underset{̲}{- x^{2} + \frac{3}{2}} \times - 54 x - \frac{15}{2}$

thus we must add $54 x + \frac{15}{2}$ to p(x).

hope this helps you.

cheers!!

what should be added to 6x^5+4x^4-27x^3-7x^2-27x-6 so that the resulting polynomial is exactly divisible by 2x^2-3.