Question

find the polynomial which when divided by:-
b) 4x² yields -5x⁴+3x²+2 as a quotient​

Answer 1

Answer:

the polynomial is $-20x^6+12x^4+8x^2$ .

Step-by-step explanation:

Let the polynomial be $P(x)$. We need the polynomial to be completely divisible by $4x^2$ and should yield $-5x^4+3x^2+2$ as a quotient.

That is

$P(x)$ ÷ $4x^2= -5x^4+3x^2+2$

Then the polynomial is,

$P(x)= 4x^2(-5x^4+3x^2+2) \\\\= 4x^2\times (-5x^4)+4x^2 \times 3x^2+4x^2\times 2\\\\=-20x^6+12x^4+8x^2$

So the required polynomial is $-20x^6+12x^4+8x^2$ .