what must be added to the polynomial p(x)=x³ + 6x² + 11x + 18, so th

1.	what must be added to the polynomial p(x)=x³ + 6x² + 11x + 18, so that the resulting polynomial is exactly divisible by x² + 2x + 3?
Answer» p(x) = x³+6x²+11x+18 Let q(x) = x²+2x+3 p(x)/q(x) \(=\frac{x^3+6x^2+11x+18}{x^2+2x+3}\) = x + \(\frac{4x^2+8x+18}{x^2+2x+3}\) = (x+4) + 6/x²+2x+3 ∴ p(x) = (x+4) (x²+2x+3) + 6 ⇒ p(x) - 6 = (x+4) (x²+2x+3) Therefore, we must add -6 to p(x) so that the resulting polynomial is exactly divisible by q(x) = x²+2x+3.

what must be added to the polynomial p(x)=x³ + 6x² + 11x + 18, so that the resulting polynomial is exactly divisible by x² + 2x + 3?

Answer»

p(x) = x³+6x²+11x+18

Let q(x) = x²+2x+3

p(x)/q(x) \(=\frac{x^3+6x^2+11x+18}{x^2+2x+3}\)

= x + \(\frac{4x^2+8x+18}{x^2+2x+3}\)

= (x+4) + 6/x²+2x+3

∴ p(x) = (x+4) (x²+2x+3) + 6

⇒ p(x) - 6 = (x+4) (x²+2x+3)

Therefore, we must add -6 to p(x) so that the resulting polynomial is exactly divisible by q(x) = x²+2x+3.

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what must be added to the polynomial p(x)=x³ + 6x² + 11x + 18, so that the resulting polynomial is exactly divisible by x² + 2x + 3?

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