Question 6 & 7, Review Exercise

Solutions of Question 6 & 7 of Review Exercise of Unit 05: Polynomials. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the value of ' $k$ ' so that the remainder upon dividing $\left(x^{2}+8 x+k\right)$ by $(x-4)$ is zero.

Solution.

Let $p(x) = x^{2} + 8x + k$. We are given that the remainder upon dividing $p(x)$ by $(x - 4)$ is zero.
By the remainder theorem, the remainder is $p(4)$.

Since $p(4) = 0$, we have: $$\begin{align*} p(4) &= (4)^2 + 8(4) + k \\ &= 16 + 32 + k \\ &= 48 + k. \end{align*}$$

For the remainder to be zero:

$$48 + k = 0.$$

Thus,

$$k = -48.$$

Suppose that the quotient upon dividing one polynomial by another is $3 x^{2}-x+32-\frac{121}{x+4}$. What is the dividend?

Solution.

The question doesn't seem to solvable.

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