Name: Introduction to Algebra
Uploaded: 2019-07-19
Duration: 11 min 18 s
Description: In this video, we have discussed basic concepts of Algebra. Having a clear idea of the concept of this chapter will helps you to solve problems which are related to this topic.

Question

Use algebraic division to show that

(x + 1)

is a factor of

(x^{3} - x^{2} + 2 x + 4)

.

Accepted Answer

If $(x + 1)$ is a factor of $(x^{3} - x^{2} + 2 x + 4)$ , then $(x^{3} - x^{2} + 2 x + 4)$ divide by $(x + 1)$ gives remainder $0$ .

Now using the algebraic division method,

$(x^{3} - x^{2} + 2 x + 4) \div (x + 1)$

Divide the first term of the polynomial by $x$ :

$x^{3} \div x = x^{2}$ .

Multiply $(x + 1)$ by $x^{2}$ : $x^{2} (x + 1) = x^{3} + x^{2}$

Subtract: $(x^{3} - x^{2}) - (x^{3} + x^{2}) = - 2 x^{2}$

Bring down the $2 x$ from the next column.

$\begin{matrix} x^{2} \\ x + 1 x^{3} - x^{2} + 2 x + 4 \\ \frac{x^{3} + x^{2}}{- 2 x^{2} + 2 x} \end{matrix}$

Divide $- 2 x^{2}$ by $x$ : $- 2 x^{2} \div x = - 2 x$ .

Multiply $(x + 1)$ by $(- 2 x)$ : $(- 2 x) (x + 1) = - 2 x^{2} - 2 x$

Subtract: $(- 2 x^{2} + 2 x) - (- 2 x^{2} - 2 x) = 4 x$

Bring down the $4$ from the next column.

$\begin{matrix} x^{2} - 2 x \\ x + 1 x^{3} - x^{2} + 2 x + 4 \\ \frac{x^{3} + x^{2}}{- 2 x^{2} + 2 x} \\ \frac{- 2 x^{2} - 2 x}{4 x + 4} \end{matrix}$

Divide $4 x$ by $x$ : $4 x \div x = 4$ .

Multiply $(x + 1)$ by $4$ : $(4) (x + 1) = 4 x + 4$

Subtract: $(4 x + 4) - (4 x + 4) = 0$

$\begin{matrix} x^{2} - 2 x + 4 \\ x + 1 x^{3} - x^{2} + 2 x + 4 \\ \frac{x^{3} + x^{2}}{- 2 x^{2} + 2 x} \\ \frac{- 2 x^{2} - 2 x}{4 x + 4} \\ \frac{4 x + 4}{0} \end{matrix}$

So, $(x^{3} - x^{2} + 2 x + 4)$ fully divisible by $(x + 1)$ and gives remainder $0$ .

Hence, $(x + 1)$ is a factor of $(x^{3} - x^{2} + 2 x + 4)$ .

Use algebraic division to show that $(x + 1)$ is a factor of $(x^{3} - x^{2} + 2 x + 4)$ .

Important Questions on Algebra

Learn and Prepare for any exam you want !

Use algebraic division to show that x+1 is a factor of x3-x2+2x+4.

Important Questions on Algebra

Learn and Prepare for any exam you want !

Use algebraic division to show that $(x + 1)$ is a factor of $(x^{3} - x^{2} + 2 x + 4)$ .