Name: Factorisation Using Difference of Two Squares
Uploaded: 2019-07-19
Duration: 5 min 14 s
Description: Sometimes writing a polynomial as the difference of two squares is the only way to factorise it. So let’s learn how to do it in this simple video!

Question

Find the quotient and remainder for the following using synthetic division:

$(8 x^{4} - 2 x^{2} + 6 x + 5) \div (4 x + 1)$

Accepted Answer

Synthetic Division is a shortcut method of polynomial division. The advantage of synthetic division is that it allows one to calculate without writing variables.

Given, $p (x) = (8 x^{4} - 2 x^{2} + 6 x + 5)$ and $q (x) = (4 x + 1)$

Arrange $p (x)$ and $q (x)$ in standard form, that is in descending order.

$p (x) = 8 x^{4} + 0 x^{3} - 2 x^{2} + 6 x + 5$ and $q (x) = (4 x + 1)$

Write the coefficients of dividend in the first row. Put $' 0'$ for missing terms

That is, $8 0 - 2 6 5$

Find out the zero of the divisor.

That is, $(8 x^{4} - 2 x^{2} + 6 x + 5) \div (4 x + 1)$

Write the zero of divisor in front of dividend in the first row. Put $' 0'$ in the first column of second row and complete the second row and third row.

All the entires except the last one in the third row are the coefficients of the quotient.

$8 x^{4} + 0 x^{3} - 2 x^{2} + 6 x + 5 = (x + \frac{1}{4}) (8 x^{3} - 2 x^{2} - \frac{3 x}{2} + \frac{51}{8}) + \frac{109}{32}$

$= \frac{(4 x + 1)}{4} \times 4 (2 x^{3} - \frac{x^{2}}{2} - \frac{3 x}{8} + \frac{51}{32}) + \frac{109}{32}$

$= (4 x + 1) (2 x^{3} - \frac{x^{2}}{2} - \frac{3 x}{8} + \frac{51}{32}) + \frac{109}{32}$

Therefore, quotient is $2 x^{3} - \frac{x^{2}}{2} - \frac{3 x}{8} + \frac{51}{32}$ and remainder is $\frac{109}{32}$ .

Find the quotient and remainder for the following using synthetic division:

$(8 x^{4} - 2 x^{2} + 6 x + 5) \div (4 x + 1)$

Important Questions on Algebra

Learn and Prepare for any exam you want !

Find the quotient and remainder for the following using synthetic division: 8x4-2x2+6x+5÷(4x+1)

Important Questions on Algebra

Learn and Prepare for any exam you want !

Find the quotient and remainder for the following using synthetic division:

$(8 x^{4} - 2 x^{2} + 6 x + 5) \div (4 x + 1)$