Quotient =x^3 x^2 x4 2916 remainder = 1316 We know , dividend=divisor× quotient +remainder 4x^4 5x^3 7x+!=(4x 1)(x^3 x^2 x4 2916 1316 ...

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Division of a Polynomial by a Monomial

4x4-5x3-7x+1÷...

Question

Solve: $(4 x^{4} - 5 x^{3} - 7 x + 1) \div (4 x - 1)$ .

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Solution

Divisor $= (4 x - 1)$
Dividend $= 4 x^{4} - 5 x^{3} - 7 x + 1$
Quotient $= x^{3} - x^{2} - \frac{x}{4} - \frac{29}{16}$
remainder $= \frac{- 13}{16}$

We know , dividend $=$ divisor $\times$ quotient $+$ remainde
$4 x^{4} - 5 x^{3} - 7 x + 1 = (4 x - 1) (x^{3} - x^{2} - \frac{x}{4} - \frac{29}{16}) - \frac{13}{16}$

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