Question

Divide the polynomial p (x) = x - 3x
- 5x² + 2.12 - 14. by another a
polynomial g (x) = x² - 7 and fend.
the quotient and remainder-​

Answer 1

Firstly write the given values in division algorithm and then find the value of g (x). Now further divide numerator of g(x) by denominator and simplify it to get g(x).

Division algorithm:

Dividend= Divisor × Quotient + Remainder

p(x) = q(x) × g(x) + r(x)

Given:

p(x) = x³ -5x² + 6x - 4

q(x) = (x-3)

r(x)= (-3x+5)

Put the values of p(X), q(x) & r(x) in Division algorithm.

p(x) = q(x) × g(x) + r(x)

x³ -5x² + 6x - 4 = (x-3) × g(x) +(-3x+5)

x³ -5x² + 6x - 4 +3x- 5 = (x-3) × g(x)

x³ -5x² + 6x +3x- 5 - 4 = (x-3) × g(x)

x³ -5x² + 9x - 9 = (x-3) × g(x)

g(x) = x³ -5x² + 9x - 9 / (x-3)

Divide x³ -5x² + 9x - 9 by (x-3)

x-3 ) x³ -5x² + 9x - 9(x²-2x+3

x³ -3x²

(-) (+)

---------------

-2x²+9x -9

-2x²+6x

(+) (-)

----------------------

3x -9

3x -9

(-) (-)

----------------------

0

On dividing x³ -5x² + 9x - 9 by x-3, we get quotient g(x)= x²-2x+3

Hence, g(x)= x²-2x+3

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