Question

Divide p(x) =7x³-5x²+6x-2 by g(x) =2x+4

Answer 1

Answer:

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

HOPE THIS WILL HELP YOU...... ☺☺☺☺☺☺☺.....