Question

Challenge!
if a ≠ 0, find the polynomial which when divided by 1/2a gives the quotient as 6a² - 22a³+ 16a² + 4 and remainder as (-3a - 8).



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Answer 1

Here is the answer for your challenge

Hey

Given :-

• Divisor = (-x2 + x - 1)

• Quotient = (x - 2)

• Remainder = 3

So,

the required polynomial =

dividend = divisor * quotient + remainder

=> dividend

= ( - x² + x - 1)*(x-2) + 3

= x (- x² + x - 1) -2 (-x² + x - 1) + 3

= -x3 + x? - x + 2x? - 2x + 2 + 3 =

= -x3 + x? + 2x² -2x - x + 5

= (-x3 + 3x2 - 3x + 5)

SO, the required polynomial is (-x³ + 3x2 - 3x + 5)