Question

If the product Using division algorithm, find the quotient and remainder on dividing f(x) by g(x), where f(x) = 6x3 + 13x2 + x - 2 and g(x) = 2x + 1. Given numbers are the sum and the product of zeroes of a polynomial respectively. Frame a quadratic polynomial in x = 7 , 2
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Answer 1

Quotient = q = 3x² + 5x - 2

Remainder =r=0

Step-by-step explanation:

Given the polynomial

P(x) = 6x³ + 13x² + x − - 2

we have to find the quotient and remainder when above polynomial is divided by 2x+1

The division is shown in attachment

The quotient and remainder is

Quotient = q = 3x² + 5x - 2

Remainder =r=0

By division algorithm

Dividend = Remainder Divisor x Quotient +

P(x) = (2x + 1) × (3x² + 5x − 0

2) +

P(x) = 2x(3x² + 5x − 2) +1(3x² +

5x - 2) 5x - 2)

P(x) = 6x³ + 10x² - 4x + (3x² +

P(x) = 6x³ + 13x² + x − - 2