Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1). Write the quotient and the remainder.
Answers
Answer:
Quotient = 3x² + 4x - 7
Remainder = 0
Step-by-step explanation:
Divide the polynomial (6x³ + 11x² - 10x - 7) by the binomial (2x + 1). Write the quotient and the remainder.
6x³ + 11x² - 10x - 7
= 6x³ + 3x² + 8x² + 4x - 14x - 7 + 0
= 3x²(2x + 1) + 4x(2x + 1) - 7(2x + 1) + 0
= (3x² + 4x - 7)(2x+1) + 0
((6x³ + 11x² - 10x - 7)/(2x + 1)
= ((3x² + 4x - 7)(2x+1) + 0) / (2x + 1)
Cancelling 2x + 1 from numerator & denominator
= 3x² + 4x - 7
Quotient = 3x² + 4x - 7
Remainder = 0
Answer:
Quotient = 3x² + 4x - 7
Remainder = 0
Step-by-step Explanation:
We will first divide the polynomial with the binomial. Then we will follow the procedure to find out the remainder and the quotient. Whole calculations are as follows.
Divide the following Polynomial
(6x³ + 11x² - 10x - 7)
by the following binomial
(2x + 1)
For Quotient and Remainder follow the given steps below:
6x³ + 11x² - 10x - 7
= 6x³ + 3x² + 8x² + 4x - 14x - 7 + 0
= 3x²(2x + 1) + 4x(2x + 1) - 7(2x + 1) + 0
= (3x² + 4x - 7)(2x+1) + 0
((6x³ + 11x² - 10x - 7)/(2x + 1)
= ((3x² + 4x - 7)(2x+1) + 0) / (2x + 1)
Cancelling (2x + 1) from both sides:
=> 3x² + 4x - 7
Quotient = 3x² + 4x - 7
Remainder =0