Question

Use synthetic division to divide the following polynomials:

(6x³ - 35x² + 30x - 25) ÷ (x - 5)

a) 6x² + 5x + 5
b) 6x² - 35x - 25
c) 6x² - 5x - 5
d) 6x² + 35x + 25

Answer 1

To divide the given polynomials using synthetic division, the quotient is 6x² + x + 5 and the remainder is 5. The correct answer is option c) 6x² - 5x - 5.

Step-by-step explanation:

To divide the polynomials using synthetic division, we set up the division as follows:

5 | 6 -35 30 -25
|-

To find the next term, we multiply the divisor (x - 5) by the quotient obtained so far, which is 6. We then subtract this product from the corresponding terms in the dividend:

5 | 6 -35 30 -25
-30 150 -120
_______________
6 -5 30
6 -5 30 -25
___________________
6 1 5 5

So the quotient is 6x² + x + 5 and the remainder is 5. Therefore, the correct answer is option c) 6x² - 5x - 5.