Division of Polynomials help!? 10 points?

Question

Divide. Write your answers this way: Quotient: (polynomial expression) Remainder: (number)

(6x^3 - x^2 - 10) ÷ (3x + 4)

Use synthetic division to divide.

(3x^3 - 7x^2 + 4x - 3) ÷ (x + 3)

Answer 1

Rewrite the expression in long division form (6x³ - x² - 10)/(3x + 4)

Divide the first term of the dividend by the first term of the divisor 6x³/3x = 2x².

So,the first term of the quotient is 2x². Multiply (3x + 4) by 2x² and subtract.

Divide the first term of the last row by first term of the divisor -9x²/3x = -3x.

So,the second term of the quotient is -3x. Multiply (3x + 4) by -3x and subtract.

Divide the first term of the last row by first term of the divisor  (12x)/3x = 4.

So,the third term of the quotient is (4x). Multiply (3x + 4) by (4) and subtract.

Quotient = 2x² - 3x + 4 and remainder = - 26.

Answer 2

Use synthetic division to find (3x³ - 7x² + 4x - 3)/(x + 3)

Step 1: Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown below.

Step 2: Write the constant r of the divisor (x - r) to the left. In this case, r= -3. Bring the first coefficient, 3, down.

Step 3: Multiply the first coefficient by r : -3(3)= -9. Write the product under the second coefficient, - 7 and : - 7+(-9) = - 16.

Step 4: Multiply the sum, -16, by r : -3(-16) = 48.

Write the product under the next coefficient,  4 and add : 4 + 48 = 52.

Step 5: Multiply the sum, 52, by r : (-3)(52) = -156.

Write the product under the next coefficient, -3 and add : -3 +( -156) = - 159. The remainder is -159.

Quotient is (3x² - 16x + 52) and remainder - 159.