How do you find the quotient of #(5x^3 − 2x^2 + x − 4) -: (x − 3)#?

Question

Abigail Allen · Accepted Answer

#5x^2 + 13x + 40 + 116/(x-3)#

To solve this, use polynomial long division:

Hope this helps!

Eva Abramson · Answer

undefined To find the quotient of (5x^3 − 2x^2 + x − 4) divided by (x − 3), you can use polynomial long division or synthetic division. Here is the solution using polynomial long division:

Step 1: Divide the first term of the dividend (5x^3) by the first term of the divisor (x). The result is 5x^2.

Step 2: Multiply the divisor (x − 3) by the quotient obtained in the previous step (5x^2). The result is 5x^3 − 15x^2.

Step 3: Subtract the result obtained in step 2 from the dividend (5x^3 − 2x^2 + x − 4). The result is 13x^2 + x − 4.

Step 4: Repeat steps 1-3 with the new dividend (13x^2 + x − 4).

Step 5: Divide the first term of the new dividend (13x^2) by the first term of the divisor (x). The result is 13x.

Step 6: Multiply the divisor (x − 3) by the quotient obtained in the previous step (13x). The result is 13x^2 − 39x.

Step 7: Subtract the result obtained in step 6 from the new dividend (13x^2 + x − 4). The result is 40x − 4.

Step 8: Repeat steps 5-7 with the new dividend (40x − 4).

Step 9: Divide the first term of the new dividend (40x) by the first term of the divisor (x). The result is 40.

Step 10: Multiply the divisor (x − 3) by the quotient obtained in the previous step (40). The result is 40x − 120.

Step 11: Subtract the result obtained in step 10 from the new dividend (40x − 4). The result is 116.

Therefore, the quotient of (5x^3 − 2x^2 + x − 4) divided by (x − 3) is 5x^2 + 13x + 40 with a remainder of 116.