Divide:
3x4+10x3−25x2

x+5

Question

Divide: 
3x4+10x3−25x2

x+5

BlackTom AI · Accepted Answer

We are asked to divide the polynomial 3x^4 + 10x^3 − 25x^2 by x + 5.

First, ignore the lower-degree terms for a moment and start the long division: divide the leading term 3x^4 by x to get 3x^3.

Multiply the divisor (x + 5) by 3x^3 to obtain 3x^4 + 15x^3, and subtract this from the current dividend: (3x^4 + 10x^3 − 25x^2) − (3x^4 + 15x^3) gives a new remainder of −5x^3 − 25x^2.

Next, divide the leading term of the remainder, −5x^3, by x to get −5x^2.

Multiply the divisor by −5x^2: (x + 5)(−5x^2) = −5x^3 − 25x^2. Subtract this from the current remainder: (−5x^3 − 25x^2) − (−5x^3 − 25x^2) = 0.

Since the remainder is zero, the division is exact and the quotient is 3x^3 − 5x^2.

Therefore, the result of the division (3x^4 + 10x^3 − 25x^2) ÷ (x + 5) is 3x^3 − 5x^2 with remainder 0.

Note: The provided answer field already corresponds to the quotient 3x^3 − 5x^2, which matches the result of the division. If there were multiple choices, we would compare the steps and verify that each candidate either matches the quotient or has a nonzero remainder or an incorrect leading term, but in this case only the quotient form is given.

ALGII141-027 Unit 4 Test

Divide: 3x4+10x3−25x2 x+5

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