Divide:
3x4+10x3−25x2

x+5

Question

Divide: 
3x4+10x3−25x2

x+5

BlackTom AI · Accepted Answer

We are given to divide the polynomial 3x^4 + 10x^3 − 25x^2 by x + 5. 
First, factor the numerator a bit to see if there is a common factor with the divisor.
- Factor out x^2: 3x^4 + 10x^3 − 25x^2 = x^2(3x^2 + 10x − 25).
- Inspect the quadratic: 3x^2 + 10x − 25 can be factored as (3x − 5)(x + 5) because (3x − 5)(x + 5) = 3x^2 + 15x − 5x − 25 = 3x^2 + 10x − 25.
Thus the numerator factors as x^2(3x − 5)(x + 5).
Now divide by x + 5. Since (x + 5) is a factor of the numerator, we can cancel it:
- The quotient is x^2(3x − 5) = 3x^3 − 5x^2.
No remainder remains because the (x + 5) factor was canceled exactly once.

Therefore, the division yields the quotient 3x^3 − 5x^2, with remainder 0.

Divide: 3x4+10x3−25x2 x+5

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