When a polynomial is divided by x+3, the quotient is x^3+x^2-4 and the remainder is 8. Find the dividend?
we know that the dividend is
(x+3)(x^3+x^2-4) + 8
Just expand that.
To find the dividend when a polynomial is divided by a given divisor, we need to multiply the quotient by the divisor and then add the remainder.
In this case, the divisor is x+3, the quotient is x^3+x^2-4, and the remainder is 8.
So, the dividend can be found by multiplying the quotient by the divisor and then adding the remainder:
Dividend = (Quotient) * (Divisor) + Remainder
Dividend = (x^3+x^2-4) * (x+3) + 8
To simplify this expression, we need to distribute the terms of the quotient:
Dividend = (x^3+x^2-4) * (x+3) + 8
= (x^3+x^2-4)*x + (x^3+x^2-4)*3 + 8
= x^4 + x^3 - 4x + 3x^3 + 3x^2 - 12 + 8
= x^4 + 4x^3 + 4x^2 - 4x - 4
Therefore, the dividend is x^4 + 4x^3 + 4x^2 - 4x - 4.