Question

What is the remainder of the quantity 5 x cubed plus 7 x plus 5 end quantity divided by the quantity x plus 2 end quantity? Show all necessary steps.

Answer 1

The remainder of the polynomial equation is -49

What is a remainder of a polynomial equation?

The remainder of a quantity in an algebraic expression of a polynomial equation is the remaining amount of the quantity left and can not be divisible by the divisor.

From the given information, we are to find the remainder of the given algebraic equation:

$\mathbf{= \dfrac{5x^3+7x+5}{x+2} }$

Using the long division method, we have:

$\mathbf{= \dfrac{5x^3+7x+5}{x+2} } \implies \mathbf{5x^2 + \dfrac{-10x^2+7x+5}{x+2}}$

Divide by $\mathbf{ \dfrac{-10x^2+7x+5}{x+2}}$, we have:

$\mathbf{= 5x^2- 10x+ \dfrac{27x+5}{x+2}}$

Divide by $\mathbf{\dfrac{27x+5}{x+2}}$, we have:

$\mathbf{= 5x^2- 10x+ 27 +\dfrac{-49}{x+2}}$

Learn more about finding the remainder of a polynomial equation here:

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