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Chapter 5: Problem 4

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{2 x^{2}+13 x+15}{x+5}$$

Short Answer

Expert verified
The simplification of the given expression is \(2x +3\). The remainder is zero, hence the original expression checks out when the divisor is multiplied with the quotient and the remainder is added.

Step by step solution

01

Polynomial Division

To start, perform the polynomial division. Divide the first term in the numerator by the first term in the denominator to get the first term of the quotient. Then multiply the entire denominator by this term and subtract it from the original numerator to get a new dividend.
02

Repeat Division

Now, repeat the process with the new dividend. Divide the first term of the new dividend by the first term in the denominator to get the next term of the quotient. Multiply the entire denominator by this term and subtract it from the new dividend. The result is the remainder.
03

Write the Result

The quotient resulting from the division and the remainder give the final result.
04

Check the Result

To check the answer, multiply the divisor \(x+5\) and the quotient, then add the remainder. The result should give back the original dividend \(2x^2 + 13x + 15\).

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Most popular questions from this chapter

In Exercises \(53-78,\) divide the polynomial by the monomial. Check each answer by showing that the product of the divisor and the quotient is the dividend. $$\frac{8 x^{6} y^{3}-12 x^{8} y^{2}-4 x^{14} y^{6}}{-4 x^{6} y^{2}}$$

Make Sense? In Exercises \(96-99\), determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I divide monomials by dividing coefficients and subtracting exponents.

In each exercise, find the product. $$4 x^{3}\left(4 x^{2}-3 x+1\right)$$

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)+(y-1)\left(y^{2}+y+1\right)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1
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