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Chapter 5: Problem 5

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{x^{2}-5 x+6}{x-3}$$

Short Answer

Expert verified
The quotient when \(x^{2}-5 x+6\) is divided by \(x-3\) is \(x-2\).

Step by step solution

01

Perform the Division

In this step, the polynomial \(x^{2}-5 x+6\) is divided by \(x-3\). By applying synthetic division or long division, the result found is that the quotient is \(x-2\) and the remainder is 0.
02

Check the Answer

Verify the result of the division by multiplying the divisor \(x-3\) with the quotient \(x-2\) and then adding the remainder (which is 0 in this case). Doing this operation results in the dividend \(x^{2}-5 x+6\), which matches the original polynomial, thus confirming that the result of the division is correct.

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Most popular questions from this chapter

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.6 \times 10^{4}\right)\left(7.2 \times 10^{-3}\right)}{\left(3.6 \times 10^{8}\right)\left(4 \times 10^{-3}\right)}$$

In Exercises \(79-82,\) simplify each expression. Divide the sum of \((y+4)^{2}\) and \((y+4)(y-4)\) by \(2 y\)

Explain how to simplify an expression that involves a product raised to a power. Provide an example with your explanation.

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

In each exercise, find the product. $$(x+3)\left(x^{2}+5\right)$$
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