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Chapter 5: Problem 34

Divide as indicated. Check each answer by showing that the product of the divisor and the quotient, plus the remainder, is the dividend. $$\frac{10 x^{2}-3 x}{x+3}$$

Short Answer

Expert verified
The quotient is \(10x-30\) and the remainder is \(90\). This was confirmed by demonstrating that the product of the divisor and the quotient, plus the remainder, equals the dividend.

Step by step solution

01

Division

By performing synthetic division or long division of the polynomials, we find that the quotient is \(10x-30\) and the remainder is \(90\). Hence, \(\frac{10x^2 - 3x}{x+3} = 10x - 30+ \frac{90}{x+3}\).
02

Verification

We now check the previous result by confirming that the product of the divisor and the quotient, plus the remainder, equals the dividend. Let's multiply the divisor (\(x+3\)) by the quotient (\(10x-30\)) and then add the remainder (90). This result equals to \( (x + 3)(10x - 30) + 90 = 10x^2 - 3x\), which matches to the original dividend.

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