Chapter 4: Q. 3 (page 209)

Find the quotient and remainder if $3 x^{4} - 5 x^{3} + 7 x - 4$ is divided by $x - 3$ .

Short Answer

Expert verified

The quotient is $3 x^{3} + 4 x^{2} + 12 x + 43$ and the remainder is $125$

Step by step solution

Step 1. Given information.

The given polynomial is $3 x^{4} - 5 x^{3} + 7 x - 4$ and it should be divided by $x - 3$ .

Step 2. Dividing the given polynomial.

First, we will insert the missing $x^{2}$ term in the dividend and divide by $x - 3$ .

localid="1646211602856" $x - 3 3 x^{3} + 4 x^{2} + 12 x + 43 3 x^{4} - 5 x^{3} + 0 x^{2} + 7 x - 4 3 x^{4} - 9 x^{3} \bar{4 x^{3} + 0 x^{2} + 7 x - 4} 4 x^{3} - 12 x^{2} \bar{12 x^{2} + 7 x - 4} 12 x^{2} - 36 x \bar{43 x - 4} 43 x - 129 \bar{125}$

Therefore, the quotient is $3 x^{3} + 4 x^{2} + 12 x + 43$ and the remainder is $125$ .

Step 3. Checking the result.

Multiplying quotient by divisor and then add the remainder then we get,

$(x - 3) (3 x^{3} + 4 x^{2} + 12 x + 43) + 125 = 3 x^{4} + 4 x^{3} + 12 x^{2} + 43 x - 9 x^{3} - 12 x^{2} - 36 x - 129 + 125 = 3 x^{4} - 5 x^{3} + 7 x - 4$

Hence this is true.

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Find the quotient and remainder if $3 x^{4} - 5 x^{3} + 7 x - 4$ is divided by $x - 3$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Dividing the given polynomial.

Step 3. Checking the result.

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Find the quotient and remainder if3x4-5x3+7x-4is divided byx-3.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Dividing the given polynomial.

Step 3. Checking the result.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Probability and Statistics

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Find the quotient and remainder if $3 x^{4} - 5 x^{3} + 7 x - 4$ is divided by $x - 3$ .