Chapter 4: Q. 2 (page 224)

What are the quotient and remainder when $3 x^{4} - x^{2}$ is divided by $x^{3} - x^{2} + 1$ ?

Short Answer

Expert verified

The quotient of dividing $3 x^{4} - x^{2}$ by $x^{3} - x^{2} + 1$ is $3 x + 3$ and remainder $2 x^{2} + 3 x - 3$

Step by step solution

Step 1. Given data

The dividend is $3 x^{4} - x^{2}$

The divisor is $x^{3} - x^{2} + 1$

Step 2. use the long division method

Divide $3 x^{4} - x^{2}$ by $x^{3} - x^{2} + 1$

$x^{3} - x^{2} + 1 \begin{matrix} 3 x + 3 \end{matrix} \begin{matrix} 3 x^{4} & + (0) x^{3} & - x^{2} & + (0) x & + 0 \\ 3 x^{4} & - 3 x^{3} & + 0 & + 3 x & + 0 \end{matrix} \begin{matrix} 0 & 3 x^{3} & - x^{2} & + 3 x & + 0 \\ 3 x^{3} & - 3 x^{2} & + 0 & + 3 \end{matrix} \begin{matrix} 0 & 2 x^{2} & + 3 x & - 3 \end{matrix}$

further division is not possible

so quotient is $3 x + 3$

remainder $2 x^{2} + 3 x - 3$

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What are the quotient and remainder when $3 x^{4} - x^{2}$ is divided by $x^{3} - x^{2} + 1$ ?

Short Answer

Step by step solution

Step 1. Given data

Step 2. use the long division method

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What are the quotient and remainder when 3x4-x2is divided by x3-x2+1?

Short Answer

Step by step solution

Step 1. Given data

Step 2. use the long division method

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

What are the quotient and remainder when $3 x^{4} - x^{2}$ is divided by $x^{3} - x^{2} + 1$ ?