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Chapter 2: Problem 31

Use synthetic division to divide. \(\left(4 x^{3}-9 x+8 x^{2}-18\right) \div(x+2)\)

Short Answer

Expert verified
The quotient of the division \(4x^{3}+8x^{2}-9x-18\) by \(x+2\) is \(4x^{2} - 9\).

Step by step solution

01

Write down the coefficients and Constant of Divisor

The coefficients of the polynomial are [4, 8, -9, -18] and the constant of divisor is -2 in the expression 'x + 2'.
02

Begin synthetic division

Begin synthetic division by bringing down the leading coefficient (4 in this case). Multiply this number by the divisor's constant (-2), and write the result underneath the second coefficient (8). Add these two numbers together (8 and -8) to get zero.
03

Continue Division Process

Continue this process of multiplying, writing the result, and adding, you multiply 0 (the result from the last addition) by -2, which gives 0, and you add that to -9 to get -9. Then multiply -9 by -2 to get 18, and add that to -18 to get zero.
04

Interpret the Result

The numbers that remain [4, 0, -9, 0] are the coefficients of the quotient polynomial. This represents: \(4x^{2} - 9\). Therefore, the expression \(4x^{3}+8x^{2}-9x-18\) divided by \(x+2\) equals \(4x^{2} - 9\).

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Most popular questions from this chapter

Solve the inequality. (Round your answers to two decimal places.) \(-0.5 x^{2}+12.5 x+1.6>0\)

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