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Chapter 2: Problem 30

Use synthetic division to divide. $$\left(2 x^{3}+14 x^{2}-20 x+7\right) \div(x+6)$$

Short Answer

Expert verified
The result of the division (quotient) is \(2x^2\) with a remainder of \(7\).

Step by step solution

01

Setting Up the Synthetic Division

First, write the coefficient of each term of the polynomial \(2, 14, -20, 7\) on the first row and the opposite of the value of 'x' in the divisor on the left outside the bracket i.e., \(-6\). We place down the first number which is \(2\).
02

Perform the Synthetic Division

Multiply \(-6\) (from the divisor) by the first number \(2\) placed down and put the product below \(14\). Add the numbers in the column, put result below. Repeat this step until you have processed all the coefficients. The final row reads \(2, 0, 0, 7\).
03

Write Down Divided Polynomial

The final row of numbers \(2, 0, 0, 7\) gives the coefficients of the quotient polynomial. We adjust the power of x by lowering them in each term. We get the quotient as \(2x^2 + 0x + 0\) with a remainder of \(7\). As the zero coefficients do not affect the polynomial, we can write the quotient simply as \(2x^2\).

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Most popular questions from this chapter

Decide whether the statement is true or false. Justify your answer. If \(x=-i\) is a zero of the function \(f(x)=x^{3}+i x^{2}+i x-1\) then \(x=i\) must also be a zero of \(f\)

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Simplify the complex number and write it in standard form. $$(-i)^{6}$$

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Use the given zero to find all the zeros of the function. Function \(f(x)=2 x^{3}+3 x^{2}+18 x+27\) Zero \(3 i\)
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