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Chapter 3: Problem 17

Divide using synthetic division. $$\left(2 x^{2}+x-10\right) \div(x-2)$$

Short Answer

Expert verified
The result of the division \((2 x^{2}+x-10) \div(x-2)\) using synthetic division is \(2 x + 5\).

Step by step solution

01

Set up the Synthetic Division Table

Write the coefficients of the polynomial being divided along the top of the box. For \(2 x^{2}+x-10\), the coefficients are 2, 1, and -10. Write the root of the divisor along the outside of the box. The root can be found by setting the divisor \(x-2\) equal to 0 and solve. The root is 2.
02

Perform Synthetic Division

Bring the first number (2) straight down. Multiply the number on the outside (2) by the number just brought down (2) and write the result (4) below the next number (1). Sum the column, which is 1 + 4 = 5. Continue this process across the row. Multiply the number on the outside (2) by the number just obtained (5) and write the result (10) below the next number (-10). Sum the column which is -10 + 10 = 0.
03

Interpret the Synthetic Division Result

The numbers on the bottom of the synthetic division table represent the coefficients of the polynomial division result. Starting from the left, the first number is the coefficient of \(x\), the next number is the constant term. So, the result of the division is \(2 x + 5\).

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