Question

Use synthetic division to divide.

a. (-10x² + 2x3³-5) = (x-4)
b. (-2x + 4x³ + 18 + x) = (x + 2)

Answer 1

To divide two polynomials using synthetic division, set up the division problem in the correct format and perform the synthetic division. The final row represents the quotient.

Step-by-step explanation:

To divide two polynomials using synthetic division, we need to set up the division problem in the correct format. The dividend should be written in descending order of exponents, with any missing terms represented by placeholders: (-10x² + 2x³ - 5) = (0x³ + 2x² + 0x - 5). The divisor is the linear factor in the form (x - c), where c is the constant term of the linear factor: (x - 4).

Now, we can perform the synthetic division. Start by writing the coefficients of the dividend inside the division symbol and the constant term of the divisor outside the symbol:

2 | 2 -10 0 -5 -4 -16 64 --------------- 2 -14 48 59

The final row of the synthetic division represents the quotient: 2x² - 14x + 48 with a remainder of 59.

Learn more about Dividing polynomials