Question

Check if x - 1 is a factor of the polynomial 12x⁴ - 5x³ + 3x² - 6 using a calculator.

A) Yes
B) No
C) Maybe
D) Undefined

Answer 1

To check if x - 1 is a factor of the polynomial 12x⁴ - 5x³ + 3x² - 6, you can use synthetic division. If the remainder is 0, then x - 1 is a factor.

Step-by-step explanation:

To check if x - 1 is a factor of the polynomial 12x⁴ - 5x³ + 3x² - 6, we can use synthetic division or substitution method. Let's use synthetic division to divide the polynomial by x - 1.

1. Write down the coefficients of the polynomial in decreasing order of the powers of x. The polynomial is 12x⁴ - 5x³ + 3x² - 6.
2. Write down 1 as the divisor (x - 1 = 0 implies x = 1).
3. Perform synthetic division using the coefficients and 1 as the divisor.
4. If the remainder is 0, then x - 1 is a factor of the polynomial. Otherwise, it is not a factor.

After performing synthetic division, if the remainder is 0, then the answer is A) Yes. If the remainder is not 0, then the answer is B) No.