Question 1 True or false: \( x-1 \) is a factor of \( 6 x^{3}-5 x^{2}-8 x+3 \) True False

To determine whether \( x-1 \) is a factor of \( 6x^3 - 5x^2 - 8x + 3 \), you can apply the Factor Theorem. According to the theorem, if \( x-c \) is a factor of a polynomial, then substituting \( c \) into the polynomial should yield zero. In this case, substitute \( x = 1 \): \( 6(1)^3 - 5(1)^2 - 8(1) + 3 = 6 - 5 - 8 + 3 = -4 \). Since the result is not zero, \( x-1 \) is **not** a factor. Hence, the answer is **False**. If you enjoy polynomial puzzles, you'll love diving into synthetic division! It's a slick method for testing factors that combines fun and efficiency. When you divide the polynomial by your suspected factor using synthetic division, if the remainder is zero, you've got yourself a winner! To further untangle polynomial mysteries, consider exploring advanced algebra textbooks or online resources focused on polynomial functions and their properties. They often present engaging explanations and visual aids that make complex topics much easier to tackle!