Question

Which of the following expressions is not a factor of 3x³−10x²−143x−90?

a) x+3
b) 3x+5
c) x−6
d) x−9

Answer 1

The expression that is not a factor of 3x³−10x²−143x−90 is option d) x−9.

Step-by-step explanation:

The expression that is not a factor of 3x³−10x²−143x−90 is option d) x−9.

To determine if an expression is a factor of the given polynomial, we can use synthetic division. If the remainder is zero, then the expression is a factor. Otherwise, it is not a factor.

1. Option a) x+3:

• Substituting -3 in the polynomial: (3x³−10x²−143x−90) / (-3).
• The remainder is not zero, so it is not a factor.

Option b) 3x+5:

• Substituting -5/3 in the polynomial: (3x³−10x²−143x−90) / (-5/3).
• The remainder is not zero, so it is not a factor.

Option c) x−6:

• Substituting 6 in the polynomial: (3x³−10x²−143x−90) / (6).
• The remainder is zero, so it is a factor.

Option d) x−9:

• Substituting 9 in the polynomial: (3x³−10x²−143x−90) / (9).
• The remainder is not zero, so it is not a factor.

Therefore, option d) x−9 is not a factor of the polynomial.