Question

Thyler thinks he knows one of the linear factors of P(x) = x^3 - 9x^2 + 23x - 15. After finding that P(1) = 0, he suspects that x - 1 is a factor of P(x). Here is the diagram he made to check if he's right, but he set it up incorrectly. What went wrong?

Answer 1

Thyler attempted to check if x - 1 is a factor of
`\(P(x) = x^3 - 9x^2 + 23x - 15\)` but set up a multiplication diagram instead of using long division or synthetic division, resulting in an incorrect analysis.

Tyler made an error in setting up his diagram to check if x - 1 is a factor of
`\(P(x) = x^3 - 9x^2 + 23x - 15\)`. The correct setup should involve long division or synthetic division. It appears Tyler attempted to create a multiplication diagram, but the values listed are incorrect.

To properly check if x - 1 is a factor, he should perform either long division or synthetic division. In synthetic division, he would use 1 as the divisor, obtaining coefficients for the quotient. The correct diagram should involve division rather than multiplication, aiming to have a remainder of zero if x - 1 is indeed a factor.

The incorrect setup with multiplication suggests Tyler misunderstood the process, leading to an inaccurate analysis of whether x - 1 is a factor.