Tyler thinks he knows one of the linear factors of P(x) = x3 – 9x2 + 23x – 15. After
finding that P(1) = 0, he suspects that x - I 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?

Diagram

Question

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Respuesta :

MrRoyal MrRoyal · Answer 1 · 2021-12-01T10:48:16+01:00

Linear factors are the factors of a polynomial

What went wrong is that: Tyler's linear factors are incorrect

The polynomial function is given as:

[tex]\mathbf{P(x) = x^3 - 9x^2 + 23x - 15}[/tex]

Rewrite as:

[tex]\mathbf{P(x) = x^3 - 8x^2 -x^2+ 15x + 8x - 15}[/tex]

Further rewrite as:

[tex]\mathbf{P(x) = x^3 - 8x^2 + 15x-x^2 + 8x - 15}[/tex]

Factorize the above polynomial

[tex]\mathbf{P(x) = x(x^2 - 8x + 15)-1(x^2 - 8x + 15)}[/tex]

Factor out x - 1 from the polynomial

[tex]\mathbf{P(x) = (x -1)(x^2 - 8x + 15)}[/tex]

This means that:

The linear factors are x - 1 and x^2 - 8x + 15

From the given diagram, Tyler's linear factors are x - 1 and x^2 - 8x - 15

Hence, Tyler's linear factors are incorrect