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PLEASE HELP!! WILL MARK BRAINLIEST!!
Devon wanted to know if x-3 is a factor of f(x)=x^3+x^2-10x+8. She applied the Factor Theorem and concluded that x-3 is not a factor of f(x), as shown in the following work.
f(-3)^3+(-3)^2-10(-3)+8=20
f(-3)=20, so the remainder is 20.
The remainder is 20, so x-3 is not a factor of f(x).
Did Devon make a mistake? If so, what was her mistake?
A. Yes, Devon evaluated f(-3) incorrectly.
B. No, Devon did not make any mistakes.
C. Yes, Devon should have evaluated f(3)

Respuesta :

Answer:

C. Yes Devon should have evaluated f(3).

Step-by-step explanation:

She substituted the wrong value. For x - 3 to be a factor f(3) must equal 0.

f(3) = 3^3 + 3^2 - 10(3) + 8 = 27 + 9 - 30 + 8

= 14,  so x- 3 is not a factor anyway but she did  substitute the wrong value.

Answer:

C.

Step-by-step explanation:

To see if x-3 is a factor you plug in what makes it 0 which is 3.

Evaluating f at 3:

[tex]3^3+3^2-10(3)+8[/tex]

[tex]27+9-30+8[/tex]

[tex]36-30+8[/tex]

[tex]6+8[/tex]

14

So the remainder of dividing f by (x-3) is actually 14.

The conclusion is still the same but the work Devon provided with her conclusion is wrong as she suppose to evaluate f(3) instead of f(-3).

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