Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

A student uses the division shown to divide -3x^4 + 15x^3 - x + 5 by x - 5, and concludes that x -5 is not a factor of the polynomial. Describe two errors the student made. Is x - 5 a factor? Explain.

A Student Uses The Division Shown To Divide 3x4 15x3 X 5 By X 5 And Concludes That X 5 Is Not A Factor Of The Polynomial Describe Two Errors The Student Made Is class=

Sagot :

ANSWER

P(3) = 0

Step-by-step explanation:

Factor Theorem is a consequence of Remainder Theorem.

Remainder Theorem states that if polynomial f(x) is divided by a binomial (x - a) then the remainder is f(a).

Factor Theorem states that if f(a) = 0, then the binomial (x - a) is a factor of f(x).

We have the polynomial

P(x) = x^5-3x^4+5x^3-15x^2-6x+18P(x)=x

5

−3x

4

+5x

3

−15x

2

−6x+18

To prove that x-3 is a factor of P, we calculate P(3):

P(3) = 3^5-3*3^4+5*3^3-15*3^2-6*3+18P(3)=3

5

−3∗3

4

+5∗3

3

−15∗3

2

−6∗3+18

P(3) = 243-243+135-135-18+18P(3)=243−243+135−135−18+18

P(3) = 0P(3)=0

Thus, x-3 is a factor of P(x)

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.