Q3 of 90 Page 31

Find the value of k if (x – 5) is a factor of the polynomial x3 – 3x2 + kx – 10.

Using Remainder Theorem:

Putting factor = 0, we get -


(x – 5) = 0


⇒ x = 5.


Now, ∵ it is given that (x – 5) is a factor of the polynomial x3 –


3x2 + kx – 10.


⇒ If we substitute x = 5 in x3 – 3x2 + kx – 10, the remainder will be zero.


⇒ 53 – 3(5)2 + k(5) – 10 = 0


⇒ 125 – 3× 25 + 5k – 10 = 0


⇒ 125 – 75 + 5k – 10 = 0


⇒ 5k + 40 = 0



⇒ k = – 8


More from this chapter

All 90 →
2

Use the factor theorem to determine whether g(x) is a factor of p(x)?

p(x) = 3x3 – x2 – 3x + 1;g(x) = x + 2

 2

Use the factor theorem to determine whether g(x) is a factor of p(x)?

p(x) = 2x3 + x2 – 2x – 1; g(x) = 2x + 1

 4

Find the value of k if (x – 1) is a factor of the polynomial 2x2 + kx + √2

 5

If (x + 1) and (x – 1) are factors of the polynomial x4 + ax3 – 3x2 + 2x + b then find the value of a and b.