Advertisements
Advertisements
Question
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Solution
p(x) = x^3 + 2x^2 - kx + 10
For (x - 2) to be the factor of p(x) = x3 + 2x2 – kx + 10
p(2) = 0
Thus (2)3 + 2(2)2 – k(2) + 10 = 0
⇒ 8 + 8 – 2k + 10 = 0
⇒ k = 13
Thus p(x) becomes x3 + 2x2 –13x + 10
Now, (x+5) would be the factor of p(x) iff p(–5) = 0
p(–5) = (–5)3 + 2(–5)2 – 13(–5) + 10 = –125 + 50 + 65 + 10 = 0
Thus, (x + 5) is also a factor of p(x).
APPEARS IN
RELATED QUESTIONS
Show that x – 2 is a factor of 5x2 + 15x – 50.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1)
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
