Advertisements
Advertisements
Question
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x3 + 2ax2 + ax - 1
Advertisements
Solution
Let p(x) x3 + 2ax2 + ax - 1 ...(i)
Since, (x - 2) is a factor of p(x), so p(2) = 0
Put x = 2 in equation (i), we get
p(2) = (2)3 - 2a(2)2 + a(2) -1
= 8 - 2a x 4 + 2a - 1
= 8 - 8a + 2a -1
= 7 - 6a
But p(2) = 0
7 - 6a = 0
⇒ -6a = -7
⇒ a = `(+7)/(+6)`
⇒ a = `(7)/(6)`.
RELATED QUESTIONS
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Factorise the expression f(x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Using remainder Theorem, factorise:
2x3 + 7x2 − 8x – 28 Completely
Find the values of a and b in the polynomial f(x) = 2x3 + ax2 + bx + 10, if it is exactly divisible by (x+2) and (2x-1).
If the polynomials ax3 + 4x2 + 3x - 4 and x3 - 4x + a leave the same remainder when divided by (x - 3), find the value of a.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
If (2x + 1) is a factor of both the expressions 2x2 – 5x + p and 2x2 + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
