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
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.
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q, factorize the given polynomial completely.
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
If (x + 3) and (x – 4) are factors of x3 + ax2 – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
If (x – a) is a factor of x3 – ax2 + x + 5; the value of a is ______.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
