Advertisements
Advertisements
प्रश्न
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
Advertisements
उत्तर
Let f (x) = 2x3 + x2 − 13x + 6
For x = 2,
f(x) = f(2) = 2(2)3 + (2)2 − 13(2) + 6 = 16 + 4 − 26 + 6 = 0
Hence, (x − 2) is a factor of f(x).
∴ `2x^3 + x^2 - 13x + 6 = (x-2) (2x^2 + 5x -3)`
= `(x-2)(2x^2 + 6x -x -3)`
= `(x-2) [2x(x + 3) -(x-3)]`
=` (x - 2)(x + 3) (2x - 1)`
संबंधित प्रश्न
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
If (x + 1) and (x – 2) are factors of x3 + (a + 1)x2 – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.
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
If (x – 2) is a factor of 2x3 – x2 + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
If x3 – 2x2 + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.
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.
(x – 2) is a factor of ______.
