Advertisements
Advertisements
प्रश्न
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
Advertisements
उत्तर
We know that
x2 - 9 = (x + 3)(x - 3)
x2 - 9 will be a factor of
f(x) = x3 + 5x2 - 9x - 45
Only when both x + 3 are factor of this polynomial.
Now, f(-3) = (-3)3 + 5(-3)2 -9(-3) -45
= -27 + 45 + 27 - 45 = 0
And f(3) = (3)3 + 5(3)2 - 9(3) -45
= 27 + 45 - 27 - 45 = 0
So, both x + 3 and x - 3 are factor of x3 + 5x2 - 9x - 45.
Hence, x2 - 9 is a factor of the given polynomial.
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).
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 x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x5 - 3x4 - ax3 + 3ax2 + 2ax + 4.
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
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
While factorizing a given polynomial using the remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student’s solution correct in stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
One factor of x3 – kx2 + 11x – 6 is x – 1. The value of k is ______.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
If f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
