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
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.
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
In the following two polynomials. Find the value of ‘a’ if x + a is a factor of each of the two:
x4 - a2x2 + 3x - a.
In the following two polynomials, find the value of ‘a’ if x – a is a factor of each of the two:
x6 - ax5 + x4 - ax3 + 3a + 2
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
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 (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.
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
