Advertisements
Advertisements
प्रश्न
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
Advertisements
उत्तर
Let f(x) = x3 + 6x2 + 11x + 6
For x = –1
f(–1) = (–1)3 + 6(–1)2 + 11(–1) + 6
= –1 + 6 – 11 + 6
= 12 – 12
= 0
Hence, (x + 1) is a factor of f(x).
x2 + 5x + 6
`x + 1")"overline(x^3 + 6x^2 + 11x + 6)`
x3 + x2
5x2 + 11x
5x2 + 5x
6x + 6
6x + 6
0
∴ x3 + 6x2 + 11x + 6 = (x + 1)(x2 + 5x + 6)
= (x + 1)(x2 + 2x + 3x + 6)
= (x + 1)[x(x + 2) + 3(x + 2)]
= (x + 1)(x + 2)(x + 3)
APPEARS IN
संबंधित प्रश्न
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.
Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial 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).
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:
x3 + ax2 − 2x + a + 4
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
Use factor theorem to factorise the following polynomials completely: x3 – 19x – 30
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.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
