Advertisements
Advertisements
प्रश्न
Use factor theorem to factorise the following polynomials completely: 4x3 + 4x2 – 9x – 9
Advertisements
उत्तर
f(x) = 4x3 + 4x2 – 9x – 9
Let x = -1, then
f(-1) = 4 (-1)3 + 4 (-1)2 – 9 (-1) – 9
= 4(–1) + 4(1) + 9 – 9
= –4 + 4 + 9 – 9
= 13 – 13
= 0
∴ (x + 1) is a factor of f(x)
Now dividing f(x) by x + 1, we get
f(x) = 4x3 + 4x2 – 9x – 9
= (x + 1)(4x2 – 9)
= (x + 1){(2x)2 – (3)2}
= (x + 1)(2x + 3)(2x – 3)
`x + 1")"overline(4x^3 + 4x^2 - 9x - 9)("4x^2 - 9`
4x3 + 4x2
– –
– 9x – 9
– 9x – 9
+ +
x
APPEARS IN
संबंधित प्रश्न
Using Remainder Theorem, factorise : x3 + 10x2 – 37x + 26 completely.
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 factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`
Hence factorise the polynomial completely.
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
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
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
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.
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
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 ______.
