Advertisements
Advertisements
प्रश्न
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
Advertisements
उत्तर
Given, P(x) = 3x3 + 8x2 – 15x + k
Put x – 1 = 0
x = 1
Now, P(1) = 3(1)3 + 8(1)2 – 15(1) + k = 0
⇒ 3 + 8 – 15 + k = 0
⇒ – 4 + k = 0
⇒ k = 4
Hence, k = 4
P(x) = 3x3 + 8x2 – 15x + 4
`x - 1")"overline(3x^3 + 8x^2 - 15x + 4)(3x^2 + 11x - 4`
3x3 – 3x2
– +
11x2 – 15x
11x2 – 11x
– +
– 4x + 4
– 4x + 4
+ –
x
∴ 3x3 + 8x2 – 15x + 4 = (x – 1) (3x2 + 11x – 4)
= (x – 1) (3x2 + 12x – x – 4)
= (x – 1) [3x(x + 4) – 1(x + 4)]
= (x – 1) (3x – 1) (x + 4)
संबंधित प्रश्न
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Using remainder Theorem, factorise:
2x3 + 7x2 − 8x – 28 Completely
Find the value of a and b so that the polynomial x3 - ax2 - 13x + b has (x - 1) (x + 3) as factor.
If x – 2 is a factor of each of the following three polynomials. Find the value of ‘a’ in each case:
x2 - 3x + 5a
Show that x2 - 9 is factor of x3 + 5x2 - 9x - 45.
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
When 3x2 – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x2 – 5x + p – 3.
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 f(x) = 3x + 8; the value of f(x) + f(– x) is ______.
