Advertisements
Advertisements
प्रश्न
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.
उत्तर
f(x) = 3x2 – 5x+ p
Let (x – 2) = 0, then x = 2
f(2) = 3 (2)2 – 5(2) + p
= 3 x 4 – 10 + p
= 12 – 10 + p
= 2 + p
∵ Remainder = 3
∴ 2 + p = 3
⇒ p = 3 – 2 = 1
Hence p = 1
Now f(x) = 3x2 – 5x + p – 3
= 3x2 – 5x + 1 – 3
= 3x2 – 5x – 2
Dividing by (x – 2), we get
`x - 2")"overline(3x^2 - 5x - 2)("3x + 1`
3x2 – 6x
– +
x – 2
x – 2
– +
x
3x2 – 5x – 2 = (x – 2)(3x + 1).
APPEARS IN
संबंधित प्रश्न
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Factorise the expression f(x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
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 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).
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
Use factor theorem to factorise the following polynomials completely: x3 – 19x – 30
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 remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
