Advertisements
Advertisements
प्रश्न
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Advertisements
उत्तर
Let p(x) = x3 - 7x2 + 15x - 9
For checking that (x - 3) is a factor of p(x), we find : p(3)
p(3) = (3)3 - 7(3)2 + 15(3) - 9
= 27 - 63 + 45 - 9
= 72 - 72
= 0.
Hence, (x - 3) is a factor of p(x).
By division of p(x) by x - 3, we get the quotient
= x2 - 4x + 3
∴ x3 - 7x2 +15x - 9
= (x - 3) (x2 - 4x + 3)
= (x - 3) (x - 3) (x - 1)
= (x - 3)2 (x - 1).
संबंधित प्रश्न
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
Show that 3x + 2 is a factor of 3x2 – x – 2.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
If (x - 2) is a factor of the expression 2x3 + ax2 + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
Factors of 4 + 4x – x2 – x3 are ______.
