Advertisements
Advertisements
प्रश्न
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Advertisements
उत्तर
Let p(x) = x2 + 2x − 3.
Divisor = x + 3
∴ Let x = −3
∴ p(−3) = (−3)2 + 2 × (−3) − 3
= 9 − 6 − 3
= 0
So, by factor theorem, (x + 3) is a factor of x2 + 2x − 3.
APPEARS IN
संबंधित प्रश्न
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.
Show that 3x + 2 is a factor of 3x2 – x – 2.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
Show that (x – 3) is a factor of x3 – 7x2 + 15x – 9. Hence factorise x3 – 7x2 + 15 x – 9
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
