Advertisements
Advertisements
प्रश्न
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
Advertisements
उत्तर
Let P(x) = x3 + 5x2 – 10x + 4
By factor theorem (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 13 + 5(12) – 10(1) + 4 = 1 + 5 – 10 + 4
P(1) = 0
∴ (x – 1) is a factor of x3 + 5x2 – 10x + 4
APPEARS IN
संबंधित प्रश्न
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
(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 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.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
Factors of 3x3 – 2x2 – 8x are ______.
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
