Advertisements
Advertisements
प्रश्न
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
उत्तर
p(x) = 2x3 − x2 − 45
Divisor = q(x) = x − 3
∴ Let x = 3
∴ p(3) = 2 × (3)3 − (3)2 − 45
= 2 × 27 − 9 − 45
= 54 − 54
= 0
So, by factor theorem q(x) = x − 3 is a factor of polynomial p(x) = 2x3 − x2 − 45.
APPEARS IN
संबंधित प्रश्न
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove by factor theorem that
(x - 3) is a factor of 5x2 - 21 x +18
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine 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) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
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
If p(a) = 0 then (x – a) is a ___________ of p(x)
