Advertisements
Advertisements
Question
Show that x – 2 is a factor of 5x2 + 15x – 50.
Advertisements
Solution
(x – a) is a factor of a polynomial f(x) if the remainder, when f(x) is divided by (x – a), is 0, i.e., if f(a) = 0.
f(x) = 5x2 + 15x – 50
f(2) = 5(2)2 + 15(2) – 50
= 20 + 30 – 50
= 0
Hence, x – 2 is a factor of 5x2 + 15x – 50
APPEARS IN
RELATED QUESTIONS
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
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
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
If both (x − 2) and `(x - 1/2)` is the factors of ax2 + 5x + b, then show that a = b
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
Factors of 4 + 4x – x2 – x3 are ______.
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
