Advertisements
Advertisements
Question
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Advertisements
Solution
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
RELATED QUESTIONS
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.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
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
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2)
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
If x – 3 is a factor of p(x), then the remainder is
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
