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 a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
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.
If (x - 2) is a factor of x3 − mx2 + 10x − 20 then find the value of m.
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
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
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.
Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
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 two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Determine the value of m, if (x + 3) is a factor of x3 – 3x2 – mx + 24
If p(a) = 0 then (x – a) is a ___________ of p(x)
If x – 2 is a factor of x3 – kx – 12, then the value of k is ______.
Factors of 3x3 – 2x2 – 8x are ______.
