Advertisements
Advertisements
Question
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
Advertisements
Solution
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
To check whether x - 2 is a factor of p(x) now put x = 2 in equation (i), we get
p(2) = (2)3 - 3(2)2 + 4(2) -4
= 8 - 3 x 4 + 8 - 4
= 8 - 12 + 8 - 4
= 16 - 16 = 0
Since, p(2) = 0, so by factor theorem (x - 2) is a factor of p(x).
RELATED QUESTIONS
Show that x – 2 is a factor of 5x2 + 15x – 50.
Show that 3x + 2 is a factor of 3x2 – x – 2.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
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.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
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 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.
