Q. 2 C4.4( 9 Votes )
Use the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:
f(x) = x3 – 4x2 + x + 6, g(x) = x – 2
Answer :
By Factor Theorem, we know that,
If p(x) is a polynomial and a is any real number, then g(x) = (x – a) is a factor of p(x), if p(a) = 0
For checking (x – 2) to be a factor, we will find f(2)
⇒ f(2) = (2)3 – 4(2)2 + (2) + 6
⇒ f(–1) = 8 – 16 + 2 + 6
⇒ f(–1) = 0
As, f(–1) is equal to zero, therefore, g(x) = (x – 2) is a factor of f(x)
Rate this question :






















Determine which of the following polynomials has (x + 1) as a factor.
x4 + 2x3 + 2x2 + x + 1
AP- MathematicsFactorize
x3 – 3x2 – 9x – 5
AP- MathematicsUse the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:
f(x) = 5x3 + x2 – 5x – 1, g(x) = x + 1
AP- MathematicsDetermine which of the following polynomials has (x + 1) as a factor.
x3 – x2 –(3 – √3 ) x + √3
AP- MathematicsUse the Factor Theorem to determine whether g(x) is factor of f(x) in the following cases:
f(x) = x3 – 4x2 + x + 6, g(x) = x – 2
AP- MathematicsFactorise
25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz
AP- Mathematics