Advertisements
Advertisements
प्रश्न
Determine the following polynomial has (x + 1) a factor:
x4 + 3x3 + 3x2 + x + 1
Advertisements
उत्तर
If (x + 1) is a factor of polynomial p(x) = x4 + 3x3 + 3x2 + x + 1, then p(−1) must be zero, as a result (x + 1) is not a factor of this polynomial.
p(−1) = (−1)4 + 3(−1)3 + 3(−1)2 + (−1) + 1
= 1 − 3 + 3 − 1 + 1
= 1
As p(−1) ≠ 0,
Therefore, x + 1 is not a factor of this polynomial.
APPEARS IN
संबंधित प्रश्न
Determine the following polynomial has (x + 1) a factor:
`x^3-x^2-(2+sqrt2)x+sqrt2`
Find the factor of the polynomial given below.
3y2 – 2y – 1
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
The factorisation of 4x2 + 8x + 3 is ______.
Which of the following is a factor of (x + y)3 – (x3 + y3)?
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
Factorise:
84 – 2r – 2r2
Factorise:
1 + 64x3
If both x – 2 and `x - 1/2` are factors of px2 + 5x + r, show that p = r.
