Advertisements
Advertisements
प्रश्न
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Advertisements
उत्तर
Let P(x) = x4 + 5x2 – 5x + 1
By factor theorem, (x – 1) is a factor of P(x), if P(1) = 0
P(1) = 14 + 5 (12) – 5(1) + 1
= 1 + 5 – 5 + 1
= 2 ≠ 0
∴ (x – 1) is not a factor of x4 + 5x2 – 5x + 1
APPEARS IN
संबंधित प्रश्न
Prove by factor theorem that
(2x+1) is a factor of 4x3 + 12x2 + 7x +1
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
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
Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
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 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.
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
Which of the following is a factor of (x – 2)2 – (x2 – 4)?
