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
Using the Factor Theorem, show that (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
If (x - 2) is a factor of the expression 2x3 + ax2 + bx - 14 and when the expression is divided by (x - 3), it leaves a remainder 52, find the values of a and b.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
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.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
