Advertisements
Advertisements
प्रश्न
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
Advertisements
उत्तर
Let f(x) = x6 - x5 + x4 - x3 + x2 - x + 1 to check whether x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1 we find f(1).
Put x = 1 in equation (i) we get
f(1) = (1)6 - (1)5 + (1)4 - (1)3 + (1)2 - (1) + 1
= 1 - 1 + 1 - 1 + 1 - 1 + 1
= 4 - 3
= 1.
Since, f(1) ≠ 0, So by factor theorem (x - 1) is not a factor of f(x).
संबंधित प्रश्न
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.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
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 (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
If p(a) = 0 then (x – a) is a ___________ of p(x)
If mx2 – nx + 8 has x – 2 as a factor, then ______.
