Advertisements
Advertisements
Question
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Solution
Let x – 2 = 0, then x = 2
Substituting the value of x in f(x),
f(x) = 3x2 – x – 10
= 3(2)2 – 2 – 10
= 12 – 2 – 10
= 0
∵ Remainder is zero
∴ x – 2 is a factor of f(x)
Dividing 3x2 – x – 10 by x – 2, we get
`x - 2")"overline(3x^2 - x - 10)("3x + 5`
3x2 – 6x
– +
5x – 10
5x – 10
– +
x
∴ 3x2 – x – 10 = (x – 2)(3x + 5).
APPEARS IN
RELATED QUESTIONS
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.
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
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 – 3) is a factor of x3 – 7x2 + 15x – 9. Hence factorise x3 – 7x2 + 15 x – 9
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Using the Remainder and Factor Theorem, factorise the following polynomial: x3 + 10x2 – 37x + 26.
If (2x + 1) is a factor of 6x3 + 5x2 + ax – 2 find the value of a.
If two polynomials 2x3 + ax2 + 4x – 12 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
