Advertisements
Advertisements
Question
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
Advertisements
Solution
f(x) = x3 – 13x – 12
Let x = 4, then
f(x) = (4)3 – 13(4) – 12
= 64 – 52 – 12
= 64 – 64
= 0
∵ f(x) = 0
∴ x – 4 is a factor of f(x)
Now, dividing f(x) by (x – 4), we get
f(x) = (x – 4)(x2 + 4x + 3)
= (x – 4)(x2 + 3x + x + 3)
= (x – 4)[x(x + 3) + 1(x + 3)]
= (x – 4)(x + 3)(x + 1)
`x – 4")"overline(x^3 – 13x – 12)("x^2 + 4x + 3`
x3 – 4x2
– +
4x2 – 13x
4x2 – 16x
– +
3x – 12
3x – 12
– +
x
APPEARS IN
RELATED QUESTIONS
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 3x + 2 is a factor of 3x2 – x – 2.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
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.
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
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.
If (x – 1) divides the polynomial kx3 – 2x2 + 25x – 26 without remainder, then find the value of k
If x – 3 is a factor of p(x), then the remainder is
