Advertisements
Advertisements
Question
Use factor theorem to factorise the following polynomials completely: x3 – 19x – 30
Solution
f(x) = x3 – 19x – 30
Let x = –2, then
f(–2) = (–2)3 – 19(–2) – 30
= –8 + 38 – 30
= 38 – 38
= 0
∴ (x + 2) is a factor of f(x)
Now dividing f(x) by (x + 2), we get
f(x) = x3 – 19x – 30
= (x + 2)(x2 – 2x – 15)
= (x + 2){(x2 –5x + 3x – 15}
= (x + 2){x(x – 5) + 3(x – 5)}
= (x + 2)(x – 5)(x + 3)
`x + 2")"overline(x^3 - 19x - 30)("x^2 - 2x - 15`
x3 + 2x2
– –
–2x2 – 19x
–2x2 – 4x
+ +
–15x – 30
–15x – 30
+ +
x
APPEARS IN
RELATED QUESTIONS
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Using Remainder Theorem, factorise : x3 + 10x2 – 37x + 26 completely.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorize the given polynomial completely.
Factorize completely using factor theorem:
2x3 – x2 – 13x – 6
The polynomial 3x3 + 8x2 – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
While factorizing a given polynomial, using remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x3 + 7x2 + 2x – 3.
- Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial?
- Give a valid reason for your answer.
Also, factorize the given polynomial completely.
For the polynomial x5 – x4 + x3 – 8x2 + 6x + 15, the maximum number of linear factors is ______.
