Factorise: 6x³
– 5x²
– 13x + 12
Answers
Required Answer:-
Given To Factorise:
- 6x³ - 5x² - 13x + 12
Solution:
1. Using factor theorem.
Let,
→ p(x) = 6x³ - 5x² - 13x + 12
Putting p = 1, we get,
→ p(1) = 6 × (1)³ - 5 ×(1)² - 13 × 1 + 12
→ p(1) = 6 - 5 - 13 + 12
→ p(1) = 1 - 13 + 12
→ p(1) = 12 - 12
→ p(1) = 0
Therefore, (x - 1) is a factor. (By Factor Theorem)
x - 1 ) 6x³ - 5x² - 13x + 12 (6x² + x - 12
6x³ - 6x²
(-) (+)
--------------------------------------------
x² - 13x
x² - 1x
(-) (+)
--------------------------------------------
-12x + 12
-12x + 12
(+) (-)
--------------------------------------------
0
Therefore,
6x³ - 5x² - 13x + 12
= (x - 1)(6x² + x - 12)
= (x - 1)(6x² - 8x + 9x - 12)
= (x - 1)[2x(3x - 4) + 3(3x - 4)]
= (x - 1)(2x + 3)(3x - 4)
→ Therefore, factorised form of the given polynomial is (x - 1)(2x + 3)(3x - 4)
2. Without using factor theorem.
Given,
= 6x³ - 5x² - 13x + 12
= 6x³ - (6 - 1)x² - (1 + 12)x + 12 (splitting)
= 6x³ - 6x² + x² - x - 12x + 12
= 6x²(x - 1) + x(x - 1) - 12(x - 1)
= (x - 1)(6x² + x - 12) (grouping)
= (x - 1)(6x² - 8x + 9x - 12)
= (x - 1)[2x(3x - 4) + 3(3x - 4)]
= (x - 1)(2x + 3)(3x - 4)
→ Therefore, factorised form of the given polynomial is (x - 1)(2x + 3)(3x - 4)
Answer:
- (x - 1)(2x + 3)(3x - 4).