Question

Factorise x square - 5 x - 6
Please give me solution

Answer 1

Answer:

(x + 1)(x - 6)

Step-by-step explanation:

Given : x² - 5x - 6

On comparing this with ax² + bx + c, we get

a = 1, b = - 5, c = - 6

Using Middle Term Factorisation Method

→ x² - 6x + x - 6

Taking out common terms, we get

→ x(x - 6) + 1(x - 6)

→ (x + 1)(x - 6)

• In Middle Term Factorisation method, we factorise the middle term only.
• First we multiply 'a' and 'c'.
• Then we have to find such a pair of number such that on addition or subtraction, the result equal to 'b' and on multiplication, the results equals to the multiplication of 'a' and 'c'.

We get the two terms : 1 and - 6

Addition = (1) + (- 6) = - 5 = b

Multiplication = (1)(- 6) = - 6 = Product of 'a' and 'c' i.e. (1)(- 6) = - 6

Answer 2

$\huge\underline\mathrm{Question-}$

Factorise x² - 5x - 6

$\huge\underline\mathrm{Answer-}$

Required factors : ( x - 6 ) ( x + 1 )

$\huge\underline\mathrm{Solution-}$

Given expression : x² - 5x - 6

Sum = -5

product = -6

Factors = (-6, 1)

By splitting middle term,

$\mapsto$ x² - 6x + x - 6

By taking as common,

$\mapsto$ x ( x - 6 ) + 1 ( x - 6 )

$\mapsto$ ( x - 6 ) ( x + 1 )

$\therefore$ Our required factors are : ( x - 6 ) and ( x + 1 )

$\rule{200}1$

Verification :

To verifying it, we have to put x = 6 or 1 in the given expression, so that we come to know whether the factors are correct or not.

Put x = 6

$\mapsto$ (6)² - 5 ( 6 ) - 6 = 0

$\mapsto$ 36 - 30 - 6 = 0

$\mapsto$ 36 - 36 = 0

$\mapsto$ 0 = 0

$\therefore$ ( x - 6 ) is a factor of given polynomial or expression.

Put x = -1

$\mapsto$ (-1)² - 5 (-1) - 6 = 0

$\mapsto$ 1 + 5 - 6 = 0

$\mapsto$ 5 - 5 = 0

$\therefore$ ( x + 1 ) is also a factor of given polynomial or expression.

Hence verified!