Question

$2. \: {x}^{2} - 7x + 6 \: and \: x {}^{2} - 1$
QUESTION:
2. What factoring techniques did you apply in item 2?​

Answer 1

Question :

Factorise the following :

• x² - 7x + 6
• x² - 1

Solution :

• x² - 7x + 6 [ By middle term splitting method ]

→ x² - 6x - x + 6

→ x(x - 6) - (x - 6)

→ (x - 6)(x - 1)

• x² - 1 [ By using the algebraic formula , a² - b² = (a + b)(a - b) ]

→ x² - 1²

→ (x + 1)(x - 1)

Answer 2

Question :

Find the LCM of following Expressions :

${x}^{2} - 7x + 6 \: \: and \: \: \: {x}^{2} - 1$

Solution :

$= {x}^{2} - 7x + 6 \\ = {x}^{2} - x - 6x + 6 \\ = x(x - 1) - 6(x - 1) \\ = (x - 6)(x - 1)$

${x}^{2} - 1 = \: ( {x}^{2} - {1}^{2} ) \\ ( {a}^{2} - {b}^{2} ) = (a + b)(a - b) \\ = (x - 1)(x + 1)$

The LCM of The expressions would be,

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