Question

In factored form please help

Answer 1

Answer:

3rd option

Step-by-step explanation:

$\frac{3x^2-3}{x^2-5x+4}$ ( factorise numerator and denominator )

3x² - 3 ← factor out 3 from each term

= 3(x² - 1²) ← x² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

x² - 1

= x² - 1²

= (x - 1)(x + 1) , then

3x² - 3 = 3²(x - 1)(x + 1) ← in factored form

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x² - 5x + 4

consider the factors of the constant term (+ 4) which sum to give the coefficient of the x- term (- 5)

the factors are - 1 and - 4 , since

- 1 × - 4 = + 4 and - 1 - 4 = - 5 , then

x² - 5x + 4 = (x - 1)(x - 4)

then

$\frac{3x^2-3}{x^2-5x+4}$ = $\frac{3(x-1)(x+1)}{(x-1)(x-4)}$ ← in factored form