Question

Factor completely 5x2 − 50x + 120.

Answer 1

Answer:

Q1. d. 5(x - 4)(x - 6)

Q2. b. (8x - 1)(8x + 1)

Step-by-step explanation:

$\bold{Q1}\\\\5x^2-50x+120=5(x^2-10x+24)=5(x^2-6x-4x+24)\\\\=5\bigg(x(x-6)-4(x-6)\bigg)=5(x-6)(x-4)\\\\\bold{Q2}\\\\64x^2-1=(8x)^2-1^2=(8x-1)(8x+1)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)$

Answer 2

Answer:

see explanation

Step-by-step explanation:

1

Given

5x² - 50x + 120 ← factor out 5 from each term

= 5(x² - 10x + 24)

To factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term ( - 10)

The factors are - 4 and - 6, since

- 4 × - 6 = 24 and - 4 - 6 = - 10, hence

x² - 10x + 24 = (x - 4)(x - 6) and

5x² - 50x + 120 = 5(x - 4)(x - 6) → d

2

64x² - 1 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

64x² = (8x)² ⇒ a = 8x and b = 1

64x² - 1

= (8x)² - 1² = (8x - 1)(8x + 1) → b