Question

Factor completely 5x2 − 50x + 120.

Select one:
a. 5(x − 3)(x − 8)
b. (5x − 15)(x − 8)
c. (x − 4)(5x − 30)
d. 5(x − 4)(x − 6)


Question 2
Factor completely 64x2 − 1
Select one:
a. (8x − 1)(8x − 1)
b. (8x − 1)(8x + 1)
c. (1 − 8x)(1 − 8x)
d. (1 − 8x)(1 + 8x)

Answer 1

see explanation

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

Answer 2

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

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

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)`