Question

name: jose bodilla
usa #4 test review (units 7 & 10)

1. which expression is equivalent to ( 3x^2 - 12 )?

a. ( (x + 4)(x - 4) )
b. ( 3(x + 2)(x - 2) )
c. ( (3x + 6)(3x - 6) )
d. ( 2(x - 2)^2 )

1. select an equivalent expression for ( 5x^2 - 125 )?

a. ( (x - 5)^2 )
b. ( 5(x + 5)(x - 5) )
c. ( (x + 25)(x - 5) )
d. ( (5x - 25)(5x + 25) )

Explanation:

Problem 1

Step 1: Factor out the common term

First, factor out the greatest common factor from \(3x^2 - 12\). The GCF of \(3x^2\) and \(12\) is \(3\), so we get \(3(x^2 - 4)\).

Step 2: Apply the difference of squares formula

The expression \(x^2 - 4\) is a difference of squares, which can be factored as \((x + 2)(x - 2)\) (since \(a^2 - b^2=(a + b)(a - b)\) with \(a = x\) and \(b = 2\)). So, \(3(x^2 - 4)=3(x + 2)(x - 2)\).

Step 1: Factor out the common term

First, factor out the greatest common factor from \(5x^2 - 125\). The GCF of \(5x^2\) and \(125\) is \(5\), so we get \(5(x^2 - 25)\).

Step 2: Apply the difference of squares formula

The expression \(x^2 - 25\) is a difference of squares, which can be factored as \((x + 5)(x - 5)\) (since \(a^2 - b^2=(a + b)(a - b)\) with \(a = x\) and \(b = 5\)). So, \(5(x^2 - 25)=5(x + 5)(x - 5)\).

Answer:

b. \(3(x + 2)(x - 2)\)

Problem 2