Question

solve.
lauren has ( x^2 ) stickers. joe has three times as many stickers as lauren.
brenda has 4 times as many stickers as joe. steve has six times the
square root of lauren’s stickers.

1. find the gcf of joe’s, brenda’s and steve’s stickers.

1. find the gcf of lauren’s, brenda’s and steve’s stickers.

1. find the gcf of joe’s and lauren’s stickers.

Explanation:

Sub - Question 1

Step 1: Find the number of stickers each has

Lauren has \(x^{2}\) stickers. Joe has \(3\times x^{2}=3x^{2}\) stickers. Brenda has \(4\times3x^{2} = 12x^{2}\) stickers. Steve has \(6\times\sqrt{x^{2}}=6x\) (assuming \(x\geq0\), since the number of stickers can't be negative).

Step 2: Factorize each expression

• Joe's stickers: \(3x^{2}=3\times x\times x\)
• Brenda's stickers: \(12x^{2}=2\times2\times3\times x\times x\)
• Steve's stickers: \(6x = 2\times3\times x\)

Step 3: Find the GCF

The common factors are \(3\) and \(x\). So the GCF is \(3x\).

Step 1: Recall the number of stickers

Lauren: \(x^{2}=x\times x\), Brenda: \(12x^{2}=2\times2\times3\times x\times x\), Steve: \(6x = 2\times3\times x\)

Step 2: Find the GCF

The common factors are \(x\) (from \(x^{2}\), \(12x^{2}\) and \(6x\)). So the GCF is \(x\).

Step 1: Recall the number of stickers

Lauren: \(x^{2}=x\times x\), Joe: \(3x^{2}=3\times x\times x\)

Step 2: Find the GCF

The common factors are \(x\times x=x^{2}\). So the GCF is \(x^{2}\).

Answer:

\(3x\)

Sub - Question 2