Question

sort the expressions.
9(t + 7) t + 12 t + 12
factors of 11(t + 12) factors of 9(t + 7)

Explanation:

Step1: Analyze \(11(t + 12)\)

The factors of \(11(t + 12)\) should include expressions that multiply to give \(11(t + 12)\). The expression \(t + 12\) is a factor (since \(11\times(t + 12)=11(t + 12)\)) and \(11\) is a factor, but from the given options, \(t + 12\) and \(11\) (but \(11\) isn't in the blue boxes, the blue boxes have \(t + 12\), \(t + 7\), \(9(t + 7)\)). Wait, the blue expressions are \(9(t + 7)\), \(t + 7\), \(t + 12\). So for \(11(t + 12)\), the factor from the options is \(t + 12\) (since \(11\times(t + 12)\), so \(t + 12\) is a factor).

Step2: Analyze \(9(t + 7)\)

The factors of \(9(t + 7)\) should include expressions that multiply to give \(9(t + 7)\). The expression \(9(t + 7)\) itself is a factor, and \(t + 7\) is a factor (since \(9\times(t + 7)=9(t + 7)\)). So from the options, \(9(t + 7)\) and \(t + 7\) are factors of \(9(t + 7)\).

So:

• Factors of \(11(t + 12)\): \(t + 12\)
• Factors of \(9(t + 7)\): \(9(t + 7)\), \(t + 7\)

Answer:

Factors of \(11(t + 12)\): \(t + 12\)
Factors of \(9(t + 7)\): \(9(t + 7)\), \(t + 7\)