Question

bailey writes the expression $g^2 + 14g + 40$ to represent the area of a planned school garden in square feet. what factors can be used to find the dimensions of her garden?

• $(g - 4)(g - 10)$
• $(g + 4)(g + 10)$
• $(g + 4)(g - 10)$
• $(g - 4)(g + 10)$

Explanation:

Step1: Recall factoring trinomials

To factor \(g^2 + 14g + 40\), we need two numbers that multiply to \(40\) and add up to \(14\).

Step2: Find the numbers

The numbers \(4\) and \(10\) multiply to \(40\) (\(4\times10 = 40\)) and add up to \(14\) (\(4 + 10=14\)).

Step3: Factor the trinomial

Using these numbers, the trinomial \(g^2+14g + 40\) factors as \((g + 4)(g + 10)\) because \((g + 4)(g + 10)=g^2+10g+4g + 40=g^2+14g + 40\).

Answer:

B. \((g + 4)(g + 10)\)