bailey writes the expression $g^{2}+14g + 40$ to represent the area of a planned school garden in square…

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?\n$(g - 4)(g - 10)$\n$(g + 4)(g + 10)$\n$(g + 4)(g - 10)$\n$(g - 4)(g + 10)$

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?\n$(g - 4)(g - 10)$\n$(g + 4)(g + 10)$\n$(g + 4)(g - 10)$\n$(g - 4)(g + 10)$

Answer

Explanation:

Step1: Recall factoring quadratic form

For a quadratic expression $ax^{2}+bx + c$ (here $a = 1$, $b=14$, $c = 40$), we need two numbers that multiply to $ac=40$ and add up to $b = 14$.

Step2: Find the two numbers

The pairs of factors of 40 are: (1,40), (2,20), (4,10), (5,8). The pair (4,10) satisfies $4 + 10=14$.

Step3: Factor the quadratic

We rewrite the middle - term: $g^{2}+14g + 40=g^{2}+4g+10g + 40$. Then group the terms: $(g^{2}+4g)+(10g + 40)=g(g + 4)+10(g + 4)=(g + 4)(g+10)$.

Answer:

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