Question

5 which of the following expressions is a factor of the polynomial below? $4h^2 + 13h + 10$ a) $(h - 2)$ the $4^{th}$ of july b) $(4h + 5)$ saturday night

Explanation:

Step1: Factor the quadratic polynomial

We factor \(4h^{2}+13h + 10\) using the AC method. For a quadratic \(ax^{2}+bx + c\), we find two numbers that multiply to \(a\times c=4\times10 = 40\) and add up to \(b = 13\). The numbers are \(8\) and \(5\) since \(8\times5=40\) and \(8 + 5=13\).
Rewrite the middle term: \(4h^{2}+8h+5h + 10\)
Group the terms: \((4h^{2}+8h)+(5h + 10)\)
Factor out the GCF from each group: \(4h(h + 2)+5(h + 2)\)
Factor out \((h + 2)\): \((4h + 5)(h+ 2)\)

Step2: Identify the factor

From the factored form \((4h + 5)(h + 2)\), we can see that \((4h+5)\) is a factor. We check option A: \((h - 2)\) is not a factor as our factors are \((4h + 5)\) and \((h + 2)\).

Answer:

B. \((4h + 5)\)