Question

what value in - place of the question - mark makes the polynomial below a perfect - square trinomial?
$x^{2}+24x+?$
a. 12
b. 144
c. 52
d. 24

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial is of the form $a^{2}+2ab + b^{2}=(a + b)^{2}$ or $a^{2}-2ab + b^{2}=(a - b)^{2}$. In the given trinomial $x^{2}+26x+?$, we have $a^{2}=x^{2}$, so $a = x$, and $2ab=26x$.

Step2: Solve for $b$

Since $a = x$ and $2ab = 26x$, substitute $a=x$ into $2ab = 26x$. We get $2\times x\times b=26x$. Divide both sides of the equation by $2x$ (assuming $x
eq0$; when $x = 0$, the coefficient of the linear - term doesn't matter for the form of the trinomial). So $b = 13$.

Step3: Find the constant term

The constant term in the perfect - square trinomial $a^{2}+2ab + b^{2}$ is $b^{2}$. Since $b = 13$, then $b^{2}=169$.

Answer:

B. 169