Question

factor. 49v² + 41v + 9 select the correct choice below and fill in any answer boxes within your choice. a. 49v² + 41v + 9 = b. the expression is prime.

Explanation:

Step1: Consider quadratic formula

For a quadratic expression $ax^{2}+bx + c$ (here $a = 49$, $b=41$, $c = 9$), we can use the discriminant $\Delta=b^{2}-4ac$.
$\Delta=(41)^{2}-4\times49\times9$
$=1681 - 1764$
$=- 83$

Step2: Analyze discriminant result

Since $\Delta=-83<0$, the quadratic expression $49v^{2}+41v + 9$ has no real - valued roots. And a non - factorable quadratic expression over the real numbers is called a prime quadratic expression.

Answer:

B. The expression is prime.