Q 66E - Intermediate Algebra

Question

In the following exercises, factor each trinomial of the form $x^2+bx+c$.

$u^2+101u+100$

Step-by-Step Solution

Answer

The factors are $(u+1)(u+100)$.

Step 1. Writing the expression

Write the factors as two binomials with first terms $u$.

$(u )(u )$.

Step 2. Finding the factors

We need to find two numbers whose product is $100$ and sum is $101$.

Since $101$ is a prime number, we know that $1$ and $100$ are the only numbers whose product is $100$ and sum is $101$.

Hence, the factorization of the trinomial is $(u+1)(u+100)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (u+1)(u+100)=u^2+100u+u+100 \\ (u+1)(u+100)=u^2+101u+100 \end{gathered}$$

Thus, the obtained factorization is correct.