Question

3y^2-17y+10 factored

Answer 1

To factor the quadratic expression \(3y^2 - 17y + 10\), we will look for two numbers that multiply to \(3 \cdot 10 = 30\) and add to \(-17\).

The two numbers that satisfy this condition are \(-15\) and \(-2\).

Now we can rewrite the middle term \(-17y\) using these two numbers:

\[
3y^2 - 15y - 2y + 10
\]

Next, we group the terms:

\[
(3y^2 - 15y) + (-2y + 10)
\]

Now factor out the common factors from each group:

\[
3y(y - 5) - 2(y - 5)
\]

Notice that we have a common factor of \((y - 5)\):

\[
(3y - 2)(y - 5)
\]

Thus, the factored form of \(3y^2 - 17y + 10\) is:

\[
(3y - 2)(y - 5)
\]