Question

Factor the trinomial below

5x^2 + 29x - 6

Which two binomials are factors of the trinomial?

x+6
5x - 1
x - 6
x + 3
5x - 2

Answer 1

To factor the trinomial \(5x^2 + 29x - 6\), we can look for two binomials of the form \((ax + b)(cx + d)\) that multiply together to give the original trinomial.

First, we need to find two numbers that multiply to \(a \cdot c \cdot -6\) (where \(a = 5\) and \(c = -6\)) and add up to \(b = 29\).

1. The product of \(a \cdot c \cdot -6 = 5 \cdot -6 = -30\).
2. We are looking for two numbers that multiply to \(-30\) and add up to \(29\).

The two numbers that fit this requirement are \(30\) and \(-1\) because:
- \(30 \times -1 = -30\)
- \(30 + (-1) = 29\)

Next, we can break the middle term \(29x\) into \(30x - 1x\):

\[
5x^2 + 30x - 1x - 6
\]

Now we can group the terms:

\[
(5x^2 + 30x) + (-1x - 6)
\]

Factor out the common factors from each group:

\[
5x(x + 6) - 1(x + 6)
\]

Now, we can factor out the binomial \((x + 6)\):

\[
(5x - 1)(x + 6)
\]

Thus, the factors of the trinomial \(5x^2 + 29x - 6\) are:

\[
(5x - 1)(x + 6)
\]

So, the two binomials that are factors of the trinomial are:

\[
5x - 1 \quad \text{and} \quad x + 6
\]