express as a trinomial (3x+1)(x-4)

Answer 1

To express \((3x+1)(x-4)\) as a trinomial, you can use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms: \(3x \cdot x = 3x^2\)
2. Outer: Multiply the outer terms: \(3x \cdot (-4) = -12x\)
3. Inner: Multiply the inner terms: \(1 \cdot x = 1x\)
4. Last: Multiply the last terms: \(1 \cdot (-4) = -4\)

Now, combine all these results:

\[ 3x^2 - 12x + 1x - 4 \]

Combine the like terms \(-12x\) and \(1x\):

\[ 3x^2 - 11x - 4 \]

So, the expression \((3x + 1)(x - 4)\) as a trinomial is:

\[ 3x^2 - 11x - 4 \]