Question
express as a trinomial (3x+1)(x-4)
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GPT-4o mini
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:
\[
3x^2 - 11x - 4
\]
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:
\[
3x^2 - 11x - 4
\]
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