Question

find the product if the polynomials (2x+1) (x-4)

Answer 1

simplify -3(2x-4)

Answer 2

To find the product of the polynomials \( (2x + 1)(x - 4) \), you can use the distributive property (also known as the FOIL method for binomials).

1. **First**: Multiply the first terms:
\[
2x \cdot x = 2x^2
\]

2. **Outer**: Multiply the outer terms:
\[
2x \cdot (-4) = -8x
\]

3. **Inner**: Multiply the inner terms:
\[
1 \cdot x = x
\]

4. **Last**: Multiply the last terms:
\[
1 \cdot (-4) = -4
\]

Now, combine all these results:
\[
2x^2 - 8x + x - 4
\]

Combine like terms:
\[
2x^2 - 7x - 4
\]

Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is:
\[
\boxed{2x^2 - 7x - 4}
\]

Answer 3

To simplify the expression \(-3(2x - 4)\), you need to distribute \(-3\) to both terms inside the parentheses:

1. Multiply \(-3\) by \(2x\):
\[
-3 \cdot 2x = -6x
\]

2. Multiply \(-3\) by \(-4\):
\[
-3 \cdot -4 = 12
\]

Now, combine these results:
\[
-6x + 12
\]

So, the simplified expression is:
\[
\boxed{-6x + 12}
\]