Question

Find the product of the polynomials left parenthesis 2 x plus 1 right parenthesis left parenthesis x minus 4 right parenthesis

Answer 1

the 7 and 4 are wrong and not only that it is suppsoed to come out a adding not subtracting

Answer 2

is this simplified if so dont and try agin and if it isn't simplify

Answer 3

then don't simplify please

Answer 4

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

Let's calculate it step by step:

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 \((-8x + x)\):
\[
2x^2 - 7x - 4
\]

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

Answer 5

Let’s go through the multiplication process of the polynomials \((2x + 1)(x - 4)\) again step by step to ensure we get the correct result.

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:
\[
2x^2 - 8x + x - 4
\]

Combining like terms gives us:
\[
2x^2 + (-8x + x) - 4 \implies 2x^2 - 7x - 4
\]

Thus, the product remains as:
\[
\boxed{2x^2 - 7x - 4}
\]

If you meant for a different operation or if there’s any additional context, please clarify, and I’ll be happy to help!

Answer 6

I apologize for any confusion. The expression we computed, \(2x^2 - 7x - 4\), is already in its simplest form as a polynomial. However, let’s verify the multiplication step-by-step once more to ensure clarity:

We are finding the product of:
\[
(2x + 1)(x - 4)
\]

Using the distributive property (or FOIL method):

1. **First**:
\[
2x \cdot x = 2x^2
\]

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

3. **Inner**:
\[
1 \cdot x = x
\]

4. **Last**:
\[
1 \cdot (-4) = -4
\]

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

Combining like terms, specifically the \( -8x + x \):
\[
2x^2 - 7x - 4
\]

This expression \(2x^2 - 7x - 4\) is indeed simplified, as it cannot be factored further with integer coefficients. If you were expecting different results, please let me know, and I'll gladly assist!

Answer 7

Got it! Let’s find the product of the polynomials \( (2x + 1)(x - 4) \) without simplifying or combining like terms.

Using the distributive property (or the FOIL method):

1. **First**:
\[
2x \cdot x = 2x^2
\]

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

3. **Inner**:
\[
1 \cdot x = x
\]

4. **Last**:
\[
1 \cdot (-4) = -4
\]

Now, put all these terms together without combining them:
\[
2x^2 - 8x + x - 4
\]

So the final product, without simplifying, is:
\[
\boxed{2x^2 - 8x + x - 4}
\]

If you decide you need any further operations or simplifications on this expression later, just let me know!