Find the product of the polynomials (2x+1)(x−4) .

Answer 1

To find the product of the polynomials \( (2x + 1)(x - 4) \), we will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

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: \( 1 \cdot x = 1x \) or just \( x \).
4. Last, multiply the last terms: \( 1 \cdot (-4) = -4 \).

Now, combine these results:

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

Next, combine the like terms:

\[ 2x^2 - 7x - 4 \]

Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is

\[ \boxed{2x^2 - 7x - 4}. \]

Answer 2

Sorry, that’s only partially correct Remember that this polynomial expression will generate two x terms. Remember that a positive value times a negative value will equal a negative value.

Answer 3

Let's carefully expand the product of the polynomials \( (2x + 1)(x - 4) \) again.

Using the distributive property, we'll multiply each term in the first polynomial by each term in the second polynomial 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 these results together: \[ 2x^2 - 8x + x - 4 \]

Next, combine the like terms (\(-8x\) and \(x\)): \[ 2x^2 - 7x - 4 \]

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

This final result is indeed correct. There's only one \(x\) term combined with \( -8x\) to give \(-7x\). I appreciate your patience, and if there's any further clarification needed, feel free to ask!