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

Answer 1

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).

\[ (2x + 1)(x - 4) = 2x \cdot x + 2x \cdot (-4) + 1 \cdot x + 1 \cdot (-4) \]

Now, we compute each term:

1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot (-4) = -8x\)
3. \(1 \cdot x = x\)
4. \(1 \cdot (-4) = -4\)

Now we can combine all these terms:

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

Combine like terms:

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

Thus, the product of the polynomials is:

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

So the coefficients in the form \( ( )x^2 + ( )x + ( ) \) are:

• Coefficient of \(x^2\) is \(2\)
• Coefficient of \(x\) is \(-7\)
• Constant term is \(-4\)

Final answer: \( (2)x^2 + (-7)x + (-4) \)