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

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

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

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!

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

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!

then don't simplify please

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!