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

3 answers

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

simplify -3(2x-4)

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: \[ \boxed{-6x + 12} \]