Questions: If the product of (5x-6) and (x+1) is written in standard form, what will the middle term be? -1

Solution Steps

To find the middle term of the product of \((5x - 6)\) and \((x + 1)\), we need to expand the expression using the distributive property (also known as the FOIL method for binomials). The middle term will be the sum of the products of the outer and inner terms.

We start with the expression \((5x - 6)(x + 1)\). Using the distributive property, we expand it as follows: \[ (5x - 6)(x + 1) = 5x \cdot x + 5x \cdot 1 - 6 \cdot x - 6 \cdot 1 \] This simplifies to: \[ 5x^2 + 5x - 6x - 6 \]

Next, we combine the like terms in the expanded expression: \[ 5x^2 + (5x - 6x) - 6 = 5x^2 - x - 6 \]

In the standard form \(ax^2 + bx + c\), the middle term corresponds to the coefficient of \(x\). From our expression \(5x^2 - x - 6\), the coefficient of \(x\) is \(-1\).

Final Answer