Questions: Multiply the polynomials using the distributive property and combine like terms. (-x-6)(2x-1)

Transcript text: Question 9 of 11, Step 1 of 1 8/11 Correct Multiply the polynomials using the distributive property and combine like terms. \[ (-x-6)(2 x-1) \] Answer

Solution

Solution Steps

Step 1: Define the Polynomials

We start with the polynomials given in the problem: \[ P_1 = -x - 6 \] \[ P_2 = 2x - 1 \]

Step 2: Apply the Distributive Property

We will multiply the two polynomials using the distributive property: \[ P_1 \cdot P_2 = (-x - 6)(2x - 1) \]

Step 3: Expand the Expression

Using the distributive property, we expand the expression: \[ (-x)(2x) + (-x)(-1) + (-6)(2x) + (-6)(-1) \] This simplifies to: \[ -2x^2 + x - 12 + 6 \]

Step 4: Combine Like Terms

Now, we combine the like terms: \[ -2x^2 + (1 - 12 + 6) = -2x^2 - 11x + 6 \]

Final Result

The result of multiplying the polynomials \((-x-6)(2x-1)\) is: \[ -2x^2 - 11x + 6 \]