Question

Complete the product expression by filling in the missing values (indicated by the boxes) to make a true multiplication statement. Explain your process and reasoning. x2+2x-8x2+9x+20x2+❐x+❐x2+❐x+❐=x-1x+5

Answer 1

To complete the product expression, we group the terms with x and x^2 together and compare the coefficients of the x terms. From this comparison, we can determine the missing values. The missing values are -10, -10, and -15.

Step-by-step explanation:

To complete the product expression, we need to fill in the missing values. The given expression is:

x^2 + 2x - 8x^2 + 9x + 20x^2 + ■x + ■x^2 + ■x + ■ = x - 1x + 5

Let's group the terms with x and x^2 together:

(-8x^2 + 20x^2 + x^2) + (2x + 9x + ■x + ■x) + (■) = x - 1x + 5

Simplifying, we get:

13x^2 + (11 + ■ + ■)x + ■ = x - 1x + 5

Now, let's compare the coefficients of the x terms:

11 + ■ + ■ = 1 - 1

From this equation, we can conclude that:

■ = -10

Substituting this value back into the equation, we can solve for the remaining missing values:

13x^2 + (11 - 10 - 10)x + (-10) = x - 1x + 5

13x^2 - 9x - 10 = x - 1x + 5

Combining like terms, we get:

13x^2 - 10x - 15 = 0

So, the missing values are -10, -10, and -15.