Question

integrated math 2: unit 3, lesson 7
cool - down: the missing numbers
here are pairs of equivalent expressions—one in standard form and the other in factored form. find the missing numbers.

1. (x^{2}+square x+square) and ((x + 1)(x + 17))

Explanation:

Step1: Expand the factored form

To expand \((x + 1)(x + 17)\), we use the distributive property (FOIL method).
First, multiply the First terms: \(x\times x=x^{2}\).
Then, the Outer terms: \(x\times17 = 17x\).
Next, the Inner terms: \(1\times x=x\).
Finally, the Last terms: \(1\times17 = 17\).
Now, combine like terms: \(x^{2}+17x+x + 17=x^{2}+(17 + 1)x+17=x^{2}+18x + 17\).

Step2: Identify the missing numbers

Comparing with \(x^{2}+\square x+\square\), the coefficient of \(x\) is \(18\) and the constant term is \(17\).

Answer:

The first missing number (coefficient of \(x\)) is \(18\) and the second missing number (constant term) is \(17\). So the expression is \(x^{2}+18x + 17\).