Expand the expression to a polynomial in standard form:

Question

left parenthesis, x, minus, 9, right parenthesis, left parenthesis, x, squared, plus, x, plus, 2, right parenthesis
(x−9)(x
2
+x+2)
Answer

Answer 1

To expand the expression \((x - 9)(x^2 + x + 2)\), we will use the distributive property (often called the FOIL method for binomials).

1. Distribute \(x\) across the second polynomial: \[ x \cdot (x^2) + x \cdot (x) + x \cdot (2) = x^3 + x^2 + 2x \]

2. Distribute \(-9\) across the second polynomial: \[ -9 \cdot (x^2) + (-9) \cdot (x) + (-9) \cdot (2) = -9x^2 - 9x - 18 \]

3. Now combine all the terms from both distributions: \[ x^3 + x^2 + 2x - 9x^2 - 9x - 18 \]

4. Combine like terms:

   • The \(x^2\) terms: \(x^2 - 9x^2 = -8x^2\)
   • The \(x\) terms: \(2x - 9x = -7x\)

Putting it all together, we have: \[ x^3 - 8x^2 - 7x - 18 \]

So, the polynomial in standard form is: \[ \boxed{x^3 - 8x^2 - 7x - 18} \]