FOIL
CONCEPTS
Definitions
• FOIL stands for first outers, inner lasts
Forms
• Standard form of a polynomial equation: ax² + bx + c = 0
• Factored form: (x + a)(x + b) = 0
Use FOIL to go from factored form to standard form of a polynomial equation
FOIL Calculation
• (ax + b)(cx + d) = acx² + bcx + adx + bd
• Typically, the bc & ad terms can be combined, but not always
PRACTICE PROBLEMS
Question 1 Create a polynomial equation for (x + 3)(x - 2)
-- Answer -- x² – 2 * 3
(x + 3)(x – 2) = x² – 2 * 3
Question 2 Create a polynomial equation for (x + √2)(x - √7)
-- Answer -- x² + √14 + √2x – √7x
(x + √2)(x – √7) = x² + √2*√7 + √2x – √7x = x² + √14 + √2x – √7x
Question 3 Create a polynomial equation for (x - 2)²
-- Answer -- x² – 4x – 4
(x – 2)² = (x – 2)(x – 2) = x2 + (–2)(–2) + (–2)(x) + (–2)(x) = x² – 4x – 4
ACT PRACTICE PROBLEMS
