Factors or solutions where the x² coefficient > 1
CONCEPTS
Example of factors or solutions where the x² coefficient > 1 (ex: 3x² + 9x + 4)
Process for Factoring when there's a leading coefficient
• Put equation into standard form by rearranging terms so the equation = 0
• Combine like terms
• Determine if there a factor which can be divided out before factoring (ex: 2x² + 4x + 8 = 0 => divide out the factor 2, x² + 2x + 4 = 0)
• Factor the equation
1: do the x² term
2: do the constant term
3: do the linear or x term
PRACTICE PROBLEMS
Question 1 Factor 2x² - 5x - 3 = 0
-- Answer -- (2x + 1)(x – 3)
Question 2 Given potential solutions of the quadratic equation (-1/2, -4, 3, -3, 1), choose which are correct for 2x² + 7x + 3 = 0
-- Answer -- only –1/2 & –3 go into the equation and have it = 0
Plug the solutions into the equation, 2x² + 7x + 3 = 0. If the result is 0, then it is a solution.
x = –1/2: 2 (–1/2)² + 7 (–1/2) + 3 = 0
x = –4: 2 (–4)² + 7 (–4) + 3 = 7
x = 3: 2 (3)² + 7 (3) + 3 = 42
x = –3: 2 (–3)² + 7 (–3) + 3 = 0
x = 1: 2 (1)² + 7 (1) + 3 = 12
ACT PRACTICE PROBLEMS