Of the Form ax 2 + bx + c where a > 1
 Students will be able to factor trinomials of the form
ax2+bx+c, where a > 1
 Illinois Standard 8.D.4 Formulate and solve linear and
quadratic equations and linear inequalities
algebraically and investigate nonlinear inequalities
using graphs, tables, calculators and computers.
 Fact: ax2+bx+c = (x + h)(x + k)
 This is called the generalized form
 Click here to listen to the correct way to read this equation
(x + 1)(2x + 3)
 F: X times 2x is?
2x2
 O: X times 3 is?
+
+
3x

I: 1 times 2x is?
2x

+
5x
L: 1 times 3 is?
3
Final Answer
2x2 + 5x + 3
+
 Remember: multipy to C and add to B
x2+bx+c
 x2+ 4x+3 = ?
(x+3)(x+1)
 B&C>0
o d2 + 9d + 20
o t2 + 12t +32
o x2 + 20x +100
 Ax2+Bx+C
 Use FOIL
 Find factors
 Find two First terms whose product equals A (a1·a2)
 Find two Last terms whose product equals C (c1·c2)
 The sum of the resulting products must equal B
 (a1x + c1)(a2x + c2)
 a1*c2 + a2*c1 = B
Outer Inner
Ax2+Bx+C
20 problems of mixed factoring practice: some
with the coefficient A being 1, some with A being
greater than 1
 For next class, see if you can solve the generalized form of
the quadratic equation for “x”
 Remember the generalized form is
“ax2 + bx + c = 0”
 Hint: You will need to complete the square, take square
roots, and simplify 
Click to watch the video and think about the shape of the path of
the ball, and compare it to the shape of a graph of a quadratic
equation.
 This game is challenging, even somewhat for me! It
will increase your speed in each form of factoring
we’ve learned. Good luck, and save those ships!