Solve by Factoring
Solve by Graphing & Factoring
Square Roots &
Imaginary Numbers
Imaginary Numbers
Solving
+, -, x & / with complex Numbers
100
x^2 +5x -14 =0
x=-2, 7
100
Solve by Graphing
f (x) = x2 − 6x + 8
x = -b/2a, x = 6/2 = 3 Axis of Sym = 3 32 - 6(3) + 8 = -1, 22- 6(2) + 8 = 0 Graph: Solutions are x = {2, 4}
x_|_y
2 | 0
3 | -1
100
5x2 = 90
x = +/- 3 Sq Rt 2
100
What is the GCF of
7b^2-63b+140=0
The GCF=7
100
(-12 + 3i) + (9 + 4i)
-3 +7i
200
x(x-4)=0
x={0,4}
200
Solve the trinomial ax2+ bx + c where a > 1
3h2 - 19h - 40
NOTE: When Factoring ALWAYS LOOK for GCF
NO GCF Multiply 3 x 40 and rewrite. h2 - 19h -120 Find Product of 120 that SUMS -120
-24 x 5 Divide both by 3, -24/3 = -8 & 5/3
(h -8)(h + 5/3) Rewrite as (h -8)(3h + 5)
200
8x2 - 3x = 597
x = +/- 5 Sq Rt 3
200
How many solutions does this equation have?
2x^2-7x+12=0
No real solution
200
(-8 + 6i) - (1 - 2i)
-9 + 8i
300
6x^2-11x+3=0
x={1/3, 3/2}
300
Solve the trinomial ax2+ bx + c where a > 1
20y2 -34y + 6
NOTE: ALWAYS LOOK For GCF
2 (10y2 -17y + 3)
Multiply 10 by 3 Rewrite y2 -17y + 30
Find Factors of 30 that SUM -17 -15 & -2
Divide both by 10, -15/10 & -2/10,
Simplify to -3/2 & -1/5 Solution: 2(2y -3)(5y -1)
300
Simplify sqrt -49
7i
300
Solve
9x^2+30x+25=0
x2 + 30x + 225 Find Product of 225 Sums 30
15 & 15 Divide both by 9 15/9 simplifies to 5/3
x = {-5/3}
300
(5 -2i)(2 +7i) - 2i(3i)2
10 + 35i - 4i -14i2 -2i(9i2)
10 + 35i - 4i -14(-1) - 18i3
10 + 31i + 14 - 18(-i)
24 + 49i
400
7b^2-63b=-140
b=4
b=5
400
Solve by Factoring
7x2 + 8x = x2
6x2 + 8x
2x(3x + 4)
x ={0 -4/3}
400
(3 + 5i)(3 - 5i)
9 - 25i2
9 - 25(-1)
9 + 25 =
34
400
Solve by taking the square roots.
3x^2-28=-1
x=3, x=-3
400
6i/(1 - i)
6i(1 + i)/(1 - i)(1 + i)
6i(1 + i)/(1 - i)(1 + i)
6i + 6(-1)/1 - i2
6i -6 /1 - (-1)
6i - 6/2 = 3i - 3
500
x^2+8x+16
x=-4
500
Give the vertex form and the factored form of
f(x) = x2 -12x + 35
Vertex Form f(x) = (x2 -12x ) + 35
(b/2)2 = (-6)2 , Add 36 inside & Subtract 36 outside
(x2 -12x +36) + 35 - 36, fx =(x -6)2 - 1
Factored Form fx = (x -7)(x - 5)
500
Roots are given: Write an equation that could represent the graph.
+/- 4i
x = Sqrt -16
x2 + 16 = 0
500
Find the x-intercepts (SOLVE)
3x^2-18=-25x
3x2 +25x - 18 Find Product of -54 Sums 25,
-2 & +27 Divide both by 3, -2/3 & 9
(x - 2/3)( x +9)
x={2/3, -9}
500
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