Expanding polynomial – 1325163

# Study sheet 1- Expanding polynomial

1. Monomial to trinomial

2x(x²-10x +6x)- Monomial

a (b+ c)= ab + bc

2x³– 20 x² +6x – trinomial

• Binomial into binomial

(4x +2 ) (3x-7)

(ax+b) (cx-d)

On expanding

=acx² –axd +bcx – bd

=acx² – (ad-bc)x – bd

4x (3x-7) +2 (3x-7)

=12x² -22x -14

• Vertex form to standard form

Vertex: y= a(x-b)² +k

Standard form: y= ax²+ bx +c

Y= 2[(x+1)²] -5: Vertex form

Y= 2[(x+1) (x+1)]-5

Y= 2(x²+2x+1) -5

Y= 2x²+4x+2-5

Y= 2x² +4x-3

Standard form

4. Factored form to standard form

Y= 3 (x+3) (x+2): Factored form

Y= 3 (x² + 2x + 3x + 6)

Y= 3 (x² + 5x + 6)

Y= 3x² + 15x + 18 standard form

# Study Sheet 2: Factoring

1. Method of Common

6x² − 2x = 0

2x 3 x X x X – 2x =0

2x ( 3x -1) =0

Common: 2x

2. Y = grouping

2x²+8x+3x+12

Ist grouping (2x²+8x)

Second grouping (3x+12)

=2x(x+4) +3 (x+4)

=(x+4)(2x +3)

= 2x^2+11x+12

3.      x2 + 7x + 6 

= x2 + x + 6x + 6

               = x(x + 1) + 6(x + 1)

               = (x + 1)(x + 6)

4:- Trinomial Shortcut

8x²– 10x +3

8x²– 10x +3

x²-10x +24

(x-4) (x-6)

x=4, x=6

# Study Sheet 3: Finding the Vertex

1. F(x) = ax² +bx +c opens upward: Concave Up

F(x) = -ax² +bx +c opens downward: Concave Down

Y= 2x² -8x +5

X=- b/2a

F (b/2a)

(-b/2a, f (-b/2a))

X=-b/2a

X= -(8)/2(-2)

X=8/4

=2

Y= 2x² -8x +5

a=2, b=-8, c=5

F(2) = 2(2)2 -8 x 2 +5

Y=-3

(2, -3)

1. F(x) = ax² +bx +c

Vertex form to completing the square form

Vertex form: y= a(x-h) ² +k

Step 1:- y = ax² +bx +c

Y= 2x² – 4x +5

So move + 5 to the other side

y- 5 =2x²– 4x

Step 2:- Factor out can current leading coefficient

y- 5 = 2 (x² – 2x)

Step 3:- Create a perfect square Trinomial

y- 5 + 2

=2 (x² -2x+      )

Step 4:- Take half of the coefficient of x term inside the paarthesis square and put its value into box

y- 5 + 2      

Step 5:- Simplify y-3 =2 (x-1) ²

Step 6:- Isolate y term   y= 2(x-1)² + 3

Step 7:- Vertex form of equation

y= a (x-h)² +k

v (1,3)