factorising quadratic expressions 1
DESCRIPTION
Factorising quadratic expressions by inspsection with quadratic coefficient equal to 1TRANSCRIPT
Factorise the following expressions:
6 y2 5y =
9 a3 3 a2 =
x2 + xy + 3 x z =
x2 + 5 x + 6 =
x2 + 5 x + 6
This expression is called a quadratic expression because the highest power of any of its terms is 2.
Factorising quadratic expressions
By the end of the lesson you will be able to:
• Factorise quadratic expressions of the form x2 + bx + c .
Expand and simplify the following:
(x+2) ( x+3) =
(x+4) ( x 5) =
(x 6) ( x+3) =
(x+5) ( x 2) =
(x 5) ( x 3) =
(x+4) ( x+5) =
Do you observe any pattern?
Expand and simplify the following:
(x+2) ( x+3) = x2 + 5 x + 6
(x+4) ( x 5) = x2 x 20
(x 6) ( x+3) = x2 3 x 18
(x+5) ( x 2) = x2 + 3 x 10
(x 5) ( x 3) = x2 8 x + 15
(x+4) ( x+5) = x2 + 9 x + 20
Do you observe any pattern?
(x+2) ( x+3) = x2 + 5 x +6
(x+4) ( x+5) = x2 + 9 x + 20
(x 6) ( x+3) = x2 3 x 18
(x+2) ( x+3) = x2 + 5 x +6 2 x 3
2 + 3
4 x 5
(x+4) ( x+5) = x2 + 9 x + 20
4+ 5
(x 6) ( x+3) = x2 3 x 18
6 x 36+ 3
(x + 4) ( x 5) = x2 x 20
(x+5) ( x 2) = x2 + 3 x 10
(x 5) ( x 3) = x2 8 x + 15
( x + 3 ) ( x + 2 ) = x2 + 5 x + 6
Expand
Factorise
Therefore,
(x +2 ) ( x + 3) x2 + 5 x + 6 =product : 6sum: 5
x2 + 7 x + 12 = ( x ) ( x )
product : 12sum: 7
x2 + 4x 12 = ( x ) ( x )
product : 12sum: 4
two numbers such that:
two numbers such that:
x2 6x + 8 = ( ) ( )product : sum:
x2 + 8 x + 15 = ( ) ( )product : sum:
x2 12 x + 20 = ( ) ( )product : sum:
x2 9 x 36 = ( ) ( )product : sum:
Solve worksheet "Factorisation of quadratics "
Extrapractice: Book Ex. 6.10 : 1 to 5
http://www.mathsbingo.com/FactoringQuadraticTrinomials.html
worksheets to print
Expand and simplify the following:
(x+2) ( x+3) =
(x+4) ( x 5) =
(x 6) ( x+3) =
(x+5) ( x 2) =
(x 5) ( x 3) =
(x+4) ( x+5) =
Do you observe any pattern?
(x+2) ( x+3) = x2 + 5 x +6
(x+4) ( x+5) = x2 + 9 x + 20
(x 6) ( x+3) = x2 3 x 18
(x + 4) ( x 5) = x2 x 20
(x+5) ( x 2) = x2 + 3 x 10
(x 5) ( x 3) = x2 8 x + 15
Therefore,
(x +2 ) ( x + 3) x2 + 5 x + 6 =product : 6sum: 5
x2 + 7 x + 12 = ( x ) ( x )
product : 12sum: 7
x2 + 4x 12 = ( x ) ( x )
product : 12sum: 4
two numbers such that:
two numbers such that:
x2 6x + 8 = ( ) ( )product : sum:
x2 + 8 x + 15 = ( ) ( )product : sum:
x2 12 x + 20 = ( ) ( )product : sum:
x2 9 x 36 = ( ) ( x )product : sum: