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Factorising a Quadratic Expression

by Atlee Kalulu
(Zambia)











































Factoring a Quadratic Expression

Factoring (US) a Quadratic Expression = Factorising (UK) a Quadratic Expression

Factorise the quadratic expression shown below:

P² - 6p + 9

Comments for Factorising a Quadratic Expression

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Feb 22, 2013
Factoring
by: Staff


Answer

a quadratic expression has the form

aP² + bP + c

your expression is:

P² - 6P + 9

for your expression

a = 1

b = -6

c = 9

1. write two sets of empty parentheses.
( )( ) = P² - 6P + 9


2. consider the first term in your expression, P²
Factor P²

P * P = P²

Put one of the factors of P² in the first set of parentheses, and the other factor in the second set of parentheses.

( P )( P )

Factor the coefficient a, which is the number 1
1 * 1 = 1

Put one of the factors of 1 in the first set of parentheses, and the other factor in the second set of parentheses.

(1P )(1P )

The two factors for the expression P² - 6p + 9 will look like this:

(1P + ? )* (1P + ?? ) = P² - 6p + 9

(P + ? )* (P + ?? ) = P² - 6p + 9


To find the unknown values ? and ??:


1st Method of factoring


List all the possible factors of the coefficient "c", or 9

9 = (1) *( 9)

9 = (-1) *( -9)

9 = (3) *( 3)

9 = (-3) *( -3)


Identify the two factors of "c" whose sum = "b", or -6

-6 1 + 9

-6 (-1) + ( -9)

-6 (3) + ( 3)


-6 = (-3) + (-3)


The final answer to the problem is:

(P + ? )* (P + ?? ) = P² - 6p + 9

(P - 3 ) * (P - 3 ) = (P - 3 )² = P² - 6p + 9


2nd Method: Factoring by Grouping

P² - 6P + 9

P² - 3P - 3P + 9

P(P - 3) - 3(P - 3)

(P - 3) * (P - 3) = P² - 6P + 9


3rd Method: Factoring using the quadratic equation

P² - 6P + 9 is an expression, not an equation.

However, you can convert the expression into an equation in order to find the factors

P² - 6P + 9

aP² + bP + c

for your expression

a = 1

b = -6

c = 9

The quadratic equation:

P = [-b ± √(b² - 4ac)]/(2a)

Substitute the values for a, b, and c

P = [-(6) ± √((-6)² - 4*1*9)]/(2*1)

P = [-(6) ± √(36 - 36)]/(2)

P = [-(6) ± √(0)]/(2)

P = -(6)/(2)

P = -3

therefore, the factors are:

(P - 3) * (P - 3) = P² - 6P + 9






Thanks for writing.

Staff
www.solving-math-problems.com



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