Simple Trinomials

Another of factoring polynomials is called "Simple Trinomials". ( x^2 + bx+ c)

trinomial which starts which starts with a coefficient of 1. ( where the a= 1)

Many Polynomials , such as x^2+ 5x+6 can be written as the product of two binomials of the form (x + r) and (x + s).

Factored Form: y = a(x-r) (x-5) *Expand and simplify to turn the factored form to standard form.

Standard Form : y = ax^2+ bx+ c

x^2 + 5x+6

a b c

value value value

Now you have two number that are multiplied to get the "c" value. However, the two numbers have to add up to the "b" value.

factor of 6:

1, 2,3, 6.

-2 + -3 = 5

-2 x -3 = 6

You put the following numbers in bracket.

like (x - 2) (x- 3)

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Another tough example; n^2 - 10n + 16

Factors of 16: 1, 2, 4,8,16.

Find two number that add up to -10 but multiply to 16.

-2 x -8 = 16

-2 + -8 = -10

To factor these trinomials, use a table to help you until you become familiar with the procedure.

To factor, you must break up the middle x term with the factors.

BUT REMEMBER ALWAYS CHECK YOUR WORK!

Example 1) The height of a rock thrown from a walkway over a lagoon can be approximated by the formula h = -5t^2+ 20t + 60, where the t is the time, in seconds, and h is height, in meters.

a) h = -5t^2+ 20t + 60

Common factor.

= -5 (t^2 + 4t - 12)

= -5 (t-2 ) ( t+6 )

b) 0= h = -5 ( t-2) (t+6)

t-2= 0

t = 2 seconds

Therefore, it took 2 seconds for the rock to hit the ground.