In biology, Punnett squares are used to show possible ways that traits can be passed from parents to their offspring.
Each parent has two genes for each trait. The letters
representing the parent’s genes are placed on the outside of the Punnett
square. The letters inside the boxes show the possible gene combinations for
their offspring.
The Punnett square at the right shows the gene combinations
for fur color in rabbits.
· G represents
the dominant gene for gray fur.
· g represents
the recessive gene for white fur.
Notice that the Punnett square is similar to the model for
multiplying binomials. The model below shows the product of (x + 1) and
(x + 3).
(x + 1)(x + 3) = x2
+ 3x + 1x + 3
= x2 + 4x + 3
In this lesson, you will factor a trinomial into the product
of two binomials.
The FOIL method will help you factor trinomials without
models. Use the following method to factor x2 + 6x + 8.
Factor each trinomial.
1.
x2 – 7x + 10
Alternative Solutions:
Find integers whose product is 10 and whose sum is 7. Recall that the product
of two negative integers is positive.
Therefore, x2 – 7x
+ 10 = (x – 2)(x – 5).
2.
x2 + 5x – 6
Alternative Solutions:
Find integers whose
product is –6 and whose sum is 5. Recall
that the product of a positive integer and a negative integer is negative
You can stop listing
factors when you find a pair that works.
Therefore, x2 + 5x – 6
= (x – 1)(x + 6)
3.
x2 – 7 – 3x
Alternative Solutions:
First,
write the trinomial as x2 – 7 – 3x.
Find two integers
whose product is –7 and whose sum is –3.
There are no factors
of –7 whose sum is –3. Therefore, x2 – 3x
– 7 is
a prime polynomial.
In the previous lesson, you learned that the terms of a
polynomial might have a GCF that can be factored using the Distributive
Property. When you factor trinomials, always check for a GCF first.
Example
4.
Factor 2x2 – 20x – 22.
Alternative Solutions:
First, check for a
GCF.
- So, 2 – 10x – 11 = (x + 1)(x – 11).
Therefore, 2x2 – 20x – 22
= 2(x + 1)(x – 11). Check
by using FOIL.
The area of a figure can often be expressed as a trinomial.
Gardening
Link
5. Tammy is planning a rectangular garden in which the width will be 4 feet
less than its length. She has decided to put a birdbath within the garden,
occupying a space 3 feet by 4 feet. How many square feet are now left for
planting? Express the answer in factored form.
Alternative Solutions:
Let l
= the length of the original rectangle.
Let l
– 4 = the width of the original rectangle.
Find
the area of the original rectangle.
Find
the area of the small rectangle.
A =
4(3) or 12
Remaining
= area area of original rectangle – area of small rectangle
= (l2
– 4l) – 12
The
remaining area is l2 – 4l –
12 or (l – 6)(l + 2).
Sumber
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