x²-2x-6x+16
Combine the two middle terms:
x²-8x+16
Make sure the trinomial is in descending order
---------------------------------------------
x²-8x+16
1. Make a 4-square box
---------------------------------------------
x²-8x+16
2. Put the first term in the upper left box:
Put the last term in the lower right box:
---------------------------------------------
x²-8x+16
3. Multiply their coefficients (ignoring signs): (1)(16) = 16
Factor the product into all factor pairs:
16
/\
16 1
8 2
4 4
---------------------------------------------
x²-8x+16
4. Add each set of factor pairs, since last term is positive.
(We would subtract them if the last term were negative)
16
/\
16 1 16+1=17
8 2 8+2=10
4 4 4+4=8
x²-8x+16
---------------------------------------------
x²-8x+16
5. Match the absolute value of the middle term coefficient with
the same term
That's 8.
16
/\
16 1 16+1=17
8 2 8+2=10
4 4 4+4=8
---------------------------------------------
x²-8x+16
6. Put one of the factors in the upper right box and put an x after it,
(or whatever the variable letter happens to be)
Put the other factor in the lower left box and put an x after it,
(or whatever the variable letter happens to be)
They're both 4, so put 4x in both boxes:
---------------------------------------------
x²-8x+16
7. Give the larger of those two the same sign as the middle term.
If the last term is positive, give the smaller the same sign.
If the last term is negative, give the smaller the opposite sign.
They're both the same, so pick one and give it a - sign, since
the middle term's sign is -. Give the other one a - sign also, since
the last term is +.
---------------------------------------------
8. Put the GCF of the top row to the left of the top row.
Put the GCF of the bottom row to the left of the bottom row.
If the bottom row begins with a -, give the GCF a -
Put the GCF of the left column above the left column.
Put the GCF of the right column above the right column.
If the right column begins with a -, give the GCF a -,
---------------------------------------------
9. Use the factors outside to make two binomials:
(x-4)(x-4)
That's it. However since they are the same binomial, write just one
of them squared:
Answer: (x-4)²
Edwin
