Factor x^2-6x+9 <<< Need Help?

2 answers:

8 0

Hey!!
So to factor it, you want to see what 2 numbers will multiply and make 9 and what 2 numbers will add and make -6.
so 9 and 1 and -9 and -1 make 9 but they dont make -6.
3 and 3 and -3 and -3 make 9, but we need to see which one makes -6. that would be -3 and -3
so the answer is (x-3)(x-3)

you can foil to make sure.
x * x is x^2
-3*x=-3x
-3*x=-3x
-3x-3x = -6x
-3*-3 is 9
so it is x^2-6x+9 which makes the original equation

Hope this helps!

Inga [223]3 years ago

5 0

X² - 6x + 9 =
(x - 3)(x - 3) or (x - 3)²

The factors would be (x - 3) and (x - 3).

If you need help factoring, you should talk to your teacher, but here's how I do it:

1. Look at the first term and its coefficient. Think of two possible numbers that would multiply to get the first term (i.e. 3x and 2x for 6x²) and put them first in the parentheses. You can also write all possible combinations on the side. However, this time, the only combination would be x and x multiplying to get x².

(x )(x )

2. Next, look at the last term. What two numbers multiply to get 9? Remember that two negative numbers can multiply to produce a positive one too. Basically, you're looking for two numbers that multiply to get 9 and add together to get -6. You might try all of the possible combinations, but none will work. In that case, you would go back to step 1 and try a different first term. In this case, though, there's only one combination for the first places, so that won't be necessary.

(x - 3)(x - 3)

Let me know if you have any more questions.

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What is the sequence of transformations that maps △ABC to △A′B′C′ ? Select from the drop-down menus to correctly identify each s

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<h3>Answer:</h3>

Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).

<h3>Step-by-step explanation:</h3>

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is <em>a sequence of transformations</em> involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

We have described transformations that will work. What we don't know is what is in your drop-down menu lists. There are many other transformations that will also work, so guessing the one you have available is difficult.