Can someone please teach me how to do this? (its about ALgebra1)?

Question

Factor each polynomial completely. The first 6 are perfect squares.

1) 4x^2+12x+9

2) 9x^2-30+25

3) 4x^2-20x+25

4) 16^2-72x+81

5) 16^2+8x+1

6) 25x^2+40x+16

7) 2m^2+9m+7

8) 5x^2-3x-2

9) 3m^2+17m+10



THank you so much

Answer 1

To factor known perfect square trinomials :
root first factor ; root last factor; place roots in parentheses with sign of middle term between them; repeat, OR use ^2 at the end.

The first one is root 4, root 9, sign + :: so it's (4x + 3) (4x +3) OR (4x + 3)^2

Second one is root 9, root 25, sign - :: so it's (3x - 5)^2

You do 3 through 6 the same way.

7) You must find factors of 2 and factors of 7, and try combos of them until you get two pairs to work. 2 * 7 + 1 * 1 is too big. So switch them around, and 2 * 1 + 1 * 7 works. This one factors to (2m + 7) (m + 1)

8) Same as above, but factors of 5 and 2. But this time they must be different signs (one + and one -) to work. Try 5 * -1 + 1 * 2, and these work, to get (5x + 2) (x - 1)

9) Same as above, but more factors involved, since 10 has more than two factors. But trying them in pairs, you can find 3 * 5 + 1 * 2 will work, to get (3m + 2) (m + 5)

Answer 2

I don't like dealing with a value other then 1 for a, so I will divide and then try to factor without using the quadratic formula.

4(x²+3x+2.25)
ok what adds up to 3 and multiplies to 2.25?
1.5+1.5=3 1.5 * 1.5=2.25
so
4(x+1.5)(x+1.5)
now you can put that 4 back in giving you
(4x+6)(x+1.5)

2)
like the first one, I'mm going to divide by 9 giving me
9(x²-3.33_x+2.77_)
ok well I don't have enough time to finish this.

Answer 3

Use this formula, [-b+/- sqrt of (b^2-4ac)]/2a
Just plug in your values. It would take too much time for me to do all 9

Answer 4

the link where you can find how to do that:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm

Answer 5

(2x+3)(2x+3)
(3x-5)(3x-5)
(2x-5)(2x-5)
(4x-9)(4x-9)
(4x+1)(4x+1)
5x+4)(5x+4)
(2m+7(m+1)
(5x+2)(x-1)
(3m+2)(m+5)