help with algebra please?

Question

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Answer 1

On problem 5

4X^2 + 5x - 6

Look at your factors for a & c.
4 has factors 1*4 and 2*2
6 has factors 1*6 and 2*3.
Now multiply the choices and find differences until a diff is 5.
1,4 times 1,6 gives us 1-24 = -23
1,4 times 6,1 gives us 6-4 = 2
1,4 times 2,3 gives us 2-12 = -10
1,4 times 3,2 gives us 3-8 = -5..... (yea!!)

Use those values in your answer 1,4 and 3,2 such that the 3 is multiplied by 1x and 2 is by the 4x.

(4x-3)(x+2)
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On problem 7,
9X^2 +12X + 4
Note that we have positive signs on b & c.

Factors of 9 are 1,9 and 3,3
factor of 4 are 1,4 and 2,2
Now multiply the factors and find when the SUM is 12.
1,9 times 1,4 leads to 1 + 36 = 37
1,9 times 4,1 leads to 4 + 9 = 13
3,3 times 1,4 leads to 3 + 12 = 15
1,9 times 2,2 leads to 2 + 18 = 20
3,3 times 2,2 leads to 6 + 6 = 12 (yea!!)

(3X + 2)(3X + 2)

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On problem 9,
12X^2 - 24X - 9

we have a negative c again so we will find differences between factor products until finding 24.

12 factors into 1,12.....2,6.... and 3,4
9 factors into 1,9 and 3,3

1,12 times 1,9 leads to 1 - 108 = -107
1,12 times 9,1 leads to 9 - 12 = -3
1,12 times 3,3 leads to 3 - 36 = -33
2,6 times 1,9 leads to 2 - 54 = -52
2,6 times 9,1 leads to 18 - 6 = 12
2,6 times 3,3 leads to 6 - 18 = -12
3,4 times 1,9 leads to 3 - 36 = -33
3,4 times 9,1 leads to 27 - 4 = 23
3,4 times 3,3 leads to 9 - 12 = -3

rats. no solution

Answer 2

For #4, note that the coeff of x^2 is 2 which is prime,

Thus (2x )(x )

Now work the other end, the constant...the negative sign with the linear (x) term means that both factors are negative
(2x - 1)(x - 1 )


Check the quadratic formula's discriminant
b^2-4ac = 25-4(2)(1) = 25-8 = 17, so that's ok

solutions: -5/4 +/- 1/4sqrt(17),
= -.22, -2.28

Check: root 1 ok, root 2 ok

So, it has roots but they are not in a convenient form that allows for easy factoring.

My recommendation is to check to discriminant to see if it can be factored and if the roots will be in a convenient form. The above example has a square root of 17, not very nice.

Answer 3

use the ac method on all of them

multiply the 1st number (a, the one beside the x^2) by the last number, the constant. find factors of the resulting number which add to the middle number, and then factor.

for example, number 7:

9x^2+12x+4

ac=36

36=2x3x2x3

6x6=36

6+6=12

so,

9x^2+6x+6x+4

factor,

3x(3x+2)+2(3x+2)

Answer: (3x+2)(3x+2)