Factor the Expression....?

Question

I need help factoring these:

1. x^2 + 3x + 2
2. x^2 - x -6
3. x^2 - 7x + 10
4. x^2 + x - 12

Thanks!

Answer 1

1. (x+2)(x+1)

2. (x-3)(x+2)

3. (x-5)(x-2)

4. (x+4)(x-3)

Basically you just need to see what adds to the middle term, and multiples to the product of term 'a' and term 'c'.

E.g. You had x^2-7x+10

Well what multiplies to 10, and adds to -7? (Note, there is really a '1' in front of that x^2 term, hence 10*1=10)

The answer is -5 and -2. That is why it's written: (x-5)(x-2).

Good luck.

Answer 2

If you are having difficulty getting the factors of a quadratic formula, you can use the quadratic formula to get the roots of the equation and then from the roots you can get the factors.

Use quadratic formula: [-b ± √(b² - 4ac)] / 2a
[-b ± √(b² - 4ac)] / 2a

Take question one for example.
x² + 3x + 2
The y value for the x axis will be zero. So let the equation equal zero.
x² + 3x + 2 = 0
[-b ± √(b² - 4ac)] / 2a
[-(3) ± √(3² - 4(1)(2))] / 2(1)
[-3 ± √(9 - 8)] / 2
[-3 ± √1] / 2
[-3 ± 1] / 2
x = -4/2 or x = -2/2
x = -2 or x = -1
x + 2 = 0 or x + 1 = 0
Factors are:
(x + 2)(x + 1)

Now take the same approach for the rest of the questions.

Answer 3

1. x^2 + 3x + 2 = (x+2)(x+1)
2. x^2 - x -6= (x+2)(x-3)
3. x^2 - 7x + 10= (x-2)(x-5)
4. x^2 + x - 12= (x-3)(x+ 4)

Answer 4

1. x^2 + 3x + 2 = (x+1)(x+2)
2. x^2 - x -6 =(x-3)(x+2)
3. x^2 - 7x + 10 = (x-5)(x-2)
4. x^2 + x - 12= (x+4)(x-3)

Answer 5

1. (x+1)(x+2)
2. (x+2)(x-3)
3. (x-5)(X-2)
4. (x+4)(x-3)

Answer 6

x^2 + 3x + 2

(x + 2 )( x +1 )

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Answer 7

(x+1)(x+2)
(x-3)(x+2)
(x-5)(x-2)
(x+4)(x-3)