Can some one explain these to me i need the factors. i am totally lost.
thanks
x^2+x-6
x^2+7x+10
x^2+5x+6
x^2+2xy+15y^2
(x+a)(x+b)
FOIL
x^2 + ax + bx + ab which can be simplified into
x^2 + (a+b)x + ab
Use this as a base for all of the your equations.
Lets do the first one.
ab will be the same as the last term which is -6. Then look at the second term which is x. In this case there is nothing in front of x. However x is the same as 1 times x since 1 times anything is the same. Look back to the equation I gave you.
(a+b)x will be equal to 1x which is equal to x. Therefore, a+b has to equal to 1 and we know ab is equal to -6. List all the two pairs of whole numbers whose product is 6.
1 6
2 3
Since 6 is negative it means one of them has to be negative
-1 6
1 -6
-2 3
2 -3
(a+b) = 1
The only pair of numbers above that add up to 1 is 3 and -2. So just let a = 3 and b = -2.
(x+a)(x+b)
(x+3)(x-2)
And there you go. Sorry, if you still don't understand, I know I'm far from being an expert on explaining stuff.
x^2+7x+10
x^2+(a+b)x+ab
ab = 10
a+b = 7
Pairs whose product is 10.
1 10
2 5
Then only pair that add up to 7 is 2 and 5. So let a = 2 and b = 5.
(x+a)(x+b)
(x+2)(x+5)
-----------------------------
x^2+5x+6
x^2+(a+b)x+ab
ab = 6
a+b = 5
Pairs whose product is 6
1 6
2 3
Then the only pair that adds up to 5 is 2 and 3. So let a = 2 and b = 3.
(x+a)(x+b)
(x+2)(x+3)
-----------------------------
The last one is complicated... and it involves material that you may not have learned yet if you just started factors. Are you sure it is correct?
Of course! I can help explain how to find the factors for these expressions.
To find the factors of a quadratic expression like the ones you mentioned, we can factorize them. Factoring an expression means writing it as a product of simpler expressions.
1. x^2 + x - 6:
To factorize this expression, we need to find two numbers that multiply to -6 and add up to +1 (coefficient of x). The numbers that satisfy these conditions are +3 and -2. Therefore, we can write the expression as (x + 3)(x - 2).
2. x^2 + 7x + 10:
For this expression, we need to find two numbers that multiply to 10 and add up to 7. The numbers that satisfy these conditions are +5 and +2. Thus, we can factorize the expression as (x + 5)(x + 2).
3. x^2 + 5x + 6:
Similarly, we need to find two numbers that multiply to 6 and add up to 5. The numbers that satisfy these conditions are +3 and +2. Therefore, we can factorize the expression as (x + 3)(x + 2).
4. x^2 + 2xy + 15y^2:
This expression has two variables, x and y. However, it cannot be factored further using real numbers unless there is more information provided or a specific factorization technique is applied. If you are looking for a specific factorization method, please let me know.
Remember, there are different methods to factorize expressions depending on their forms. These examples use the simple factorization method, but there are other techniques like factoring by grouping, quadratic formula, or completing the square that can be used for more complex expressions.
I hope this explanation helps you understand how to find the factors of these quadratic expressions! Let me know if you have any further questions.