factor
1) X^2+4X-6
2) X^2-3X-28
Go to quickmath (since this won't let me post URLs, just put the w's and com on both sides of the word "quickmath").
1.
What two integers have a difference of 4 and multiply to get 6 ? none
so your first question does not factor.
2.
What two integers have a difference of 3 and multiply to get 28 ?
4 and 7
so (x-7)(x+4)
To factor a quadratic equation like these, we need to break them down into two binomial expressions. Let's go through each equation to find their factors.
1) X^2+4X-6:
To factor this equation, we are looking for two numbers that multiply to give -6 and add up to 4. The factors of -6 are:
1 * -6 = -6
2 * -3 = -6
-1 * 6 = -6
-2 * 3 = -6
Now, we need to find which combination of these factors adds up to 4. From the options above, we can see that 2 and -3 add up to 4. So, we can rewrite the equation as:
X^2 + 2X - 3X - 6
Now, we factor by grouping:
(X^2 + 2X) - (3X + 6)
X(X + 2) - 3(X + 2)
Notice that (X + 2) appears in both terms. We can factor this out:
(X + 2)(X - 3)
Therefore, the factored form of the equation X^2+4X-6 is (X + 2)(X - 3).
2) X^2-3X-28:
In this equation, we need to find two numbers that multiply to -28 and add up to -3. The factors of -28 are:
1 * -28 = -28
2 * -14 = -28
-1 * 28 = -28
-2 * 14 = -28
4 * -7 = -28
-4 * 7 = -28
By checking the combinations, we can see that -4 and 7 add up to -3. So, we can rewrite the equation as:
X^2 - 4X + 7X - 28
Now, we factor by grouping:
(X^2 - 4X) + (7X - 28)
X(X - 4) + 7(X - 4)
Again, we have a common factor, (X - 4):
(X - 4)(X + 7)
The factored form of the equation X^2-3X-28 is (X - 4)(X + 7).