can someone show me how to factor this: i keep getting -6 and 5
but i want to factor:
x^2+7x+6
x^2+7x+6 = (x+1)(x+6)
This means the roots of
x^2+7x+6 = 0 ar -1 and -6
duhhhhh...i was thinking completely wrong..thank you
75
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To factor the quadratic expression x^2 + 7x + 6, you can use the method of factoring by grouping or the quadratic formula. Here, I will explain how to factor it using the factoring by grouping method.
1. Write down the quadratic expression: x^2 + 7x + 6.
2. Find two numbers that multiply to give you the constant term (6) and add up to give you the coefficient of the linear term (7).
In this case, the two numbers are 1 and 6, because 1 * 6 = 6 and 1 + 6 = 7.
3. Split the middle term (7x) into two terms using the two numbers you found in the previous step.
x^2 + 1x + 6x + 6
4. Group the terms.
(x^2 + 1x) + (6x + 6)
5. Factor out the greatest common factor from each group.
x(x + 1) + 6(x + 1)
6. Notice that (x + 1) appears in both terms. Factor out this common binomial.
(x + 1)(x + 6)
So, the factored form of the quadratic expression x^2 + 7x + 6 is (x + 1)(x + 6).
The roots of the quadratic equation x^2 + 7x + 6 = 0 can be found by setting each factor equal to zero:
x + 1 = 0 or x + 6 = 0.
Solving these equations gives you the roots:
x = -1 or x = -6.