Solve the equation by factoring: x2 − 7x + 12 = 0

x = 3 . . . or . . . x = 4

Step-by-step explanation:

The factored form is ...

(x -3)(x -4) = 0

The zero product rule tells you the solutions are the values of x that make the factors be zero:

x = 3

x = 4

Comment on factoring

When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:

(x +a)(x +b) = x^2 +(a+b)x + ab

What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.

12 = -1×-12 = -2×-6 = -3×-4

The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...

(x -3)(x -4) = 0

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If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).

if he has no friends he cant give them out to his friends

step-by-step explanation:

no friends = cant give anything out

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.