Answer:
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
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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).
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Step-by-step explanation:
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Answer: y = 
x + 1
Step-by-step explanation:
First, we will find the slope. The slope of perpendicular lines are negative reciprocals.
In this case, the first slope is 2. The negative of 2 is -2, and the reciprocal of -2 is .
Now, we will plug in this new slope, the point given, and solve for the <em>b</em>, or the y-intercept.
y = <em>m</em>x + <em>b</em>
(-1) = ()(4) + <em>b</em>
-1 = -2 + <em>b</em>
1 = <em>b</em>
Lastly, we will write our equation.
y = <em>m</em>x + <em>b</em>
y = x + 1
The line is y = x + 1, or y = 1 - 
.
