Factor the following polynomials completely. How do you???
First question? 8x-4
Find the equation of the line that is perpendicular to 2x-y=3, and passes through the point (-4,1)
The answer is -1/2x-1 ///how do you work it out to get the answer???
8x - 4
= 4(2x-1)
2nd question:
slope of given line is 2, so the slope of the new line is -1/2
new equation:
y = mx + b
1 = (-1/2)(-4) + b
1 = 2 + b
b = -1
so y = (-1/2)x -1 is the new equation.
(if their answer was -1/2x-1, then they used quite improper mathematical form)
Furthermore, I am curious.
Since you did not know how to factor such a fundamentally easy common factor question as your first question, how can you possibly handle the second type of question ?
Thanks, Oh o.k.
To factor the polynomial 8x - 4 completely, you can follow these steps:
Step 1: Look for a common factor (if any) among all the terms. In this case, both terms have a common factor of 4. So, we can factor out 4 from both terms:
4(2x - 1)
Step 2: Now, you have a binomial (2x - 1). This binomial cannot be factored further, so the factored form of the polynomial is:
4(2x - 1)
Now, let's move on to the second question.
To find the equation of the line that is perpendicular to 2x - y = 3 and passes through the point (-4,1), you can use the following steps:
Step 1: Find the slope of the given line. The slope-intercept form of a line is y = mx + c, where m represents the slope. To find the slope, rearrange the given equation in slope-intercept form (y = mx + c):
2x - y = 3
-y = -2x + 3
y = 2x - 3
From this equation, we can see that the slope of the given line is 2.
Step 2: Find the perpendicular slope by taking the negative reciprocal of the given slope. So, the perpendicular slope, m_perpendicular, would be -1/2.
Step 3: Use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line passing through the point (-4,1) with the perpendicular slope:
y - 1 = -1/2(x - (-4))
y - 1 = -1/2(x + 4)
y - 1 = -1/2x - 2
y = -1/2x - 2 + 1
y = -1/2x - 1
Therefore, the equation of the line that is perpendicular to 2x - y = 3 and passes through the point (-4,1) is y = -1/2x - 1.