Kevin's Responses in WyzAnt Answers

For the first two, find a common factor. In the first, pull a 7 out:

7(d² - 2d - 3) = 0 . Now factor and solve. 

For the third, distribute across the parentheses, gather like terms, and set equal to zero. If there are any common factors, pull them out and factor what is left:

6c(c - 4) = 2 (18c + 168)

6c² - 24c = 36c + 336

6c² - 60c - 336 = 0

6(c² - 10 c - 56) = 0

The rest is left to the student. 

A line that is perpendicular will have a slope that is the negative reciprocal of the slope of a given line. For example, if the slope of a line was 3, then the perpendicular line would have slope -1/3

Given x - y = 3, let's get this into slope-intercept form y = mx + b

-y = -x + 3   (now divide by -1)

y = x - 3

So our slope is 1. Therefore, the slope of our perpendicular line is -1/1 = -1

Factors of 25 are 1 * 25, 5 * 5

Factors of 12 are 1 * 12, 2 * 6, 3 * 4

Since we're looking for two values that, when the  difference of the products is 5, I'm thinking we need values close together... So I'm going to look at 5*5 and 3 * 4:

(3x + 5)(4x - 5)

Since the constant is -25, i knew that one of my signs was going to be negative.  Since the linear term (5x) was positive, I knew my larger product was going to be positive. 

5 * 4x - 5 * 3x = 20x - 15x = 5x.

One method is "long division" . Using this method, you compare the leading terms of your numerator and denominator. 

How many times does x (from x + 2) go into 4x³ ? 4x² times (x * 4x² = 4x³). So we also multiply the 2 (from x + 2) by 4x² (to get 8x²), and now we subtract it from our numerator, and we are left with (-x-2)/(x + 2)

Now, how many times does x go into -x ? -1 times. Multiply and subtract:

-x - 2 - (-1)(x + 2) = 0 

So our result is 4x² - 1

__4x² ______   -1  _________________

x + 2      | 4x³ + 8x² - x - 2

4x³ + 8x²
---------------------

-x - 2
-x - 2

--------

      0

When finding the LCD, it is often helpful to factor the denominators, then see what you have:

In the first problem, our denominators are

x² - 12x + 35     and x - 7

x² - 12x + 35  factors into (x - 5)(x - 7). 

So your LCD is (x - 5)(x - 7)

So, multiply the second term by (x-5)/(x-5) to get your new fractions:

17/[(x - 5)(x - 7)] - [6(x - 5)]/[(x - 5)(x - 7)]

simplify the second numerator and rewrite:

[17 - 6x +30]/[(x - 5)(x - 7)] = [ -6x + 47]/[(x - 5)(x - 7)]

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For the second one, approach the LCD the same way. You'll just wind up with three factors in the denominator as opposed to two

For the third, you've got a good start. Now factor 7 from (7c + 49) and factor (c² - 49) and I think you'll see terms that you can reduce.