Johanna's Responses in WyzAnt Answers

When factoring trinomials that are in the form of ax²⁺bx+c=0 these are the steps you will need to take:

1. See if the coeffiecients a, b, and c all have any common factors that you can factor out.

For example, the coeffiecients of 2x²+12x+6=0 all have a common factor of 2, so you can factor the 2 out to get:

2(x²+6x+3)=0.

In the case of 8x²+2x-3=0, we cannot factor anything out since 8, 2, and -3 have no common factors.

2. Multiply a*c and list out all of the factor pairs of the product.

In this case a=8 and c=-3, so a*c=-24. The factor pairs of 24 are: -1 and 24, 1 and -24, -2 and 12, 2 and -12, -3 and 8, 3 and -8, -4 and 6, and 4 and -6.

3. Find which pair of factors' sum is equal to b.

In this case b=2. So we want the pair of factors' sum to equal (positive) +2. If we choose the pair -4 and 6, and add them to eachother, we get -4+6= 2. So this is the pair of factors we will need to use.

4. In the original equation, write bx in terms of the sums of the factors you chose.

In this case 2x=-4x+6x. So we will write the original equation as:

8x²-4x+6x-3=0.

5. Group the first two terms together in a set of paranthesis, and the second two terms together in a set of separate paranthesis and factor out the greatest common factors for each set of paranthesis.

(8x²-4x)+(6x-3)=0

4x(2x-1)+3(2x-1)=0     Whatever is left inside of the paranthesis should be equal to eachother, so if your paranthesis do not match you know that you did something wrong. In this case we have 2x-1 in both of our paranthesis so we know we are on the right track.

6. Add the terms that you factored out of the paranthesis and multiply by the paranthesis that has a match.

So we have (4x+3)(2x-1)=0. This is the factored form of your trinomial.

7. To solve the trinomial, set each paranthesis equal to 0 and solve for x.

So,

4x+3=0

4x=-3

x=-3/4

and

2x-1=0

2x=1

x=1/2

So your final answer is x=-3/4 and x=1/2.

 

 

The function f(x)=mx+b is in slope-intercept form. Where m = slope and b = the y intercept. When you are given a point in the form (0, y), this is your y-intercept and y = b in the slope-intercept equation. So in this case f(x)=(-11/7)x-7.

Since Jessie can weed a garden in 30 minutes, her rate is 1/j of the garden per minute, which equals 1/30th of the garden per minute. Norton's rate is 1/n of the garden per minute. Working together, their rate is:

(1/j)+(1/n)=(1/20) of the garden per minute

(1/30)+(1/n)=(1/20) of the garden per minute

We want to solve for n so subtract 1/30 from boths sides:

(1/n)=(3/60)-(2/60) of the garden per minute

(1/n)=(1/60) of the garden per minute

So since Norton's rate is 1/n which equals 1/60, this means that he can weed 1/60th of the garden per minute. Which means that it would take him 60 minutes, or 1 hour, to finish the garden by himself.

To determine the "steepness" of a graph, you need to look at the absolute value of slope of the graph. All these equations are in slope-intercept form, y=mx+b, where m is the slope. So the slopes we have are 1/2, 10, 4, and -3/4. The absolute values of these slopes are 1/2, 10, 4, and 3/4. The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2. So the equation with the least steep graph would be y=1/2x+2. You can confirm this by graphing all four equations.

First you'll want to see if each term in the polynomial has any common factors, in this case 63 and 7 both have a common factor of 7, since 63 = 9*7 and 7 = 1*7. So we factor out their greatest common factor, which in this case is 7:

63v²-7 =

7(9v²-1)

Can we factor (9v²-1) any more? Well, we can't factor it by trying to pull out greatest common factors from each term, since 9 and 1 do not share any factors greater than 1. But it can actually be factored in a different way...

9v²-1 is in a special kind of form, that requires a special kind of factoring called "Differences of Squares."

(a²-b²) = (a - b)(a + b)

We can use this formula for 9v²-1 since 9v² is the sqaure of 3v and 1 is the square of 1. So we write:

7(9v²-1) =

7(3v-1)(3v+1)

Which is your final answer since it cannot be factored any further.