Factor the following expressions using your method of choice. after factoring each expression completely, check your
answers using the distributive property. remember to always look for a gcf prior to trying any other strategies.
1. 2x^2 − x − 10
2. 6x^2 + 7x − 20
3. −4x^2 + 4x − 1
4. the area of a particular triangle can be represented by x^2 + 3 / 2 x − 9
2. what are its base and height in terms of x?

1.

2.

3.

4.

b = 2x-3 and h = x+3.

Step-by-step explanation:

1. First, we need to find two numbers that multiply together to get -10 and 2x².

For example we chose this combination:

2x² = 2x*x let's define a=2x and b=x

-10 = (-5)*2 let's define c=-5 and d=2

Now we must verify that a*d + b*c = -x (-x is the middle term of the polynomial)

2*2x + (-5)*x = 4x - 5x = -x, so these values are correct.

Then we can rewrite the polynomial as:

2. We can use the same method.

6x² = 3x*2x let's define a=3x and b=2x

-20 = (-4)*5 let's define c=-4 and d=5

Now we must verify that a*d + b*c = 7x

3x*5 + 2x*(-4) = 15x - 8x = 7x, it is correct!

Then we can rewrite the polynomial as:

3. Before factoring it, we can multiply by -1 each term, we will have

4x² = 2x*2x let's define a = 2x and b = 2x

1 = (-1)*(-1) let's define c = -1 and d = -1

Now we must verify that a*d + b*c = -4x

2x*(-1) + 2x*(-1) = -4x, it is correct!

Then we can rewrite the polynomial as:

4.

If we factor out 1/2 of each term, we will have:

And using the above method we can factorize

So, the area will be:

and the area of the triangle is base times height over 2 ((b*h)/2)

Therefore, b = 2x-3 and h = x+3.

I hope it helps you!

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)