Answer:
1. [tex]2x^{2}-x-10 =(2x-5)(x+2)[/tex]
2. [tex]6x^{2}+7x-20 = (3x-4)(2x+5)[/tex]
3. [tex]4x^{2}-4x+1 = (2x-1)(2x-1) = (2x-1)^{2}[/tex]
4. [tex]A=\frac{1}{2}(2x-3)(x+3)=\frac{1}{2}(b*h)[/tex]
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:
[tex]2x^{2}-x-10 = (a+c)(b+d)=(2x-5)(x+2)[/tex]
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:
[tex]6x^{2}+7x-20 = (3x-4)(2x+5)[/tex]
3. Before factoring it, we can multiply by -1 each term, we will have [tex]4x^{2}-4x+1[/tex]
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:
[tex]4x^{2}-4x+1 = (2x-1)(2x-1) = (2x-1)^{2}[/tex]
4. [tex]A=x^{2}+\frac{3}{2}x-\frac{9}{2}[/tex]
If we factor out 1/2 of each term, we will have:
[tex]A=\frac{1}{2}(2x^{2}+3x-9)[/tex]
And using the above method we can factorize
[tex]2x^{2}+3x-9=(2x-3)(x+3)[/tex]
So, the area will be:
[tex]A=\frac{1}{2}(2x-3)(x+3)[/tex]
and the area of the triangle is base times height over 2 ((b*h)/2)
[tex]A=\frac{1}{2}(2x-3)(x+3)=\frac{1}{2}(b*h)[/tex]
Therefore, b = 2x-3 and h = x+3.
I hope it helps you!
