Question

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?

Answer 1

1.
`2x^(2)-x-10 =(2x-5)(x+2)`

2.
`6x^(2)+7x-20 = (3x-4)(2x+5)`

3.
`4x^(2)-4x+1 = (2x-1)(2x-1) = (2x-1)^(2)`

4.
`A=(1)/(2)(2x-3)(x+3)=(1)/(2)(b*h)`

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

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:

`2x^(2)-x-10 = (a+c)(b+d)=(2x-5)(x+2)`

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:

`6x^(2)+7x-20 = (3x-4)(2x+5)`

3. Before factoring it, we can multiply by -1 each term, we will have
`4x^(2)-4x+1`

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:

`4x^(2)-4x+1 = (2x-1)(2x-1) = (2x-1)^(2)`

4.
`A=x^(2)+(3)/(2)x-(9)/(2)`

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

`A=(1)/(2)(2x^(2)+3x-9)`

And using the above method we can factorize

`2x^(2)+3x-9=(2x-3)(x+3)`

So, the area will be:

`A=(1)/(2)(2x-3)(x+3)`

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

`A=(1)/(2)(2x-3)(x+3)=(1)/(2)(b*h)`

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

I hope it helps you!