Question

Can anyone explain how to factor quadratics? i have a whole page of stuff like the picture.

Answer 1

Answer:

7) (s + 2)(s + 5)

   s = -2, -5

8) (x + 7)(x + 4)

   x = -7, -4

9) (d - 3)(d + 9)

    d = 3, -9

Step-by-step explanation:

To start you will want to try and look for two numbers that multiply to equal a*c and have a sum equal to b. So with number 7, a=1 b=7 and c=10. We need to find two numbers that multiply to equal 1*10 and add to equal 7. so the numbers 5 & 2 work perfectly. 5*2 = 10 and 5+2 = 7. so now we will split up the 7s into 5s+2s.

s^2 + 5s + 2s + 10

The next step would be to group each side together. Using parentheses will help keep us organized.

(s^2 + 5s)(2s + 10)

So now it's time to factor something out of each side. You are going to work on one side at a time and find something that the two have in common. so starting with (s^2 + 5s), we can see that the s^2 and the 5s both have an s in common, so we can go ahead and factor that out.

s(s + 5)

Now with the (2s + 10), we can see that you can easily divide a 2 from both sides.

2(s + 5)

So now if we reassemble to two parts we would have something that looks like this.

s(s + 5) + 2(s + 5)

So now, the numbers/variables that we factored out, s & 2, would be put together in their own parentheses and the two (s + 5)s can be combined into their own set of parentheses. This would look something like this:

(s + 2)(s + 5)

Now this is your fully factored form, if you wanted to take it a step further and solve the equation you could take each side and set it equal to 0 and solve for your s.

s + 2 = 0

s = -2

&

s + 5 = 0

s = -5

7) s^2 + 7s + 10

   s^2 + 5s + 2s + 10

   (s^2 + 5s) + (2s + 10)

   s(s + 5) + 2(s + 5)

   (s + 2)(s + 5)

   s = -2, -5

8) x^2 + 11x + 28

   x^2 + 4x + 7x + 28

   (x^2 + 4x) + (7x +28)

   x(x + 4) + 7(x + 4)

   (x + 7)(x + 4)

   x = -7, -4

9) d^2 + 6d - 27

    d^2 + 9d - 3d - 27

    (d^2 + 9d) + (-3d - 27)

    d(d + 9) + -3(d + 9)

    (d + -3)(d + 9)

    (d - 3)(d + 9)

    d = 3, -9