Question

Please help me figure out how to create a quadratic equation in standard form that can be factored.

Answer 1

well one way ss to think of 2 numbers a and b where ab = say 6, now find some factors of 6 for example 3 and 2
so let a = 3 and b = 2

(x +a)(x + b) = 0

(x + 3)(x + 2) = 0

expand to get

x^2 + 5x + 6 = 0

Answer 2

what we are doing is finding integers to fit the expression
x^2 + ax + bx + ab

Answer 3

we can of course have negatives

fo example
x^2 - 2x + 7x - 14

Answer 4

giving x^2 + 5x - 14 = 0

Answer 5

honestly I'm very confused I think we should start at the top and maybe you could explain this a little easier to me.

Answer 6

Ok the factored form of a trinomial ( or quadratic) as like

(x + a)(x + b) = 0

now if we expand this we get

x^2 + ax + bx + ab

ok?

Answer 7

ok

Answer 8

so we want to fit integers to a and b
lets pick ab ( a times b) first
ab = 8

now we can choose 2 integers that when multiplied give 8
we can pick 2 and 4 , or if we like 8 and 1
lets pick 2 and 4
now plug these in to the expression
x^2 + ax + bs + ab

= x^2 + 2x + 4x + 8
= x^2 + 6x + 8

so our quadratic equation is
x^2 + 6x + 8 = 0

Answer 9

just keep in mind the identity x^2 + ax + bx + ab and its easy

Answer 10

so is that equation in standard form?

Answer 11

yes

Answer 12

oh ok so how would we put it into factored form

Answer 13

well x^2 + 6x + 8 = 0 is in standard form
its more accurate to write the a b form as

x^2 + (a+ b)x + ab = 0 standard form

Answer 14

to facto x^2 + 6x + 8 = 0

by observation we see that 2*4 = 8 and 2 + 4 = 6 so we write

x^2 + 2x + 4x + 8 = 0
now factor the first 2 terms and the last 2 terms ( this is called grouping)

x(x + 2) + 4(x + 2) = 0

note that the parentheses are equal so we can write
(x+ 2)(x + 4) = 0