Question

Solve the polynomial x² - 7x + 12 = 0 Show each step used to find the solutions.

Answer 1

x² - 7x + 12 = 0

doing middle term factorization

x²-4x-3x+12=0

taking common from each two term

x(x-4)-3(x-4)=0

taking common

(x-4)(x-3)=0

either

x-4=0

:. x=4

or

x-3=0

x=3

:.x=4,3

Answer 2

x=4 and x=3

Explanation:

The first step to find all factors of 12

1,2,3,4,6,12

and their negative form

-1,-2,-3,-4,-6,-12

we must add two of these numbers to get -7

and the two numbers that add up to -7 are -3 and -4

we can simply plot them into the polynomial (x-3)(x-4)

since x-3=0

we add three to both sides to get x=3

and since x-4=0

add four to both sides

we get x=4

and now check out work which

we can use First out in last (foil) method

(x-3)(x-4)

first

x^2

out

-4x

in

-3x

last

12

now we simplify to get x^2-7x+12

so it x=4 x=3 works