Question

Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.

Answer 1

Answer:

please see analysis

Step-by-step explanation:

x^2+ 7x+12= 0 is a quadratic equation because the heighest power of the unknown variable is 2 ( unknown variable = X).

solving the above equation using factorization method:

X^2 + 7X +12=0

we get two numbers such that when we add them, they give 7 and when we multiply them they will give 12

so, the numbers are 4 and 3 . because

4×3= 12

4+3= 7

replace 7 with 4 and 3

X^2+4x+3x+12=0

x(x+4)+3(x+4)

(X+4) (x+3)= 0

(X+4)= 0

(x+3)= 0

therefore.

X= -4

or

X=-3

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Answer 2

Answer:

An example of a quadratic equation is:

${x}^{2} + 5x + 6 = 0$

Step-by-step explanation:

This answer follows the standard form for a quadratic equation:

$a {x}^{2} + bx + c = 0$

To solve this equation you do the following:

x^2 + 5x + 6 =0

The factors that can be added to get *5* and multiplied to get *6* are 3 & 2.

Therefore the new equation would be:

x^2 +3x + 2x + 6 = 0

group the terms: (x^2 +3x) (+2x + 6) = 0

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

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

x = -1 x =-3