Please I need help with this question 1 Create two factoring

Please I need help with this question:

1) Create two factoring problems, trinomial expression in the form of \"ax² + bx + c\", unique from any of the other problems in your text (or other students). Your expressions and equation must be factorable. Also, the constant \"a\" must be positive. In one of the factoring expressions and your equation, \"a\" must be greater than 1. Also, \"a\" should not have any common factor with any other terms.

a) Create a quadratic equation that can be solved by factoring.

Solution

Lets take first quadratic equation : 5x^2 +20x +15 (trinomial expression)

Now in this example a is +ve and a>1

So, in a quadratic equation in descending order with a leading coefficient of one, look for the product of the roots to be the constant tern and the sum of the roots to be the coefficient of the middle term.

5x^2 + 15x +5x +15 =0

5x( x+3) +5(x +3) =0

(5x+5)(x+3) =0

Now the only way to multiply and get zero is to multiply by zero. (This is sometimes called \"The Zero Factor Property\" or \"Rule\" or \"Principle\".)

equating each factor to zero: we get 5x+5=0 ----> x= -1

x+3 =0 ----> x=-3

Another example : x² + 5x + 6 = (x + 2)(x + 3) =0

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

x = -2 ; x =-3