Question

Consider the quadratic equation 3x² - 23x - 8 = 0 from the question above. Rewrite

the trinomial using the "magic numbers" to split the middle term.

Answer 1

I'm pretty sure the answer is 3x² - 24x + 1x - 8 = 0

Explanation:

The magic numbers in the equation are -24 and 1 and if you put them in the equation as above, it does equal 23x.

Answer 2

3x²-24x+x-8 = 0

Explanation:

Given the equation 3x² - 23x - 8 = 0, in order to split the middle term which is -23x, first we will need to multiply the coefficient of x² by the constant of the equation i.e 3×(-8) to give -24.

Then we will find two numbers such that if the two numbers are multiplied together, it will give -24 and if the same 2numbers are added together, it will give the coefficient of x in the function i.e -23.

The two numbers are therefore -24 and +1.

-24×+1 = -24

-24+1 = -23

The trinomial can then be rewritten as thus;

3x²(-24x+x)-8 = 0

Note that the -23x has been splitted into -24x and +x