Attempting to factor \(\displaystyle{\left({x}^{{2}}\right)}+{5}{x}={0}\) via the grouping

Thaddeus Nolan

Thaddeus Nolan

Answered question

2022-03-18

Attempting to factor (x2)+5x=0 via the grouping method.

Answer & Explanation

y888umjy

y888umjy

Beginner2022-03-19Added 1 answers

Only your last statement is wrong. You're right that if you want to use the grouping method (also called splitting the middle term, the AC method, and possibly other names) the numbers should be 5 and 0. But remember, from there you split the linear term and get
x2+5x+0x+0=x(x+5)+0(x+5)=(x+0)(x+5)=x(x+5)
Kasen Alexander

Kasen Alexander

Beginner2022-03-20Added 7 answers

ax2+bx+c=x2+5x+0=0.
This will have roots
12a[b±b24ac].
This equals
12[5±25].
This simplifies to the two roots of
[12×0] and [12×10].

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