How do you factor the trinomial $30x²+x-1$ ?

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Answer 1 · 2016-01-24T12:19:39

Find a pair of factors of $30$ that differ by $1$ , namely $6$ and $5$ , hence:

$30x^2+x-1 = (6x-1)(5x+1)$

Ignoring signs, call the coefficients of this quadratic $A$ , $B$ and $C$ .

Look for a pair of factors of $AC = 30*1 = 30$ which differ by $B=1$ .

The pair $6$ , $5$ works.

We can use this pair to split the middle term then factor by grouping as follows:

$30x^2+x-1$

$=30x^2+6x-5x-1$

$=(30x^2+6x)-(5x+1)$

$=6x(5x+1)-1(5x+1)$

$=(6x-1)(5x+1)$

How do you factor the trinomial 30x²+x-130x²+x-1?