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x\left(3x^{2}-20x-7\right)
Factor out x.
a+b=-20 ab=3\left(-7\right)=-21
Consider 3x^{2}-20x-7. Factor the expression by grouping. First, the expression needs to be rewritten as 3x^{2}+ax+bx-7. To find a and b, set up a system to be solved.
1,-21 3,-7
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -21.
1-21=-20 3-7=-4
Calculate the sum for each pair.
a=-21 b=1
The solution is the pair that gives sum -20.
\left(3x^{2}-21x\right)+\left(x-7\right)
Rewrite 3x^{2}-20x-7 as \left(3x^{2}-21x\right)+\left(x-7\right).
3x\left(x-7\right)+x-7
Factor out 3x in 3x^{2}-21x.
\left(x-7\right)\left(3x+1\right)
Factor out common term x-7 by using distributive property.
x\left(x-7\right)\left(3x+1\right)
Rewrite the complete factored expression.