# Factor by Grouping 8x^3+3x-7x^3-4

8×3+3x-7×3-4
Subtract 7×3 from 8×3.
x3+3x-4
Factor x3+3x-4 using the rational roots test.
If a polynomial function has integer coefficients, then every rational zero will have the form pq where p is a factor of the constant and q is a factor of the leading coefficient.
p=±1,±4,±2q=±1
Find every combination of ±pq. These are the possible roots of the polynomial function.
±1,±4,±2
Substitute 1 and simplify the expression. In this case, the expression is equal to 0 so 1 is a root of the polynomial.
Substitute 1 into the polynomial.
13+3⋅1-4
Raise 1 to the power of 3.
1+3⋅1-4
Multiply 3 by 1.
1+3-4
4-4
Subtract 4 from 4.
0
0
Since 1 is a known root, divide the polynomial by x-1 to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
x3+3x-4x-1
Divide x3+3x-4 by x-1.
x2+x+4
Write x3+3x-4 as a set of factors.
(x-1)(x2+x+4)
(x-1)(x2+x+4)
Factor by Grouping 8x^3+3x-7x^3-4