8×3+3x-7×3-4

Subtract 7×3 from 8×3.

x3+3x-4

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

Add 1 and 3.

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