Rearrange terms in descending order: First, we need to rearrange the terms of the polynomial in descending order of the powers of x. s(x)=x4+3x3−9x2−10x2−27x+90 Combine like terms. s(x)=x4+3x3−19x2−27x+90
Combine like terms: Next, we look for common factors in pairs of terms or try to group terms to factor by grouping.Group the terms as follows:s(x)=(x4+3x3)+(−19x2−27x)+90
Group terms for factoring: Factor out the greatest common factor from each group.s(x)=x3(x+3)−9x(2x+3)+90
Factor out common factors: Now, we look for a common binomial factor among the grouped terms.There is no common binomial factor, and the constant term 90 does not seem to factor with the other terms.At this point, we realize that we cannot factor the polynomial further using common factoring techniques.