Solve f(x)=2a^3-a^2-7a+6 | Microsoft Math Solver

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\left(2a-3\right)\left(a^{2}+a-2\right)

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 6 and q divides the leading coefficient 2. One such root is \frac{3}{2}. Factor the polynomial by dividing it by 2a-3.

p+q=1 pq=1\left(-2\right)=-2

Consider a^{2}+a-2. Factor the expression by grouping. First, the expression needs to be rewritten as a^{2}+pa+qa-2. To find p and q, set up a system to be solved.

p=-1 q=2

Since pq is negative, p and q have the opposite signs. Since p+q is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

\left(a^{2}-a\right)+\left(2a-2\right)

Rewrite a^{2}+a-2 as \left(a^{2}-a\right)+\left(2a-2\right).

a\left(a-1\right)+2\left(a-1\right)

Factor out a in the first and 2 in the second group.

\left(a-1\right)\left(a+2\right)

Factor out common term a-1 by using distributive property.

\left(2a-3\right)\left(a-1\right)\left(a+2\right)

Rewrite the complete factored expression.