Q. Factor as the product of two binomials.x2−3x+2=
Identify quadratic trinomial form: Identify the quadratic trinomial and its form.The given expression is x2−3x+2, which is in the standard form of a quadratic trinomial ax2+bx+c, where a=1, b=−3, and c=2.
Find numbers for multiplication and addition: Find two numbers that multiply to give ac (a times c) and add to give b.Since a=1 and c=2, we need to find two numbers that multiply to 2 (1×2) and add to −3. The numbers that satisfy these conditions are −1 and a0.
Rewrite middle term: Rewrite the middle term using the two numbers found in Step 2.We can express −3x as −1x−2x, so the expression becomes x2−1x−2x+2.
Factor by grouping: Factor by grouping.Group the terms into two pairs: (x2−1x) and (−2x+2).Factor out the greatest common factor from each pair.From (x2−1x), we can factor out an x, resulting in x(x−1).From (−2x+2), we can factor out a −2, resulting in −2(x−1).
Write factored form: Write the factored form of the expression.Since both groups contain the common factor (x−1), we can factor this out to get the final factored form as (x−1)(x−2).