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Factor as the product of two binomials.

x^(2)-3x+2=

Factor as the product of two binomials.\newlinex23x+2=x^{2}-3x+2=

Full solution

Q. Factor as the product of two binomials.\newlinex23x+2=x^{2}-3x+2=
  1. Identify quadratic trinomial form: Identify the quadratic trinomial and its form.\newlineThe given expression is x23x+2x^2 - 3x + 2, which is in the standard form of a quadratic trinomial ax2+bx+cax^2 + bx + c, where a=1a = 1, b=3b = -3, and c=2c = 2.
  2. Find numbers for multiplication and addition: Find two numbers that multiply to give acac (aa times cc) and add to give bb.\newlineSince a=1a = 1 and c=2c = 2, we need to find two numbers that multiply to 22 (1×21 \times 2) and add to 3-3. The numbers that satisfy these conditions are 1-1 and aa00.
  3. Rewrite middle term: Rewrite the middle term using the two numbers found in Step 22.\newlineWe can express 3x-3x as 1x2x-1x - 2x, so the expression becomes x21x2x+2x^2 - 1x - 2x + 2.
  4. Factor by grouping: Factor by grouping.\newlineGroup the terms into two pairs: (x21x)(x^2 - 1x) and (2x+2)(-2x + 2).\newlineFactor out the greatest common factor from each pair.\newlineFrom (x21x)(x^2 - 1x), we can factor out an xx, resulting in x(x1)x(x - 1).\newlineFrom (2x+2)(-2x + 2), we can factor out a 2-2, resulting in 2(x1)-2(x - 1).
  5. Write factored form: Write the factored form of the expression.\newlineSince both groups contain the common factor (x1)(x - 1), we can factor this out to get the final factored form as (x1)(x2)(x - 1)(x - 2).