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Factor.\newlinec26c+9c^2 - 6c + 9

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Q. Factor.\newlinec26c+9c^2 - 6c + 9
  1. Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (ab)2=a22ab+b2(a - b)^2 = a^2 - 2ab + b^2. We need to check if c26c+9c^2 - 6c + 9 fits this pattern.
  2. Identify Square Roots: Identify the square root of the first term and the last term.\newlineThe square root of c2c^2 is cc, and the square root of 99 is 33. So, we have a=ca = c and b=3b = 3.
  3. Verify Middle Term: Check if the middle term fits the pattern 2ab2ab. For our expression, 2ab2ab should be 2×c×3=6c2 \times c \times 3 = 6c, which matches the middle term of our quadratic.
  4. Write Factored Form: Write the factored form using the square of a binomial.\newlineSince the quadratic fits the pattern of a perfect square trinomial, we can write it as (c3)2(c - 3)^2.