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Factor.\newline2k2+13k+112k^2 + 13k + 11

Full solution

Q. Factor.\newline2k2+13k+112k^2 + 13k + 11
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression 2k2+13k+112k^2 + 13k + 11 by comparing it to the standard form ax2+bx+cax^2 + bx + c.a=2a = 2, b=13b = 13, c=11c = 11.
  2. Find suitable numbers: Find two numbers that multiply to aca*c (211=222*11 = 22) and add up to bb (1313).\newlineThe numbers that satisfy these conditions are 22 and 1111 because 211=222*11 = 22 and 2+11=132+11 = 13.
  3. Rewrite middle term: Rewrite the middle term 13k13k using the two numbers found in the previous step.\newline2k2+13k+112k^2 + 13k + 11 can be rewritten as 2k2+2k+11k+112k^2 + 2k + 11k + 11.
  4. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms.\newline(2k2+2k)+(11k+11)(2k^2 + 2k) + (11k + 11).
  5. Factor out common factor: Factor out the greatest common factor from each group. 2k(k+1)+11(k+1)2k(k + 1) + 11(k + 1).
  6. Final factored form: Since both groups contain the common factor (k+1)(k + 1), factor this out.\newlineThe factored form is (2k+11)(k+1)(2k + 11)(k + 1).