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Let’s check out your problem:

2x^(2)+7x+6

2x2+7x+6 2 x^{2}+7 x+6

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Full solution

Q. 2x2+7x+6 2 x^{2}+7 x+6
  1. Identify coefficients: Identify coefficients aa, bb, and cc in the quadratic expression 2x2+7x+62x^2 + 7x + 6. \newlinea=2a = 2, b=7b = 7, c=6c = 6.
  2. Find multiplication and addition: Find two numbers that multiply to acac (2×6=122\times6 = 12) and add up to bb (77).\newlineNumbers are 33 and 44 because 3×4=123\times4 = 12 and 3+4=73+4 = 7.
  3. Rewrite middle term: Rewrite the middle term 7x7x using the numbers found: 3x3x and 4x4x.\newline2x2+7x+6=2x2+3x+4x+62x^2 + 7x + 6 = 2x^2 + 3x + 4x + 6.
  4. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms.\newline(2x2+3x)+(4x+6)(2x^2 + 3x) + (4x + 6).
  5. Factor out common factor: Factor out the greatest common factor from each group. x(2x+3)+2(2x+3)x(2x + 3) + 2(2x + 3).
  6. Factor out common binomial: Factor out the common binomial factor (2x+3)(2x + 3).\newline(x+2)(2x+3)(x + 2)(2x + 3).

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