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Factor.\newlinez2+5z+4z^2 + 5z + 4

Full solution

Q. Factor.\newlinez2+5z+4z^2 + 5z + 4
  1. Identify Coefficients: Identify the coefficients for z2z^2, zz, and the constant term in the quadratic expression z2+5z+4z^2 + 5z + 4. The coefficient of z2z^2 is 11 (a=1a = 1), the coefficient of zz is 55 (b=5b = 5), and the constant term is 44 (zz00).
  2. Find Multiplying Numbers: Find two numbers that multiply to give the constant term, c=4c = 4, and add up to the coefficient of zz, b=5b = 5. The numbers 11 and 44 multiply to give 44 (1×4=41 \times 4 = 4) and add up to 55 (1+4=51 + 4 = 5).
  3. Write Factored Form: Write the factored form of the quadratic expression using the two numbers found in the previous step.\newlineThe factored form is (z+1)(z+4)(z + 1)(z + 4).