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Factor.\newlinej3+2j2+5j+10j^3 + 2j^2 + 5j + 10

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Q. Factor.\newlinej3+2j2+5j+10j^3 + 2j^2 + 5j + 10
  1. Grouping terms: We will look for common factors in pairs of terms. First, we will factor the polynomial by grouping. We will group the first two terms together and the last two terms together.
  2. Factoring first group: Factor out the greatest common factor from the first group, j3+2j2j^3 + 2j^2. The greatest common factor is j2j^2.\newlinej3+2j2=j2(j+2)j^3 + 2j^2 = j^2(j + 2)
  3. Factoring second group: Now, factor out the greatest common factor from the second group, 5j+105j + 10. The greatest common factor is 55.\newline5j+10=5(j+2)5j + 10 = 5(j + 2)
  4. Factoring common factor: We now have two groups factored as follows:\newlinej3+2j2+5j+10=j2(j+2)+5(j+2)j^3 + 2j^2 + 5j + 10 = j^2(j + 2) + 5(j + 2)\newlineNotice that (j+2)(j + 2) is a common factor in both groups.
  5. Final factored form: Factor out the common factor (j+2)(j + 2) from both groups.\newline(j2+5)(j+2)(j^2 + 5)(j + 2)\newlineThis is the factored form of the polynomial.