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Factor.\newline5j3+10j2+7j+145j^3 + 10j^2 + 7j + 14

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Q. Factor.\newline5j3+10j2+7j+145j^3 + 10j^2 + 7j + 14
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 5j35j^3 and 10j210j^2, the common factor is 5j25j^2.\newlineFor the last two terms, 7j7j and 1414, the common factor is 77.
  2. Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms.\newline5j3+10j2=5j2(j+2)5j^3 + 10j^2 = 5j^2(j + 2)\newline7j+14=7(j+2)7j + 14 = 7(j + 2)
  3. Combine Factored Parts: Now, we have factored the polynomial into two parts: 5j2(j+2)5j^2(j + 2) and 7(j+2)7(j + 2). We can see that (j+2)(j + 2) is a common factor in both parts.
  4. Factor Out Final Common Factor: Factor out the common factor (j+2)(j + 2) from both parts.\newline5j2(j+2)+7(j+2)=(5j2+7)(j+2)5j^2(j + 2) + 7(j + 2) = (5j^2 + 7)(j + 2)