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Factor.\newline16x3+8x2+14x+716x^3 + 8x^2 + 14x + 7

Full solution

Q. Factor.\newline16x3+8x2+14x+716x^3 + 8x^2 + 14x + 7
  1. Identify Common Factors: Look for common factors in the first two terms and the last two terms separately.\newlineFor the first two terms, 16x316x^3 and 8x28x^2, the common factor is 8x28x^2.\newlineFor the last two terms, 14x14x and 77, 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.\newline16x3+8x2=8x2(2x+1)16x^3 + 8x^2 = 8x^2(2x + 1)\newline14x+7=7(2x+1)14x + 7 = 7(2x + 1)
  3. Combine Common Factors: Now, we have two groups: 8x2(2x+1)8x^2(2x + 1) and 7(2x+1)7(2x + 1). Since both groups have a common factor of (2x+1)(2x + 1), we can factor this out.\newlineThe factored form is (2x+1)(8x2+7)(2x + 1)(8x^2 + 7).