Factor completely. \( 56 v^{2}-17 v-3 \) Select the correct choice below and fill in any answe A. The answer is B. The expression is prime.

To factor the expression \( 56v^2 - 17v - 3 \) completely, we can use the method of grouping. First, we need to find two numbers that multiply to \( 56 \times -3 = -168 \) and add up to \( -17 \). The numbers are \( -21 \) and \( 8 \). Rewriting the middle term: \( 56v^2 - 21v + 8v - 3 \) Now, grouping: \( (56v^2 - 21v) + (8v - 3) \) Factoring out the common terms: \( 7v(8v - 3) + 1(8v - 3) \) Now, factor out \( (8v - 3) \): \( (8v - 3)(7v + 1) \) So, the completely factored expression is: A. The answer is \( (8v - 3)(7v + 1) \). To verify, we can multiply the factors back together using the distributive property (a.k.a the FOIL method). When you expand \( (8v - 3)(7v + 1) \), you’ll find that indeed, it simplifies back to the original expression \( 56v^2 - 17v - 3 \). Remember, practice makes perfect; try factoring different quadratic expressions to sharpen your skills!