Determine the factors of the polynomial equation y=2x^3-7x^2-8x+28 - square In order to solve the polynomial equation you need to set each factor equal to square

To determine the factors of the polynomial equation , we can use the factor theorem and synthetic division.1. **Find a root of the polynomial:** We need to find a value of that makes the polynomial equal to zero. Let's test some possible rational roots using the Rational Root Theorem, which states that any rational root of the polynomial must be a factor of the constant term (28) divided by a factor of the leading coefficient (2). Possible rational roots are . Testing : So, is a root.2. **Use synthetic division to factor out :** The quotient is .3. **Factor the quadratic polynomial :** To factor , we look for two numbers that multiply to \( 2 \cdot (-14) = -28 \) and add up to . These numbers are and . Rewrite the middle term: Factor by grouping: 4. **Combine all factors:** The complete factorization of the polynomial is: 5. **Set each factor equal to zero to solve the polynomial equation:** So, the factors of the polynomial equation are \( (x - 2)(2x - 7)(x + 2) \), and the solutions to the equation are and .