Question

State the end behavior and roots of the following equation f(x)=(5-3x)(x+7)(-x-8)

Answer 1

The equation f(x)=(5-3x)(x+7)(-x-8) has the end behavior of approaching positive infinity as x approaches negative infinity and approaching negative infinity as x approaches positive infinity. The roots of the equation are x = 5/3, x = -7, and x = -8.

Step-by-step explanation:

The end behavior of a polynomial is determined by the leading term, which is the term with the highest power of x. In this equation, the leading term is -3x^3. Since the degree of the polynomial is odd and the leading coefficient is negative, the end behavior is as follows:

• As x approaches negative infinity, f(x) approaches positive infinity.
• As x approaches positive infinity, f(x) approaches negative infinity.

To find the roots of the equation, set each factor equal to zero and solve for x:

• Setting 5-3x = 0 gives x = 5/3.
• Setting x+7 = 0 gives x = -7.
• Setting -x-8 = 0 gives x = -8.

Therefore, the roots of the equation are x = 5/3, x = -7, and x = -8.