Final answer:
To solve the inequality (x²-3x+2)(x²+7x-8) <= 0, we can use the zero product property to find the solutions for each factor separately.
Step-by-step explanation:
To solve the inequality (x²-3x+2)(x²+7x-8) <= 0, we can use the zero product property. This property states that if a product of factors is equal to zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x.
First, we set x²-3x+2=0:
(x-1)(x-2)=0
Then, we set x²+7x-8=0:
(x+8)(x-1)=0
We can now examine each factor separately to determine the solution set for the inequality.