Section 2.7 Question 36 x^4(x - 3) ≤ 0 Set each factor to zero and solve for x. (x^4)^(1/4) = (0)^(1/4) x = 0 x - 3 = 0 x = 3 The key numbers are x = 0 and x = 3. Our real number line looks like this: <--------------0------------3-------------> We now select a number from each interval to evaluate in the given polynomial inequality. Let x = -1 (-1)^4(-1 - 3) ≤ 0 -4 ≤ 0...true statement. Let x = 0 (0)^4(0 - 3) ≤ 0 0 ≤ 0...true statement. Let x = 1 (1)^4(1 - 3) ≤ 0 -2 ≤ 0...true statement. Let x = 3 (3)^4(3 - 3) ≤ 0 0 ≤ 0...true statement. Let x = 4 (4)^4(4 - 3) ≤ 0 256 ≤ 0...true statement. As we can see, the polynomial inequality is satisfied in the interval (-infinity, 3]. See attachment for graph of the solution set.
you needed to do just this: x^4(x - 3) ≤ 0 do each factor x^4≤ 0=> x≤ 0 (x - 3)≤ 0 x ≤ 3 your solution is correct and number line is also correct
I see two factors: x^4 and (x - 3). By setting each factor to and solving for x, I must take the fourth root on each side for x^4 = 0. In place of taking the fourth root of x^4, I simply raised each side to the (1/4) power. (x^4)^(1/4) = x.
