Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 + x − 7 = 0, (1, 2) f(x) = x4 + x − 7 is ---Select--- on the closed interval [1, 2], f(1) = , and f(2) = . Since −5 < ? < 11, there is a number c in (1, 2) such that f(c) = ? by the Intermediate Value Theorem. Thus, there is a ---Select--- of the equation x4 + x − 7 = 0 in the interval (1, 2).

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

Amuffin recipe, which yields 12 muffins, calls for cup of milk for every 1 cups of flour. the same recipe calls for cup of coconut for every cup of chopped apple. to yield a batch of 30 muffins, how much flour will be needed in the mix?

Simplify 15(x - 4)(x -1)-3(x + 4)(x - 1) with steps