What is the slope of the line described by the equation shown in the picture?

answer: the slope is 10

step-by-step explanation:

  x^4 -11x^2 +28

Step-by-step explanation:

The FOIL method tells you to form the products of ...

  First terms: (x^2)(x^2) = x^4

  Outer terms: (x^2)(-4) = -4x^2 . . . . first term of first factor × last term of last factor

  Inner terms: (-7)(x^2) = -7x^2 . . . . terms next to the adjacent parentheses

  Last terms: (-7)(-4) = 28 . . . . . . . . . second term of each binomial

The only terms that need to be combined are the Outer and Inner terms. In this product, their sum is ...

  -4x^2 -7x^2 = -11x^2

Then the product is x^4 -11x^2 +28.

Apart from your multiplication tables (or use of your calculator), you only need to know how to find the exponent of the product of powers of x. That result is the sum of the exponents of the factors:

  (x^a)(x^b) = x^(a+b)

  (x^2)(x^2) = x^(2+2) = x^4

Comment on FOIL

The term FOIL is intended to be a mnemonic to remind you how to multiply two binomials. The method only works with two binomials.

The more general case is the use of the distributive property, which is needed for multiplying sums that are not binomials.

Using the distributive property gets you the same place in the end:

  (x^2 -7)(x^2 -4) = x^2(x^2 -4) -7(x^2 -4) . . . . . second factor multiplies each term of the first factor

Now you can go the next step to distribute the outside factor to all the inside terms:

  = (x^2)(x^2) +(x^2)(-4) -7(x^2) -7(-4)

  = x^4 -4x^2 -7x^2 +28 . . . . . . . same terms as FOIL, above

  = x^4 -11x^2 +28 . . . . . . . . . . . . same product as above