One factor of f(x)=4x3-4x2-16x+16 is (x – 2). what are all the roots of the function? use the remainder theorem.

Remark

For the first two terms, factor out 4x^2

For the second two terms, factor out 16

The factor using the difference of squares.

Solution

f(x) = 4x^2(x - 1) - 16(x - 1)       x - 1 is a common factor.

f(x) = (4x^2 - 16) (x - 1)            factor out 4 from the first factor.

f(x) = 4(x^2 - 4)(x - 1)               Factor the difference of squares

x^2 - 4 = (x - 2)(x + 2)             Substitute this difference in the line above

f(x) = 4(x - 2)(x + 2)(x - 1)

Answer

The roots are 2, - 2, 1

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation: