9x^4+ 20x^2 + 12 in quadratic form

A "pure" quadratic has the form:

ax^2 + bx + c

To put this in broad, general (and crude) terms, a quadratic is:

"Some number, 'a', times a perfect square plus some number. 'b', times whatever-is being squared-next to-the-a (x) plus some other number, 'c'"

So can we make 9x^4+20x^2+12 fit this pattern? Let's look at this expression term-by-term:

9x^4

Can this be expressed as "Some number, 'a', times a perfect square"? Yes, in two ways:

9x^4 = 9*(x^2)^2

or

1*(3x^2)^2

Next

10x^2

Can this be expressed as "some number. 'b', times whatever-is being squared-next to-the-a"? The answer depends on which of the expressions we use for 9x^4.

If we use 9*(x^2)^2 then "whatever-is being squared-next to-the-a" would be x^2. Can we express 20x^2 as some number times x^2? Obviously yes: 20*x^2.

If we try to use 1*(3x^2)^2 for the 9x^4 then "whatever-is being squared-next to-the-a" would be 3x^2. Can we express 20x^2 as some number times 3x^2? Although not very obvious, the answer is yes: 20x^2 = (20/3)*3x^2

And of course 12 can be our 'c'. So there are two ways to express 9x^4+20x^2+12 in quadratic form:

9x^4+20x^2+12 = 9*(x^2)^2 + 20*x^2 + 12 with the a = 9, b = 20 and the c = 12

or

9x^4+20x^2+12 = 1*(3x^2)^2 + (20/3)*3x^2 + 12 with the a = 1, b = 20/3 and the c = 12.

If you really want these to look like a quadratic, then you can use a temporary variable. Make the temporary variable equal to "whatever-is being squared-next to-the-a". So for 9*(x^2)^2 + 20*x^2 + 12, let q = x^2. This makes the expression: 9q^2 + 20q + 12. For 1*(3x^2)^2 + (20/3)*3x^2 + 12, let q = 3x^2. This m

Step-by-step explanation:

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)