Answer:
x^2 -12x+36
Step-by-step explanation:
x^2 – 12x
Take the coefficient of x
-12
Divide by 2
-12/2 = 6
Square it
6^2 = 36
We need to add 36 to make x^2 -12x a perfect square trinomial
x^2 -12x+36
Answer:
f(g(x)) = 4x² + 16x + 13
Step-by-step explanation:
Given the composition of functions f(g(x)), for which f(x) = 4x + 5, and g(x) = x² + 4x + 2.
<h3><u>Definitions:</u></h3>
- The <u>polynomial in standard form</u> has terms that are arranged by <em>descending</em> order of degree.
- In the <u>composition of function</u><em> f </em>with function <em>g</em><em>, </em>which is alternatively expressed as <em>f </em>° <em>g,</em> is defined as (<em>f </em> ° <em>g</em>)(x) = f(g(x)).
In evaluating composition of functions, the first step is to evaluate the inner function, g(x). Then, we must use the derived value from g(x) as an input into f(x).
<h3><u>Solution:</u></h3>
Since we are not provided with any input values to evaluate the given composition of functions, we can express the given functions as follows:
f(x) = 4x + 5
g(x) = x² + 4x + 2
f(g(x)) = 4(x² + 4x + 2) + 5
Next, distribute 4 into the parenthesis:
f(g(x)) = 4x² + 16x + 8 + 5
Combine constants:
f(g(x)) = 4x² + 16x + 13
Therefore, f(g(x)) as a polynomial in <em>x</em> that is written in standard form is: 4x² + 16x + 13.
A^2 + 2AB + B^2 = (A + B)^2 ==>
16X^2 + 40X + 25 =
= (4X)^2 + 2*4*5X + 5^2 =
= (4X + 5)^2
<span>(4x + 5)(4x + 5)</span>
Answer:
Exact form: √
29
Decimal form: 5.38516480
Step-by-step explanation:
11^2=121
12^2=144
You can write either 11 or 12.
