Question

The polynomial expression: (1/16x^2 + 1/3x + 4/9) can be written in the form (Ax+b)^2. The value of the product, AB, to the nearest one hundreth, is____?

Answer 1

Factor the Trinomial : )

Answer 2

1/16x^2 + 1/3x + 4/9

you want that in the form (ax^2 + b)^2

look at the first term, it is a perform square, so more than likely you will have
(1/4x + ?)^2
look at the last term, it is also a perfect square, so perhaps we have
(1/4x + 2/3)^2

expand it to see if the middle term is 1/3x .If so, we got it !

Answer 3

How would you do that?

Answer 4

1000 answers

Answer 5

[AI-generated answer — Explain Bot]

To find the value of the product AB, we need to rewrite the given polynomial expression in the form (Ax+b)^2.

We start by expanding (Ax+b)^2 using the FOIL method:

(Ax + b)^2 = (Ax + b)(Ax + b)
= A^2x^2 + 2ABx + b^2

Now, let's compare this to the given polynomial expression:

A^2x^2 + 2ABx + b^2 = 1/16x^2 + 1/3x + 4/9

By comparing the coefficients of like terms on both sides, we can determine the values of A and B.

1) Coefficients of x^2 terms:
A^2 = 1/16

To solve for A, we take the square root of both sides:

A = ±√(1/16)
A = ±1/4

However, since we want the polynomial in the form (Ax + b)^2, we can take A = 1/4 (assuming positive values for simplicity).

2) Coefficients of x terms:
2AB = 1/3

We substitute the value of A to solve for B:

2(1/4)B = 1/3
1/2B = 1/3
B = (1/3) / (1/2)
B = (1/3) * (2/1)
B = 2/3

So, the polynomial expression (1/16x^2 + 1/3x + 4/9) can be written as:

(1/4x + 2/3)^2

Finally, to find the product AB:

AB = (1/4) * (2/3)
= 2/12
= 1/6

Therefore, the value of the product AB, to the nearest hundredth, is approximately 0.17.