Question

(a) Decompose the function 37216.015(213) into its partial tion form.

(b) Use the solution in (a) to evaluate 3:12 | 16 | 15(3) correct to 4 significant figures.

A (4x - 3)(4x + 3) and (4x - 3)²
B (2x + 1)(3x - 5) and (2x + 1)(3x - 5)
C (3x - 2)(5x + 7) and (3x - 2)(5x + 7)²
D (x + 2)(2x - 4) and (x + 2)(2x - 4)²

Answer 1

The simplified form upto 4 significant figures is D (x + 2)(2x - 4) and (x + 2)(2x - 4)².

Step-by-step explanation:

The given function is 37216.015(213). To decompose it into partial fraction form, we need to factorize the quadratic expressions. In this case, we observe that the function can be factored as (x + 2)(2x - 4) . Therefore, the partial fraction decomposition form is (x + 2)(2x - 4) and (x + 2)(2x - 4)² .

Now, moving on to part (b) where we are asked to evaluate 3:12 | 16 | 15(3) using the solution from part (a). We substitute x = 3 into the decomposed form. First, for (x + 2)(2x - 4) , we get (3 + 2)(2 x 3 - 4) = 5 x 2 = 10. Then, for (x + 2)(2x - 4)² , we have (3 + 2)(2 x 3 - 4)² = 5 x 2² = 20.

Thus, the final evaluated result for 3:12 | 16 | 15(3) is 10 + 20 = 30, correct to 4 significant figures.

In summary, by decomposing the original function into partial fraction form, we could easily evaluate the given expression. The correct choice is option D, and the final result is 30, rounded to 4 significant figures.