anja divides (8x³ - 36x² + 54x - 27) by (2x - 3) as shown below. what error does anja make? 4x² - 12x + 9 2x…
anja divides (8x³ - 36x² + 54x - 27) by (2x - 3) as shown below. what error does anja make? 4x² - 12x + 9 2x - 3 ) 8x³ - 36x² + 54x - 27 8x³ - 12x² -24x² + 54x -24x² + 36x 18x - 27 18x + 27 -54 she makes a subtraction error. she makes an error choosing the x - term in the quotient. she makes a multiplication error. she makes an error rewriting the problem in long division.
Answer
Explanation:
Step1: Analyze long - division step
In long - division of polynomials, when subtracting (-24x^{2}+54x) and (-24x^{2}+36x), we subtract the like - terms. The subtraction of the (x) terms should be (54x-36x = 18x), and the subtraction of the constant terms is (0) (since there is no constant in (-24x^{2}+36x)). But Anja wrote (18x - 27-(18x + 27)) which is incorrect. The correct subtraction of (-24x^{2}+54x-(-24x^{2}+36x)) gives (18x), not (18x-27-(18x + 27)).
Step2: Identify the error type
Anja made a subtraction error when subtracting the two polynomial expressions (-24x^{2}+54x) and (-24x^{2}+36x).
Answer:
She makes a subtraction error.