Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Answer: 3x^2+4x-2
=====================================================
Explanation:
Assume the polynomial we want to find is in the form Ax^2+Bx+C
The goal is to find the values of A, B, and C.
We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:
(3x^2+4x-1) - (Ax^2+Bx+C) = 1
3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1
(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1
(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1
From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.
Do the same for the x terms to get 4-B = 0 leading to B = 4
Finally, we have -1-C = 1 lead to C = -2
The polynomial Ax^2+Bx+C becomes 3x^2+4x-2
-------------------
Checking the answer:
(3x^2+4x-1) - (Ax^2+Bx+C)
(3x^2+4x-1) - (3x^2+4x-2)
3x^2+4x-1 - 3x^2-4x+2
(3x^2-3x^2) + (4x-4x) + (-1+2)
0x^2 + 0x + 1
0 + 0 + 1
1
We get a difference of 1, so the answer is confirmed.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.