If the polynomial 4x4 + 6x3 + 13x2 + 20x + 7 is divided by another polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’. (3 marks)
Answers
Answer:
hello.....
Step-by-step explanation:
Hey friend here is your answer in the above attachment.
please mark brainliest and follow me...plz...
good noon... have a great day...
Answer:
After dividing (4 x⁴ + 6 x³ + 13 x² + 20 x + 7) by (3 x² + 4 x + 1), we get that:
a = 142 / 9
b = 6.
Step-by-step explanation:
(4 x⁴ + 6 x³ + 13 x² + 20 x + 7) ÷ (3 x² + 4 x + 1).
We need to divide the two polynomials.
We will do this by long division method:
4/3 x² + 2/9 x + 1
(3 x² + 4 x + 1) √(4 x⁴ + 6 x³ + 13 x² + 20 x + 7)
- 4 x⁴ -16/3 x³ - 4/3 x²
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
2/3 x³ + 35/9 x² +20 x + 7
-2/3 x³ - 8/9 x² - 2/9 x
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
3 x² + 178/9 x + 7
-3 x² - 9 x - 1
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
142/9 x + 6
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
So, we get the remainder as 142/9 x + 6
ATQ, we have:
a x + b = 142 / 9 x + 6
By comparing, we get that:
a = 142 / 9 and b = 6.
Therefore, a is 142 / 9 and b is 6.
#SPJ2