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Answers
Answer:
a = -5, b = -6
Step-by-step explanation:
Given f(x) = 8x⁴ + 14x³ - 2x² + ax + b.
Given g(x) = 4x² + 3x + 2.
Long division method:
4x² + 3x + 2 ) 8x⁴ + 14x³ - 2x² + ax + b ( 2x² + 2x - 3
8x⁴ + 6x³ + 4x²
----------------------------------
8x³ - 6x² + ax + b
8x³ + 6x² + 4x
-----------------------------------
12x² + x(a - 4) + b
12x² - 9x - 6
------------------------------------
x(a + 5) + b + 6
Since f(x) is exactly divisible by g(x), the remainder x(a + 5)+ b+ 6 = 0
⇒ a + 5 = 0 and b + 6 = 0
⇒ a = -5, b = -6.
Hope it helps!
a = -5, b = -6
Step-by-step explanation:
Given f(x) = 8x⁴ + 14x³ - 2x² + ax + b.
Given g(x) = 4x² + 3x + 2.
Long division method:
4x² + 3x + 2 ) 8x⁴ + 14x³ - 2x² + ax + b ( 2x² + 2x - 3
8x⁴ + 6x³ + 4x²
----------------------------------
8x³ - 6x² + ax + b
8x³ + 6x² + 4x
-----------------------------------
12x² + x(a - 4) + b
12x² - 9x - 6
------------------------------------
x(a + 5) + b + 6
Since f(x) is exactly divisible by g(x), the remainder x(a + 5)+ b+ 6 = 0
⇒ a + 5 = 0 and b + 6 = 0
⇒ a = -5, b = -6.