Question

if the polynomial 6x^+8^+17^+21+7 is divided by other polynomial 3x^+4x+1 the remainder comes out to be (ax+b), find the value of a and B.

❌❌❌no irrelevant answers it will be reported❌❌❌......​

Answer 1

Answer:

f(x)=6x4+8x3+17x2+21x+7

g(x)=3x2+4x+1=(3x+1)(x+1)

Roots of g(x)=−1,−13

f(x)=[h(x)×g(x)]+ax+b(E01)

∴ Substituting x=−1 and x=−13 in f(x)will knock off the terms containing h(x) and give 2 equations for solving a and b

f(−1)=6.(−1)4+8.(−1)3+17.(−1)2+21.(−1)+7=−a+b

⟹1=b−a(E02)

f(−13)=6.(−13)4+8.(−13)3+17.(−13)2+21.(−13)+7=a(−13)+b

⟹5=3b−a(E03)

(E03)−(E02):2b=4⟹b=2

From (E02):b−a=1⟹a=1

Ans: a=1,b=2

Answer 2

Step-by-step explanation:

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