Question

Giúp em với

Answer 1

d: \(f\left(x-3\right)=2\left(x-3\right)^2-\left(x-3\right)+2021\)

\(=2\left(x^2-6x+9\right)-x+3+2021\)

\(=2x^2-12x+18-x+2024=2x^2-13x+2042\)

c: \(A\left(x\right)=x^4+a\cdot x^2+b\)

\(=x^4-3x^3+2x^2+3x^3-9x^2+6x\) +\(\left(a+7\right)x^2-\left(3a+21\right)x+\left(2a+14\right)\) +x(3a+21-6)+b-2a-14

\(=\left(x^2-3x+2\right)\left(x^2+3x+a+7\right)\) +x(3a+15)+b-2a-14

Để A(x)⋮B(x) thì 3a+15=0 và b-2a-14=0

=>3a=-15 và b=2a+14

=>a=-5 và b=2(a+7)=2(-5+7)=2*2=4

b: \(5_{}^{n+2}+2\cdot5^{n+1}+4\cdot5^{n}\)

\(=5^{n}\cdot25+2\cdot5^{n}\cdot5+4\cdot5^{n}\)

\(=5^{n}\cdot\left(25+10+4\right)=5^{n}\cdot39\) ⋮39