请问这条代数题是不是有更简单的方法计算?11^5-4x11^4-72x11^3-56x11^2+15x11+7
2019-05-07
请问这条代数题是不是有更简单的方法计算?
11^5-4x11^4-72x11^3-56x11^2+15x11+7
优质解答
记f(x)=x^5-4x^4-72x^3-56x^2+15x+7
f(x)=x^5-4x^4-72x^3-56x^2+15x+7
=x^5-11x^4+7x^4-77x^3+5x^3-55x^2-x^2+11x+4x-44+51
=x^4(x-11)+7x^3(x-11)+5x^2(x-11)-x(x-11)+4(x-11)+51
=(x-11)(x^4+7x^3+5x^2-x+4)+51
所以f(11)=51
记f(x)=x^5-4x^4-72x^3-56x^2+15x+7
f(x)=x^5-4x^4-72x^3-56x^2+15x+7
=x^5-11x^4+7x^4-77x^3+5x^3-55x^2-x^2+11x+4x-44+51
=x^4(x-11)+7x^3(x-11)+5x^2(x-11)-x(x-11)+4(x-11)+51
=(x-11)(x^4+7x^3+5x^2-x+4)+51
所以f(11)=51