①求701,1254的最大最大公约数（两种方法）②求多项式f(x)=3x^5+2x^4+x^3+2x^2+4x+5当x=0.2时的值③把12301（5）转成十进制④已知函数f（x）＝2sin^2x+2sinxcosx-1（1）求f（x）的单调区间,最值.（2）求f

Question

①求701,1254的最大最大公约数（两种方法）②求多项式f(x)=3x^5+2x^4+x^3+2x^2+4x+5 当x=0.2时的值③把12301（5）转成十进制④已知函数f（x）＝2sin^2x+2sinxcosx-1 （1）求f（x）的单调区间,最值.（2）求f（x）的对称轴,对称中心

Answer 1

x^5+x^4+x^3+x^2+x+1)^2-x^5
=x^10+2x^9+3x^8+4x^7+5x^6+6x^5+5x^4+4x^3+3x^2+2x+1-x^5
=(x^10+2x^9+3x^8+4x^7+5x^6+5x^5+5x^4+4x^3+3x^2+2x+1)
=[x^10+(1+1)x^9+(1+1+1)x^8+(1+1+1+1)x^7+(1+1+1+1+1)x^6+(1+1+1+1+1) x^5+(1+1+1+1+1)x^4+(1+1+1+1)x^3+(1+1+1)x^2+(1+1)x+1]
=[(1x^10+1x^9+x^8+x^7+x^6)+(x^9+x^8+x^7+x^6+x^5)+(x^8+x^7+x^6+x^5+x^4)+(x^7+x^6+x^5+x^4+x^3)+(x^6+x^5+x^4+x^3+x^2)+(x^5+x^4+x^3+x^2+x)+(x^4+x^3+x^2+x+1)]
=(x^4+x^3+x^2+x+1)(x^6+x^5+x^4+x^3+x^2+x+1)
4、题目应为：x^4-11x^2y^2+y^4
=[x^4+(3-3)x^3y+(-1-9-1)x^2y^+3xy^3-3xy^3+y^4
=[(x^4+3x^3y-x^2y^2)+(-3x^3y-9x^2y^2+3xy^3)+(-x^2y^2-3xy^3+y^4)
=(x^2+3xy-y^2)(x^2-3xy-y^2)
5、x^4-12x+323
=(x^2+6x+19)(x^2-6x+17)
6、(2x^2-3x+1)^2-22x^2+33x-1
=(2x^2-3x+1)^2-22x^2+33x-11+10
=(2x^2-3x+1)^2-11(2x^2-3x+1)+10
=x(x-3)(2x-3)(2x+3)
7、 x^4+7x^3+14x^2+7x+1
=[x^4+(3+4)x^3+(1+12+1)x^2+(3+4)x+1
=[(x^4+3x^3+x^2)+(4x^3+12x^2+4x)+(x^2+3x+1)
=(x^2+3x+1)(x^2+4x+1)
8、(x+y)^3+2xy(1-x-y)-1
=(x+y)^3 -1-2xy(x+y-1)
=(x+y-1)((x+y)^2 +(x+y)+1)-2xy(x+y-1)
=(x+y-1)(x^2+y^2+x+y+1)
9、(x+3)(x^2-1)(x+5)-20
=(x+3)(x+1)(x-1)(x+5)-20
=(x^2+4x+3)(x^2+4x-5)-20
=(x^2+4x+3)[(x^2+4x+3)-8]-20
=(x^2+4x+3+2)(x^2+4x+3-10)
=(x^2+4x+5)(x^2+4x-7)