Question

因式分解 要用(配方法) 有过程

x^2+3x-10
x^2-3x-28
a^2+4a-21
m^2+4m-12
p^2-8p+7
b^2+11b+28

Answer 1

x^2+3x-10
=x^2+3x+9/4-9/4-10
=(x+3/2)^2-49/4
=(x+3/2+7/2)(x+3/2-7/2)
=(x+5)(x-2)

x^2-3x-28
=x^2-3x+9/4-9/4-28
=(x-3/2)^2-121/4
=(x-3/2-11/2)(x-3/2+11/2)
=(x-7)(x+4)

a^2+4a-21
=a^2+4a+4-4-21
=(a+2)^2-25
=(a-2+5)(a-2-5)
=(a+3)(a-7)

m^2+4m-12
=m^2+4m+4-4-12
=(m+2)^2-16
=(m+2-4)(m+2+4)
=(m-2)(m+6)

p^2-8p+7
=p^2-8p+16-16+7
=(p-4)^2-9
=(p-4-3)(p-4+3)
=(p-7)(p-1)

b^2+11b+28
=b^2+11b+121/4-121/4+28
=(b+11/2)^2-9/4
=(b+11/2+3/2)(b+11/2-3/2)
=(b+7)(b+4)