Đáp án:
Giải thích các bước giải:
Bài 1
a)15x²+7x-2
= 15x²-3x+10x-2
=3x(5x-1)+2(5x-1)
=(3x+2)(5x-1)
b)2x²+5x+2
=2x²+4x+x+2
=2x(x+2)+(x+2)
=(2x+1)(x+2)
Bài2
a)$x^{4}$ +x²-2
=$x^{4}$+2x²-x²-2
=x²(x²+2)-(x²+2)
=(x²-1)(x²+2)
=(x-1)(x+1)(x²+2)
b)$x^{4}$+4x²-5
=$x^{4}$-x²+5x²-5
=x²(x²-1)+5(x²-1)
=(x²+5)(x²-1)
=(x²+5)(x-1)(x+1)
c)x³-19x-30
=x³-4x-15x-30
=x(x²-4)-15(x+2)
=x(x+2)(x-2)-15(x+2)
=[x(x-2)-15](x+2)
=(x²-2x-15)(x+2)
=(x²-2x+1-16)(x+2)
=[(x-1)²-4²](x+2)
=(x-1+4)(x-1-4)(x+2)
=(x+3)(x-5)(x+2)
d)x³-7x-6
=x³-x-6x-6
=x(x²-1)-6(x+1)
=x(x-1)(x+1)-6(x+1)
=[x(x-1)-6](x+1)
=(x²-x-6)(x+1)
=(x²-2x*$\frac{1}{2}$ +$\frac{1}{4}$ - 6-$\frac{1}{4}$)(x+1)
=[(x-$\frac{1}{2}$)²-$\frac{25}{4}$ )(x+1)
=(x-$\frac{1}{2}$-$\frac{5}{2}$)(x-$\frac{1}{2}$+$\frac{5}{2}$)(x+1)
=(x-3)(x+2)(x+1)
e)x³-5x²-14x
=x³-2x²+7x²-14x
=x²(x-2)+7x(x-2)
=(x²+7x)(x-2)
=x(x+7)(x-2)
