已知:A=ax2+x-1,B=3x2-2x+1(a為常數(shù))
(1)若A與B的和中不含x2項(xiàng),求a的值.
(2)在(1)的基礎(chǔ)上化簡(jiǎn):B-2A,并求出當(dāng)x=-1時(shí),B-2A的值.
解:(1)A+B=ax2+x-1+3x2-2x+1=(a+3)x2-x,
∵A與B的和中不含x2項(xiàng),
∴a+3=0,
則a=-3;
(2)B-2A=3x2-2x+1-2×(-3x2+x-1)
=3x2-2x+1+6x2-2x+2
=9x2-4x+3,
當(dāng)x=-1時(shí),
原式=9-4×(-1)+3=10.
分析:(1)A與B的和中不含x2項(xiàng),即x2項(xiàng)的系數(shù)為0,依此求得a的值;
(2)先將表示A與B的式子代入B-2A,再去括號(hào)合并同類項(xiàng).
點(diǎn)評(píng):本題考查了整式的加減,解答本題的關(guān)鍵是掌握多項(xiàng)式加減的運(yùn)算法則,合并同類項(xiàng)的法則.