Factoring Review



Identify the type of factoring (simple/hard trinomial, difference of squares, perfect squares, common factoring, grouping, not factorable). You do NOT have to factor (but you can if you want!)Factor the following.a) 3x2a-7+5y(2a-7)b) 4a22a-5b-7b2(5b-2a)c) 12x24x2-7x+9-5xy4x2-7x+9-(4x2-7x+9)a) 5x2y3x2-11y2+4(3x2-11y2)b) 6x24x-7y-2y27y-4xc) 3a22a2+9ab-5b2+4ab2a2+9ab-5b2-2b22a2+9ab-5b2a) xm-xn+ym-ynb) 9am+3bm+6an+2bnc) 28x2-16xy+21x-12ya) x2-xz-xy+yzb) 21x3+2y-6x2y-7xc) 2x3-3x2+3-2xa) x3+x2+2x+2b) a3-3a+3-a2c) a+ab-ac-abca) a4-2a3-a3b+2a2bb) 3m3+12m2+12mn+3m2nc) 10m4-10m3n-15m3+15m2nFactor the following equation for surface area. SA=πa22-πb22Any 3-digit number can be represented by the expression 100x+10y+z where x,y,z?R. The reverse of the above number is 100z+10y+x. Prove that the difference of a 3-digit number and its reverse is divisible by 99.Solutionsa) 3x+5y(2a-7)b) 4a2+7b2(2a-5b)c) 4x2-7x+9(12x2-5xy-1)a) 5x2y+43x2-11y2b) 24x-7y(3x2+y2)c) 3a2+4ab-2b2(2a2+9ab-5b2)a) x+4m-nb) 3m+2n3a+bc) 4x+3(7x-4y)a) x-yx-zb) 7x-2y3x2-1c) 2x-3x-1(x+1)a) x2+2x+1b) a2-3a-1c) ab+a1-ca) a2a-2a-bb) 3mm+4m+nc) 5m2m-n(2m-3)SA=π4a+ba-bVarious solutions available.Factor the following.a) 4m2-6m-72b) (5m+2)2-(3m-8)2c) 9(2a+5b)2-4(7a-3b)2a) 49m2+70m+25b) 16s2+88s+121a) a2-b2+8bc-16c2b) 25-m2-12mn-36n2c) x2-a2-y2-2aya) x2+9y2-25z2-6xyb) x3+x2-x-1c) a2n-b2na) 8x3-64b) 64x3+1a) (x+y)3+(x-y)3b) (x+3)2+(x-3)31+64y6SOLUTIONSa) -4m+7(8m-7)b) 4m+5(4m-3)c) -8a+21b(20a+9b)a) (7m+5)2b) (4s+11)2a) a-b+4c(a+b-4c)b) 25-m-6n(25+m+6n)c) x-a-y(x+a+y)a) x-3y-5z(x-3y+5z)b) x+12(x-1)c) an-bnan+bna) 8x-2(x2+2x+4)b) 4x+1(16x2-4x+1)a) 2x(x2+3y2)b) 2x(x2+27)1+4x2(1-4y2+16y4) ................
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