**TI86** Program file dated 06/23/04, 19:57 0 ZTHEOR1D àToìoé-FACTORING POLYNOMIALSoëD3/D3/-F1 GENERALLY F2 SPECIAL FACTORSoëD5/D3/-F3 BINOMIAL THEOREM F4 QUADRATICSoLD1/-F1/3A/D2/-F2/3B/D3/-F3/3C/D4/-F4/3D/D5/-EXIT/3XoàXnßoàQnD1 3KnßoàAo7ZINITn4ZLoŽD0/D5/-FUNDAMENTAL THEOREM OF ALGEBRAo6ZLINoŽD9/D0/-AN nTH DEGREE POLYNOMIAL HAS noŽD15/D0/-ZEROS. A ZERO IS THE VALUE OF THE xoŽD21/D0/-VARIABLE THAT MAKES A POLYNOMIALoŽD27/D0/-=0. THE ZEROS OF A POLYNOMIAL AREoŽD33/D0/-ALSO ITS roots. ZEROS MAY BE IMAG-oŽD39/D0/-INARY, THOUGH REAL POLYNOMIALSo4ZKoLD1/4MO/4A1/D2/4PR/3T/D4/4EX/3T/D5/4QU/3QoàA1oƒo4ZLoŽD0/D0/-OF ODD DEGREE MUST HAVE AT LEASToŽD6/D0/-ONE real ZERO.o4ZKoLD2/4PR/3A/D4/4EX/3T/D5/4QU/3QoàBo7ZINITo4ZLoŽD0/D0/-SPECIAL FACTORS:oŽD12/D0/-x-A =(x-A)(x+A)oŽD18/D0/-x^3-A^3=(x-A)(x+Ax+A)oŽD24/D0/-x^3+A^3=(x+A)(x-Ax+A)oŽD30/D0/-x^4-A^4=(x-A)(x+A)(x+A)oŽD36/D0/-x^4+x^4=(x+2Ax+A)(x-2Ax+A)o4ZKoLD1/4MO/4B1/D2/4PR/3T/D4/4EX/3T/D5/4QU/3QoàB1oƒo4ZLoŽD0/D0/-x^n-A^n=(x-A)(x^(n-1)+Ax^(n-2)+...oŽD6/D90/-+A^(n-1))oŽD12/D0/-FOR ODD noŽD18/D0/-x^n+A^n=(x+A)(x^(n-1)-Ax^(n-2)+...oŽD24/D90/-+A^(n-1)oŽD30/D0/-x^(2n)-A^(2n)=(x^n-A^n)(x^n+A^n)o4ZKoLD1/4MO/4B2/D2/4PR/3B/D4/4EX/3T/D5/4QU/3QoàB2oƒo4ZLoŽD0/D0/-SPECIAL FACTOR EXAMPLES:oŽD6/D0/-x-4=(x-2)(x+2)oŽD12/D0/-x^3-64=(x-4)(x+4x+16)oŽD18/D0/-x^3+64=(x+4)(x-4x+16)oŽD24/D0/-x^4-32=(x-2)(x+2)(x+4)oŽD30/D0/-x^4+32=(x+2*2+4)(x-2*2x+4)oŽD36/D0/-x^5-64=(x-2)(x^4+2x^3+2x+2x+32)o4ZKoLD1/4MO/4B3/D2/4PR/4B1/D4/4EX/3T/D5/4QU/3QoàB3oƒo4ZLoŽD0/D0/-x^5+64=(x+2)(x^4-2x^3+2x-2x+32)oŽD6/D0/-x^8-2=(x^4-16)(x^4+16)o4ZKoLD2/4PR/4B2/D4/4EX/3T/D5/4QU/3QoàCo7ZINITn4ZLoŽD0/D0/-BINOMIAL THEOREMoŽD8/D0/-(x+A)=x+2Ax+AoŽD14/D0/-(x-A)=x-2Ax+AoŽD20/D0/-(x+A)^3=x^3+3Ax+3Ax+A^3oŽD26/D0/-(x-A)^3=x^3-3Ax+3Ax-A^3oŽD32/D0/-(x+A)^4=x^4+4Ax^3+6AxoŽD38/D40/-+4(A^3)x+A^4o4ZKoLD1/4MO/4C1/D2/4PR/3T/D4/4EX/3T/D5/4QU/3QoàC1oƒo4ZLoŽD0/D0/-(x-A)^4=x^4-4Ax^3+6AxoŽD6/D40/--4(A^3)x+A^4oŽD12/D0/-(x+A)^n=(x^n)+nAx^(n-1)+((n(n-1))oŽD18/D9/-/2!)Ax^(n-2)+...+nA^(n-1)x+A^noŽD24/D0/-(x-A)^n=x^n-nAx^(n-1)+(n(n-1)/2!)oŽD30/D9/-*Ax^(n-2)-...+-nA^(n-1)x-+A^noŽD38/D0/-EXAMPLES:(x+2)=x+4x+4o4ZKoLD1/4MO/4C2/D2/4PR/3C/D4/4EX/3T/D5/4QU/3QoàC2oƒo4ZLoŽD0/D0/-(x-4)=x^4-8x+16oŽD6/D0/-(x+2)^3=x^3+6x+12x+8oŽD12/D0/-(x-2)^3=x^3-6x+12x-8oŽD18/D0/-(x+2)^4=x^4+8x^3+24x+32x+16oŽD24/D0/-(x-4)^4=x^4-16x^3+96x-256x+256oŽD30/D0/-(x+2)^5=x^5+10x^4+40x^3+80x+80x+32oŽD36/D0/-(x-2)^6=x^6-12x^5+60x^4-160x^3oŽD42/D9/-+240x+192x+64o4ZKoLD2/4PR/4C1/D4/4EX/3T/D5/4QU/3QoàDo7ZINITo4ZLoŽD0/D20/-COMPLETING THE SQUAREo6ZLINoŽD10/D0/-x+Ax+b=(x+Ax+(A/2))-(A/2)+boŽD16/D0/-(x+(A/2))=(A/2)-boŽD22/D0/-x+A/2=(A/2)-b)oŽD28/D0/-x=(A/2)-b)-A/2oŽD34/D0/-ie. x+8x+3=0oŽD40/D0/-(x+8x+16)-16+3=0o4ZKoLD1/4MO/4D1/D2/4PR/3T/D4/4EX/3T/D5/4QU/3QoàD1oƒo4ZLoŽD0/D0/-(x+4)-13=0oŽD6/D0/-(x+4)=13oŽD12/D0/-x+4=13oŽD18/D0/-x=13-4oŽD24/D0/-QUADRATIC FORMULA: Let Ax+bx+c=0oŽD32/D30/-Then x=(b+-(b-4Ac)o–D56/D23/D106/D23oŽD40/D75/-2AoŽD41/D0/-ie. 3x+5x-4=0o4ZKoLD1/4MO/4D2/D2/4PR/3D/D4/4EX/3T/D5/4QU/3QoàD2oƒo4ZLoŽD0/D0/-x=(1/6)(5+-(25+48)oŽD6/D0/-x=(5+73)/6 AND x=(5-73)/6oŽD12/D0/-ALWAYS CHECK THIS RESULT BY PLUG-oŽD18/D0/-GING x INTO THE EQUATION.oŽD24/D0/-ie.2x-3x+1=4oŽD30/D0/-2x-3x+5=0oŽD36/D0/-x=(1/4)(3+-(9+40))oŽD42/D0/-x=(1/4)(3+-7) THUS,x=5/2, x=1o4ZKoLD1/4MO/4D3/D2/4PR/4D1/D4/4EX/3T/D5/4QU/3QoàD3oƒo4ZLoŽD0/D25/-FACTOR BY GROUPINGoŽD6/D0/-acx^3+adx+bcx+bdoŽD12/D0/-=ax(cx+d)+b(cx+d)oŽD18/D0/-=(ax+b)(cx+d)oŽD24/D0/-EXAMPLE: 15x^3-10x-8x+6oŽD30/D0/-=5x(4x+3)+2(4x+3)oŽD36/D0/-=(5x+2)(4x+3)o4ZKoLD2/4PR/4D2/D4/4EX/3T/D5/4QU/3Q¶¶