w**4 - 1/90*w**6 + 0*w**3. Factor p(n).
-n**3*(n - 1)*(n + 2)/3
Suppose -12*j - 20 = 3*b - 8*j, -20 = 4*j. Let w be (-2 - 192/(-105))/((-108)/720). Factor -2*o**2 - 6/7*o**3 + b*o + w.
-2*(o + 1)*(o + 2)*(3*o - 2)/7
Let p = 5472338153/11622 + -6121086/13. Let j = p + -4/447. Factor -j*c**2 + 3/2 + 6*c.
-3*(c - 1)*(5*c + 1)/2
Let c be 23 + -10 + -30 - -19. Factor -9/8*x**c + 3*x - 2 + 1/8*x**3.
(x - 4)**2*(x - 1)/8
Let u(m) be the second derivative of -m**4/4 + 41*m**3 + 1950*m. Let u(j) = 0. What is j?
0, 82
Let z(a) = -115*a**2 + 227*a**2 - 17 + 0 + 19*a - 109*a**2. Let d(j) = -3*j**2 - 21*j + 18. Let c(l) = 5*d(l) + 6*z(l). Factor c(s).
3*(s - 1)*(s + 4)
Factor 72*m**2 - 198*m**2 + 44 - 17 - 7*m**4 - 51*m**3 - 31 - 116*m - 20.
-(m + 2)**2*(m + 3)*(7*m + 2)
Suppose -2848*j + 29893/3*j**3 + 1708/3 - 49/3*j**5 - 1261/3*j**2 + 6951*j**4 = 0. Calculate j.
-1, 2/7, 427
Let m(j) be the third derivative of -j**7/70 + 41*j**6/40 - 79*j**5/20 + 39*j**4/8 + 4*j**2 + 10. Determine p so that m(p) = 0.
0, 1, 39
Let b be (10605/(-126) - -85) + (-146)/(-84). Determine z, given that 2/7*z**3 - b*z + 16/7*z**2 + 0 = 0.
-9, 0, 1
Let i(k) be the first derivative of k**4/8 - 11*k**3/6 - 3*k**2 - 1078. Suppose i(c) = 0. What is c?
-1, 0, 12
Suppose 0 = -3*c - 133*c. Let l(s) be the second derivative of c*s**3 - 8*s + 0*s**4 + 0 - 1/150*s**6 - 1/100*s**5 + 0*s**2. What is m in l(m) = 0?
-1, 0
Let u(l) = l**4 - 13*l**3 - l**2 + 3*l - 3. Let x(o) = 5*o**4 + 103*o**3 + 1529*o**2 + 1401*o - 9. Let z(v) = 6*u(v) - 2*x(v). Determine i so that z(i) = 0.
-58, -12, -1, 0
Suppose 0*g + 141 = -4*g - 5*h, 0 = -2*g + 2*h - 66. Let o = g - -37. What is l in -32 + 20*l**3 + 0*l**4 + o*l**4 - 16*l + l**4 - 3*l**2 + 27*l**2 = 0?
-2, 1
Let s(o) be the third derivative of -3/2*o**5 + 0 - 2*o**2 + 95/3*o**3 + 35/8*o**4 + 19*o - 1/24*o**6. Factor s(h).
-5*(h - 2)*(h + 1)*(h + 19)
Let g(q) = 12*q**2 + 145*q - 1603. Let x be g(7). Let m(z) = -z**3 + 7*z**2 - 6*z. Let a be m(6). Factor -1/2*k**5 + 0*k**2 + 1/2*k**3 + x + 0*k + a*k**4.
-k**3*(k - 1)*(k + 1)/2
Suppose -73*d - 5*a = -77*d - 13, 4*d - 4*a + 8 = 0. Suppose -2*k = -3 - 1. Find y, given that 0 - 1/3*y**d + 2/3*y - 1/3*y**k = 0.
-2, 0, 1
Suppose -16*r**2 + 10*r**5 - 45*r**3 + 184*r**4 - 73*r**3 - 29*r**2 - 31*r**2 = 0. Calculate r.
-19, -2/5, 0, 1
Let f = -226 + 230. Let 34*j - 55*j**2 - 2*j**4 - 4*j - 3*j**f + 30*j**3 = 0. Calculate j.
0, 1, 2, 3
Factor 175*v**4 - 228*v**2 + 173*v**4 + 355*v + 41*v - 344*v**4 + 20*v**3.
4*v*(v - 3)**2*(v + 11)
Let l(w) be the first derivative of -80*w**3 + 11520*w**2 - 737280*w + 319 + 5/24*w**4. Factor l(x).
5*(x - 96)**3/6
Let k(q) be the first derivative of -3*q**5/5 + 2397*q**4/4 - 159200*q**3 - 240000*q**2 - 2753. Suppose k(a) = 0. What is a?
-1, 0, 400
Let m(y) = y**2 + y + 1. Let o(d) be the third derivative of d**5/60 - 11*d**4/24 - 4*d**3/3 - 30*d**2. Let n(f) = 4*m(f) - o(f). Factor n(j).
3*(j + 1)*(j + 4)
Let z(v) be the third derivative of 10*v + 0 - 1/10*v**5 + 1/2*v**3 + 1/8*v**4 - 7*v**2 + 1/112*v**8 - 1/20*v**6 + 1/70*v**7. Suppose z(j) = 0. Calculate j.
-1, 1
Factor 1829276567/4 + 1/4*x**3 + 4487187/4*x + 3669/4*x**2.
(x + 1223)**3/4
Suppose -16*b - 13*b + 33*b = 0. Let u(i) be the second derivative of 0 + 6*i + b*i**2 + 1/40*i**5 - 1/6*i**4 + 0*i**3. Factor u(f).
f**2*(f - 4)/2
Suppose -16*m - 9*m - 172 = -222. Find w such that 0*w + 3/7*w**m - 3/7 = 0.
-1, 1
Suppose -875880 = 527*l - 2149*l. Let -5/2*n**4 - l*n**2 + 3645/2 + 65*n**3 + 1215*n = 0. Calculate n.
-1, 9
Let w(l) = -9*l**2 + 795*l + 660. Let p(q) = -8*q**2 + 794*q + 689. Let r(u) = 6*p(u) - 7*w(u). Factor r(g).
3*(g - 54)*(5*g + 3)
Let i(w) be the first derivative of w**4/20 + 17*w**3/15 - 19*w**2/5 + 1844. Factor i(x).
x*(x - 2)*(x + 19)/5
Suppose -t = 2*d + 12, -3*t + 0*t = -d - 6. Let y be d/14 - -183*(-8)/(-280). Factor -18*n**4 - 15*n**5 - y*n**2 + 0 + 108/5*n**3 + 0*n.
-3*n**2*(n + 2)*(5*n - 2)**2/5
Let o = 182 + -178. Factor -o*z**5 - 457*z**3 - 576*z - 70*z**4 + 165*z**3 + 14*z**4 - 672*z**2.
-4*z*(z + 3)**2*(z + 4)**2
Suppose -8*j + 493 = 477. Factor 112*a**j + 123*a**2 - 238*a**2 + 150 + 147*a.
-3*(a - 50)*(a + 1)
Suppose 3*j - 249 = 4*t, 0 = 9*j - 5*j + 4*t - 304. Suppose -j*x = -100*x + 84. Find o, given that 25/7*o**3 + 0 - 2*o**x + 8/7*o**2 - 4/7*o = 0.
-1/2, 0, 2/7, 2
Determine f so that f + 3/5*f**3 + 9/5*f**2 + 0 - 1/5*f**4 = 0.
-1, 0, 5
Suppose 7*z + 177 = -174 + 372. Suppose 0 + 0*p - 9/2*p**2 + 1/2*p**z = 0. Calculate p.
0, 9
Factor -2*q**4 + 8/3*q**2 + 2/3*q**5 + 0 + 0*q + 0*q**3.
2*q**2*(q - 2)**2*(q + 1)/3
Let x(h) be the first derivative of 5*h**6/6 - 12*h**5 + 15*h**4/4 + 1040*h**3/3 + 480*h**2 - 4105. Factor x(j).
5*j*(j - 8)**2*(j + 1)*(j + 3)
Let j be (-3 - -4) + 0 + 4. Determine v so that -48*v - 43 + 133 - j*v**2 + 133*v = 0.
-1, 18
Suppose 0 = -4*n - 3*j + 1, -3*j = -4*n + 31. Factor -28*o**2 + 13*o**2 + 3*o**n + 3*o**3 - 3*o**3 - 12*o**3.
3*o**2*(o - 5)*(o + 1)
Let m(t) = 2408*t - 269690. Let q be m(112). Suppose 0 + 10*j**2 - 8/5*j**5 - q*j**4 + 0*j**3 - 12/5*j = 0. Calculate j.
-3, -2, 0, 1/4, 1
Let m(i) = 83*i**2 - 701*i + 2011. Let o(t) = 200*t**2 - 1752*t + 5028. Let h(z) = 12*m(z) - 5*o(z). Solve h(v) = 0.
3, 84
Factor 1/2*x**2 - 185/2 - 92*x.
(x - 185)*(x + 1)/2
Let h = 175 + -171. Determine n so that 5*n**h + 5*n**3 - 3*n**2 + 3*n**2 + 0*n**3 = 0.
-1, 0
Let p(i) = -i**5 - i**4 + 2*i**3 + i**2 - 3. Let j(w) = -4*w**5 + 37*w**4 - 519*w**3 + 2253*w**2 - 9. Let t(r) = -j(r) + 3*p(r). Factor t(b).
b**2*(b - 15)**2*(b - 10)
Let f be (13 - 2397/187)*(-3)/((-48)/44). Suppose 16*o = 20*o. Factor f*v**2 + 5/2*v**4 + v**5 + 2*v**3 + o + 0*v.
v**2*(v + 1)**2*(2*v + 1)/2
Let w(s) be the third derivative of 2 + 0*s - 7/264*s**4 - 1/660*s**5 - 2/11*s**3 - 25*s**2. Suppose w(g) = 0. Calculate g.
-4, -3
Let v be (-2601)/(-1190) - (-1 + 187/238). Factor v*m - 3/5*m**2 + 3.
-3*(m - 5)*(m + 1)/5
Let q(z) = -z**2 + 12*z - 2. Let m be q(10). Let o be 4/15*45/m. Factor 2/3 + 2/9*g - o*g**2 - 2/9*g**3.
-2*(g - 1)*(g + 1)*(g + 3)/9
Let z(w) be the first derivative of -3/8*w**2 + 3/16*w**4 + 5 - 5/8*w**3 + 3/8*w**5 + 0*w. Solve z(b) = 0.
-1, -2/5, 0, 1
Let g(b) = 19*b - 2446. Let m be g(129). Solve 0*q + 4/5*q**4 + 0 + 6/5*q**3 + 0*q**2 - 2/5*q**m = 0 for q.
-1, 0, 3
Let g(m) be the third derivative of m**8/112 + 542*m**7/35 + 297001*m**6/40 + 175607*m**5/2 + 873719*m**4/2 + 1162084*m**3 - 6689*m**2. What is p in g(p) = 0?
-539, -2
Suppose -5*p - 62 + 87 = 5*f, -6*p = -4*f. Let z(c) be the second derivative of 0*c**3 - 1/40*c**6 + 0 + 0*c**p - 4*c + 3/20*c**5 - 3/16*c**4. Factor z(m).
-3*m**2*(m - 3)*(m - 1)/4
Determine h so that 7938 + 32*h**2 + 7*h**2 - 7872 - 2*h**3 - 107*h + 4*h**3 = 0.
-22, 1, 3/2
Let k(d) = -137*d**3 + 103*d**2 - 419*d + 327. Let a(i) = 434*i**3 - 309*i**2 + 1256*i - 982. Let z(o) = -6*a(o) - 19*k(o). Determine n, given that z(n) = 0.
-107, 1, 3
Let g(h) = 20*h**2 + 58*h - 59 + 16*h**2 - 39*h**2. Let z(y) = -30*y**2 + 579*y - 591. Let k(i) = -21*g(i) + 2*z(i). Let k(u) = 0. Calculate u.
1, 19
Let b(o) be the second derivative of -o**4/32 - 133*o**3/16 - 99*o**2/4 + 2982*o. Factor b(n).
-3*(n + 1)*(n + 132)/8
Let u = -11120/3 + 3708. Let m(f) be the third derivative of -u*f**3 + 1/30*f**6 + 0 - 20*f**2 - 4/15*f**5 + 0*f + 5/6*f**4. Factor m(j).
4*(j - 2)*(j - 1)**2
Let s(j) be the third derivative of j**5/210 - 73*j**4/42 + 5329*j**3/21 - 126*j**2. Factor s(z).
2*(z - 73)**2/7
Suppose -1201*v + 820 = 1011*v - 1883*v - 167. Let j be -2*(18/(-8) - -2). Solve -2*r**v - 9/2 + 6*r - j*r**4 + r**2 = 0.
-3, 1
Let v(p) be the first derivative of -p**5/10 + 7*p**4/4 - 13*p**3/2 - 27*p**2/2 - 3529. Factor v(g).
-g*(g - 9)*(g - 6)*(g + 1)/2
Let q(z) be the first derivative of -1/4*z**5 - 3*z**2 - 1 + 0*z + 1/4*z**4 + 0*z**3 - 3/40*z**6. Let i(h) be the second derivative of q(h). Factor i(w).
-3*w*(w + 2)*(3*w - 1)
Let d(i) be the first derivative of i**4/16 - i**3/3 - 11*i**2/8 + 15*i/2 + 622. Determine h so that d(h) = 0.
-3, 2, 5
Let b be (0 - (-6 - -5))*2. Solve -i**3 - 105*i + 9707*i**2 - 75 - 2*i**3 - 9740*i**b = 0.
-5, -1
Factor 1/6*z**2 + 26912/3 - 232/3*z.
(z - 232)**2/6
Let i(o) be the third derivative of -20*o**2 + 1/2184*o**8 + 1/78*o**4 + 0*o**3 + 0*o + 3/260*o**6 + 7/390*o