5, 12
Let r = -6551 + 6599. Suppose 1652/3*x**4 + 0 - 992/3*x**3 + 196/3*x**5 + 0*x + r*x**2 = 0. What is x?
-9, 0, 2/7
Let o(h) = -6*h - 1. Let a(b) = b**2 + 4048*b + 4133086. Let x(c) = 2*a(c) - 6*o(c). Factor x(l).
2*(l + 2033)**2
Let q be 212/(-159)*(-18)/4. Let n(c) = 3*c**3 - 19*c**2 + c - 5. Let b(y) = 3*y**3 - 21*y**2 - 6. Let t(x) = q*n(x) - 5*b(x). Suppose t(g) = 0. What is g?
0, 1, 2
Let n(p) = -42*p**2 + 42*p + 44. Let r(a) = -20*a**2. Let k(z) = -n(z) + 2*r(z). Factor k(x).
2*(x - 22)*(x + 1)
Let 2/13*p**5 + 56/13*p**2 - 12/13*p**4 + 90/13*p - 12/13*p**3 + 36/13 = 0. Calculate p.
-1, 3, 6
Let q = 383 + -380. Factor 140*b**q + 4*b**5 - 44*b**4 + 0*b**5 + 1170*b**2 - 1270*b**2.
4*b**2*(b - 5)**2*(b - 1)
Suppose 4*i - 5*i = 0. Suppose -15*l + 5*l + 29 = -11. Determine r, given that -6/5*r**5 - 4/5 + 2*r + i*r**2 + l*r**4 - 4*r**3 = 0.
-2/3, 1
Let w = -616 - -618. Factor -7*h**2 + 2*h**w - 4*h**2 + 66*h + 12*h**2 - h**2.
2*h*(h + 33)
Let m be (7 + (-894)/126)/(2*2/(-28)). Suppose 4*c - 6 = 2. Let m*s**c - 8/3*s + 0 = 0. Calculate s.
0, 4
Factor -585*x**4 - 66 - 151*x + 586*x**4 - 44*x**3 + 27*x**3 - 103*x**2.
(x - 22)*(x + 1)**2*(x + 3)
Let o(t) be the first derivative of -2/3*t**3 + 1/30*t**6 + 20 + 1/2*t**4 - 1/5*t**5 - 11*t**2 + 0*t. Let d(y) be the second derivative of o(y). Factor d(j).
4*(j - 1)**3
Let b be (1 - -2) + ((-8)/2 - -1). Suppose b*q + 4*s = -3*q - 3, 2*q - s - 9 = 0. Factor 0*n**2 + 0*n - 3/5*n**4 + 0 + 9/5*n**q.
-3*n**3*(n - 3)/5
Let v = -84747 - -84747. Factor 0 - 18/5*g**2 + v*g**3 + 0*g + 2/5*g**4.
2*g**2*(g - 3)*(g + 3)/5
Let y = 491 + -483. Determine f, given that -3 - 8*f + y*f**4 - 30*f**2 + 27*f + 12*f**3 - 2*f = 0.
-3, 1/2
Let t(n) be the second derivative of 8/3*n**3 + 2*n - 1/6*n**4 - 15*n**2 - 33. Determine b so that t(b) = 0.
3, 5
Let b(q) be the second derivative of -q**4/8 - 351*q**3/2 + 2109*q**2/4 + 2*q - 2908. Determine r so that b(r) = 0.
-703, 1
Let w = -48 - -44. Let k be w*(3/(-18))/((-2)/(-6)). What is v in 4*v + 32 - 34 + 10*v**2 - 12*v**k = 0?
1
Factor 2/7*c**2 - 22/7*c + 8.
2*(c - 7)*(c - 4)/7
Let w = 24865 - 24857. Let i(q) be the first derivative of -48*q - w - 8/3*q**3 + 22*q**2. Factor i(y).
-4*(y - 4)*(2*y - 3)
Let u = -1268445/8 - -158556. Factor 0 + 15/4*i + 39/8*i**2 - u*i**4 + 3/4*i**3.
-3*i*(i - 5)*(i + 1)*(i + 2)/8
Let n(s) = 2*s**3 - 243*s**2 - 1031*s - 792. Let v(d) = -9*d**3 + 971*d**2 + 4122*d + 3164. Let t(b) = 11*n(b) + 3*v(b). Solve t(g) = 0.
-3, -1, 52
Let j be ((-70)/539)/((-1188)/154 - -7). Solve -j*q**3 - 2/11*q**4 + 0*q**2 + 0*q + 0 = 0 for q.
-1, 0
Let h be 896/30 - (-14)/105. Let -20557*o**4 - 169*o**3 + 300*o**2 + 4*o**3 + 20577*o**4 - 185*o + h = 0. Calculate o.
1/4, 1, 6
Let v be 3 + 2841/63 + 7. Let f = v + -55. Determine i, given that 50/21 - 20/21*i + f*i**2 = 0.
5
Let f(s) be the first derivative of 2*s**5/25 + 133*s**4/5 + 35906*s**3/15 + 35112*s**2/5 + 34848*s/5 - 1239. Factor f(z).
2*(z + 1)**2*(z + 132)**2/5
Let n = -811 - -799. Let r be (-5 + 10 - 6)/(4/n). Factor z**2 + 1/2*z - 1 - 1/2*z**r.
-(z - 2)*(z - 1)*(z + 1)/2
Let r = 132148 - 132148. Factor -3/5*o**4 + 48/5 + 48/5*o + r*o**2 - 12/5*o**3.
-3*(o - 2)*(o + 2)**3/5
Let j(g) be the second derivative of 1/42*g**7 - 19/6*g**6 - 17825/6*g**4 - 29791/2*g**2 + 6 + g + 62465/6*g**3 + 307/2*g**5. Solve j(l) = 0 for l.
1, 31
Suppose -4*w = 2*x - 70, 5*w - 5 = -15. Let o be 3/(-7)*(442/x - 12). Factor -o + 0*c + 6/7*c**2 - 4/7*c**3.
-2*(c - 1)**2*(2*c + 1)/7
Let i(n) = 2*n - 2. Let z(s) = 10158*s**2 + 3 - 43*s + s - 10155*s**2. Let y(x) = -12*i(x) - z(x). Factor y(p).
-3*(p - 7)*(p + 1)
Let q(r) be the first derivative of 8/27*r**3 + 4 + 0*r - 11/2*r**2 - 1/54*r**4 - 1/270*r**5. Let m(z) be the second derivative of q(z). What is k in m(k) = 0?
-4, 2
Let m(w) = -40*w - 98. Let k be m(-5). Solve -k*v**4 - 4*v**2 + 5*v**3 - 2*v**2 + 30*v**4 + 37*v**4 + 36*v**4 = 0.
-6, 0, 1
Let p(b) = -b + 23. Let w be p(21). Suppose 5 = g + w. Factor g*u**2 + 14*u**4 - 17*u**4 + 3*u**3 - 3*u**3.
-3*u**2*(u - 1)*(u + 1)
Let b(r) be the first derivative of -r**6/1800 - 4*r**5/75 - 2*r**3 + 19*r**2/2 - 279. Let o(g) be the third derivative of b(g). Suppose o(q) = 0. Calculate q.
-32, 0
Let o be ((25 + -21)*(-1)/2)/(-1). Let u be (-2)/(-5) + 2 - o/5. Factor -424/5*c**3 - 16*c**u - 266/5*c**4 + 176/5*c - 32/5 - 49/5*c**5.
-(c + 2)**3*(7*c - 2)**2/5
Let n be 2/28*142 - (-4)/(-28). Let t be (0 - -1)*(n + -10). Factor -10*x**3 - 20*x**2 + 15*x**3 + t*x**2.
5*x**2*(x - 4)
Let o(p) be the third derivative of p**8/5040 + p**7/630 - p**6/60 - 3*p**5/4 - p**2 + 1. Let f(j) be the third derivative of o(j). What is t in f(t) = 0?
-3, 1
Suppose 323*p + 288 = 339*p. Suppose 0 = 2*k + 2*b + 4, -14*k - b - 12 = -p*k. Factor -12/7*z + 30/7*z**k - 18/7.
6*(z - 1)*(5*z + 3)/7
Let f(b) = 19 + 19 + 30*b**2 - 3 - 5*b. Let q be (-9 + 4 + -6)*6/(-11). Let t(k) = 5*k**2 - k + 6. Let u(w) = q*f(w) - 35*t(w). Factor u(y).
5*y*(y + 1)
Let j(a) = -56*a - 432. Let q be j(-46). Let l be (q/(-1064) - -2)*-14. Factor 10/19*s**2 + l + 22/19*s.
2*(s + 2)*(5*s + 1)/19
Suppose -61*h - 1250 = -1372. Suppose 0 + 2/5*w**h - 12/5*w = 0. What is w?
0, 6
Let c(m) be the third derivative of -m**8/112 - m**7/70 + m**6/40 + m**5/20 - 17*m**2 + 5*m. Suppose c(f) = 0. Calculate f.
-1, 0, 1
Let c(a) = a**2 - 11*a + 13. Let s be c(11). Suppose -g + 2 = -2*j, s = 2*g + g + j. Factor -91*o**4 + 52*o**g - 5*o**2 + 44*o**4.
5*o**2*(o - 1)*(o + 1)
Suppose -5*c = 3*n - 18, c - 13 + 12 = 2*n. Suppose 3/7*m**c - 3/7*m - 6/7*m**2 + 6/7 = 0. What is m?
-1, 1, 2
Let n(v) = 24*v**2 + 254*v - 108. Let b be n(-11). Factor -6/5*u**b - 18/5 - 24/5*u.
-6*(u + 1)*(u + 3)/5
Let f(s) be the first derivative of 20 - 3*s**3 + 15/16*s**2 + 0*s - 15/32*s**4. Factor f(t).
-3*t*(t + 5)*(5*t - 1)/8
Suppose -q + 10 = 7. Let c(s) = -8*s**3 + 52*s**2 + 125*s + 65. Let u(m) = -25*m**3 + 155*m**2 + 375*m + 195. Let w(k) = q*u(k) - 10*c(k). Factor w(g).
5*(g - 13)*(g + 1)**2
Let t be (0 - 11) + -1 + -7 + 19. Let d(i) be the third derivative of 14*i**2 - 5/3*i**3 + t*i + 1/8*i**4 + 1/60*i**5 + 0. Factor d(m).
(m - 2)*(m + 5)
Let u(d) be the second derivative of -d**5/15 + d**4 + 6*d**2 + 59*d - 2. Let c(s) be the first derivative of u(s). What is b in c(b) = 0?
0, 6
Suppose 556 = t + 5*v, 8*t - 3*v + 566 = 9*t. Let h = -5222/9 + t. Factor -h*f**3 + 4/9 + 4/3*f - f**2.
-(f - 1)*(f + 2)*(7*f + 2)/9
Let c(l) be the third derivative of l**6/90 + 13*l**5/15 - 20*l**4/9 + 140*l**2. Factor c(i).
4*i*(i - 1)*(i + 40)/3
Let l(v) be the third derivative of v**5/80 + 569*v**4/96 - 95*v**3/12 + 4*v**2 - 60. Solve l(u) = 0 for u.
-190, 1/3
Suppose -5*h - 16 = -31. Suppose -m + 13 = 4*w, h = -0*m - m. Determine x so that 2*x - 2 - x - 2 - 8*x**3 + 7*x + w*x**4 = 0.
-1, 1
Let k(u) = -u**2 - 58*u + 784. Suppose -9*z + 7*z = 4. Let j(w) = 5*w**2 + 233*w - 3136. Let c(o) = z*j(o) - 9*k(o). Factor c(r).
-(r - 28)**2
Factor -37*m**3 - 219/2 + 181*m - 34*m**2 - 1/2*m**4.
-(m - 1)**2*(m + 3)*(m + 73)/2
Let j(k) be the first derivative of -2/17*k**2 - 1/34*k**4 + 0*k + 15 + 2/17*k**3. Let j(v) = 0. Calculate v.
0, 1, 2
Let d(f) be the third derivative of f**5/15 + 265*f**4/6 + 272*f**2. Determine u, given that d(u) = 0.
-265, 0
Suppose 68*q - 99115 = 25*q. Let w = q - 2303. Factor -2/5*r**3 - 486/5*r + 1458/5 + 54/5*r**w.
-2*(r - 9)**3/5
Let k(t) be the second derivative of t**4/66 - 53*t**3/11 + 468*t**2/11 + 614*t - 4. Determine b, given that k(b) = 0.
3, 156
Suppose -12 = -3*r + 39. Let a = r - 14. Factor 2*z**4 + 8*z**2 + z**4 + 3*z**4 - a*z**5 + 3*z - 14*z**2.
-3*z*(z - 1)**3*(z + 1)
Let j(s) be the first derivative of -s**5/5 - 153*s**4/4 - 152*s**3/3 - 4474. Determine w so that j(w) = 0.
-152, -1, 0
Let -3004/7*b**2 - 2/7*b**3 + 0 + 0*b = 0. What is b?
-1502, 0
Let o(k) be the third derivative of -2685619*k**6/40 + 637593*k**5/20 - 50457*k**4/8 + 1331*k**3/2 - 12*k**2 + 287*k. Factor o(q).
-3*(139*q - 11)**3
Let u be (1 + 0)*(1035/540)/((-1)/(-3)). Find g, given that -1 + 9/4*g**3 - u*g - 15/2*g**2 = 0.
-1/3, 4
Let u be 6/(-81) + (-980)/(-108) + -1. Let j be u/(-26)*962/(-148). Factor -20/7*c**j - 16/7*c + 0 - 4/7*c**3.
-4*c*(c + 1)*(c + 4)/7
Let a be 476/294 - 4/(-28)*-2. Let n(k) be the third derivative of -3/5*k**5 + 10