6/60 + 7*h**5/8 - 41*h**4/4 + h - 1561. Factor w(j).
j**2*(j - 6)*(j + 41)/2
Factor -121/3*p**2 + 134/3*p - 19/3 + 2*p**3.
(p - 19)*(p - 1)*(6*p - 1)/3
Let q = 197 + -177. Suppose -136 - 104 = -q*y. Factor -y*k**4 - 3/2*k**5 - 33*k**3 - 36*k**2 + 0 - 27/2*k.
-3*k*(k + 1)**2*(k + 3)**2/2
Let -3*h**3 - 161*h + 3603*h**2 - 6010*h + 1986*h**2 + 2324 - 4998*h + 3259 = 0. Calculate h.
1, 1861
Suppose -x - 5 = -0, 2*x + 12 = j. Suppose 7*b - 30 = 5*b - 4*g, 0 = j*b - 3*g - 16. Factor 8*a**3 - a**5 + b*a + 0*a**5 - 11*a - 2*a**4.
-a**3*(a - 2)*(a + 4)
Let 23206851*n**3 - 23206852*n**3 - 1864 - 528*n**2 + 66*n**2 + 1860*n = 0. What is n?
-466, 2
Let z(r) be the second derivative of r**4/24 - 35*r**3/6 + 69*r**2/4 + 3049*r. Factor z(q).
(q - 69)*(q - 1)/2
Let d(u) = -6*u**3 + u**2 - 2*u - 1. Let q(l) = 134*l**3 + 46*l**2 - 98*l + 94. Let t(j) = -44*d(j) - 2*q(j). Solve t(k) = 0 for k.
-36, 1
Let b be (-36)/21*(7*-3)/3. Factor -47*w - 120*w**2 - 65*w - 23*w**3 + b*w**3 - 32 - 25*w**3.
-4*(w + 2)*(3*w + 2)**2
Let z(n) be the second derivative of 6/13*n**2 + 7/39*n**3 + 0 + 1/78*n**4 + 45*n. Factor z(i).
2*(i + 1)*(i + 6)/13
Let a(w) be the second derivative of 2*w**6/15 - 13*w**5/5 + 10*w**4/3 + 16*w**3 + 1819*w. What is r in a(r) = 0?
-1, 0, 2, 12
Let p(h) = 3189*h + 60594. Let m be p(-19). Let -21/2*q**4 - m*q**5 + 27/2*q**3 + 12*q + 33*q**2 + 0 = 0. Calculate q.
-4, -1, -1/2, 0, 2
Let g(p) be the first derivative of 0*p + 0*p**2 + 0*p**4 + 1/5*p**5 + 0*p**3 + 40 - 1/6*p**6. Factor g(b).
-b**4*(b - 1)
Let r = -22 + 24. Suppose 62 = r*l + 5*o, -3*o = 5*l + 2*o - 125. Factor l*x**2 + 4*x**3 + 18*x - 9*x**2 - 2*x**3.
2*x*(x + 3)**2
Let b = -52076 - -104197/2. Find m such that b*m**5 + 12*m**4 - 1 - 11*m**2 + 19/2*m - 32*m**3 = 0.
-1, 2/15, 1/3, 1
Suppose -8*f + 18*f - 200 = 0. Let j be ((-50)/(-250))/(2/f). What is t in -3/2*t**j + 9/2*t + 0 = 0?
0, 3
Let n(f) be the second derivative of f**7/105 - 79*f**6/15 + 19601*f**5/25 - 19207*f**4/15 - 39203*f**3/15 + 38809*f**2/5 - 20*f + 40. Solve n(s) = 0.
-1, 1, 197
Let q be 445/(-900) + (-2 - 5/(-2)). Let y(p) be the third derivative of -1/36*p**4 + 1/18*p**3 - 6*p**2 + q*p**5 + 0*p + 0. Determine i so that y(i) = 0.
1
Suppose -144*u - 4/3*u**4 - 58/3*u**3 + 0 + 298*u**2 = 0. Calculate u.
-24, 0, 1/2, 9
Let n(v) be the third derivative of -v**6/10 + 119*v**5/15 - 293*v**4/6 - 74*v**3 + 834*v**2. Solve n(u) = 0.
-1/3, 3, 37
Let k be (-2)/3 - (3 + 20/(-12)). Let l be k/(-9) + (-2 - 86/(-18)). Factor 2630*h**l + 7203*h**4 + 1486*h**3 + 192 - 158*h**2 - 1606*h**2 - 672*h.
3*(7*h - 2)**2*(7*h + 4)**2
Suppose -4*v - 3*k = -6*k - 4732, 3*v + k = 3549. Let o = v + -1155. Factor -61/3*t**2 - 12*t**4 - 14/3*t - o*t**3 - 1/3.
-(t + 1)**2*(6*t + 1)**2/3
Let s(t) be the first derivative of -2*t**2 + 17/3*t**3 + 13/10*t**5 + 1 + 9*t - 14/3*t**4. Let l(v) be the first derivative of s(v). Solve l(x) = 0.
2/13, 1
Let m(j) be the second derivative of 14/3*j**3 + 6 + 0*j**2 + 2/21*j**7 + 24/5*j**5 + 6*j + 4/3*j**6 + 22/3*j**4. Factor m(w).
4*w*(w + 1)**3*(w + 7)
Factor -90*y**2 + 401956 + 112*y - 2648*y + 179*y**2 - 85*y**2.
4*(y - 317)**2
Let z(a) be the first derivative of -4/3*a**3 + 16 + 4*a**2 - a**4 + 0*a. Let z(j) = 0. What is j?
-2, 0, 1
Let g(t) be the first derivative of -t**6/6 + 22*t**5/5 - 153*t**4/4 + 272*t**3/3 + 224*t**2 - 6765. Factor g(d).
-d*(d - 8)**2*(d - 7)*(d + 1)
Suppose -17*t - 18*t = -39*t. Solve 93*o + t*o**2 - 65*o + 16*o**2 - 8 = 0 for o.
-2, 1/4
Let g = -3163 - -4649. Let w = g - 1482. Factor 2/7*l**2 - 8/7*l**w + 0 - 6/7*l**3 + 0*l.
-2*l**2*(l + 1)*(4*l - 1)/7
Let u(a) be the third derivative of -a**6/40 + 73*a**5/20 - 152*a**4 - 2166*a**3 + 4*a**2 + 85*a. Factor u(f).
-3*(f - 38)**2*(f + 3)
Factor 49*b**3 - 2188*b + 128*b**3 - 2184*b**2 - 173*b**3.
4*b*(b - 547)*(b + 1)
Let w(b) = b**2 - 8*b - 12. Let n be w(10). Suppose -5*a - 16 = -4*h, -2*h + 21*a = 19*a - n. Factor -3/8*m**3 + 0 + 3/4*m**h + 0*m**2 + 0*m - 3/8*m**5.
-3*m**3*(m - 1)**2/8
Let y = 14518 - 14518. Let s(g) be the second derivative of y*g**2 + 0*g**3 + 6/5*g**5 + 1/14*g**7 + 1/2*g**6 + g**4 - 11*g + 0. Factor s(v).
3*v**2*(v + 1)*(v + 2)**2
Let v = 1372 + -109719/80. Let g = v - -11/16. Factor 3/5*w - 3/5*w**3 + g - 6/5*w**2.
-3*(w - 1)*(w + 1)*(w + 2)/5
Let i(f) be the first derivative of f**8/5880 - f**6/1260 + 2*f**3/3 - 2*f**2 - 22. Let k(q) be the third derivative of i(q). Find n such that k(n) = 0.
-1, 0, 1
Factor -74*v**2 - 151*v**2 + 41*v**3 + 0*v**4 + 90*v + 444*v**2 - 10*v - 100 + 2*v**4.
(v + 1)*(v + 10)**2*(2*v - 1)
Let y = 9497 + -9474. Let m(b) be the first derivative of 15/7*b**3 - y - 3/7*b**4 + 0*b + 6/7*b**2. Factor m(t).
-3*t*(t - 4)*(4*t + 1)/7
Factor 409*s - 447*s**3 + 41*s + 223*s**3 - 105*s**2 + 229*s**3.
5*s*(s - 15)*(s - 6)
Let o(z) be the second derivative of -z**6/15 - 2*z**5/5 - z**4/3 + 4*z**3/3 + 3*z**2 - 541*z. Factor o(i).
-2*(i - 1)*(i + 1)**2*(i + 3)
Let h(p) be the third derivative of p**8/84 + 16*p**7/105 + p**6/5 - 8*p**5/3 + 25*p**4/6 - 6*p**2 + 177*p. Determine i so that h(i) = 0.
-5, 0, 1
Let d(n) be the first derivative of -n**4 + 0*n - 32*n**2 - 104 - 32/3*n**3. Factor d(g).
-4*g*(g + 4)**2
Suppose 2*r = 2 + 2. Let a(s) = -5*s**3 - 9*s**2 + s + 24. Let p be a(0). What is q in -p*q**r + 52*q**2 + 4 - q**3 - 31*q**2 = 0?
-2, 1
Determine c so that -1/9*c**5 - 1/3 + 2/9*c**3 - 1/9*c - 1/3*c**4 + 2/3*c**2 = 0.
-3, -1, 1
Let o(d) = d**3 + 4*d**2 + 20*d - 33. Let k be o(14). Factor -18 + 36*n**3 + 14*n**4 - k*n + 3741*n + 4*n**2 - 3*n**5 + n**5.
-2*(n - 9)*(n - 1)*(n + 1)**3
Let p(x) be the second derivative of -13*x**5/90 - x**4/6 + 10*x**3/9 - 8*x**2/9 - 3*x + 22. Find f, given that p(f) = 0.
-2, 4/13, 1
Factor 1/2*z**3 + 0 - 5/2*z + 2*z**2.
z*(z - 1)*(z + 5)/2
Let d = 8/37111 + 148420/111333. Determine b so that 0 + 68/3*b - 4/3*b**2 + d*b**4 - 68/3*b**3 = 0.
-1, 0, 1, 17
Let d = -112 - -159. Suppose 17*u - 80*u = -189. Solve 54*w**2 - 72*w**2 - 2*w**u + d + 3 - 30*w = 0 for w.
-5, 1
Let y(i) = 3*i**3 + 28*i**2 + 55*i - 76. Let z(p) = -2*p + 0 - 21*p**2 + 60*p**2 - 1 - 38*p**2. Let k(n) = y(n) + 5*z(n). Factor k(v).
3*(v - 1)*(v + 3)*(v + 9)
Let x(o) be the first derivative of 3/16*o**4 - 1/80*o**5 - 5/2*o**2 + 0*o - 5/8*o**3 + 13. Let j(w) be the second derivative of x(w). Factor j(f).
-3*(f - 5)*(f - 1)/4
Let m = -97029 + 97059. Factor 125/6*i**3 + 175/6*i**2 - 20*i - m.
5*(i - 1)*(5*i + 6)**2/6
Suppose 299*i + 2*i**3 - 466 - 313*i + 4*i**2 + 474 = 0. What is i?
-4, 1
Let s(j) be the second derivative of -1/189*j**7 + 1/27*j**6 + 0*j**2 + 0 - 5/54*j**4 + 4/27*j**3 - 1/30*j**5 + 126*j. Determine v so that s(v) = 0.
-1, 0, 1, 4
Let w = 69605 + -69602. Factor -18 + 4/9*y**w + 70/9*y**2 + 32*y.
2*(y + 9)**2*(2*y - 1)/9
Let b(q) be the second derivative of 5*q**4/36 - 55*q**3/4 - 3025*q**2/12 - 5240*q. Solve b(p) = 0 for p.
-11/2, 55
Let c(t) = 17*t**4 - 522*t**3 - 1053*t**2 + 510*t + 1044. Let u(p) = 20*p**4 - 525*p**3 - 1055*p**2 + 510*p + 1045. Let m(z) = 5*c(z) - 4*u(z). Solve m(i) = 0.
-2, -1, 1, 104
Let t(u) = -5*u**2 + 10*u + 16. Let h(o) = 92*o**2 - 182*o - 288. Let d(p) = -6*h(p) - 111*t(p). Let d(v) = 0. Calculate v.
-2, 8
Let x(k) be the third derivative of k**9/3024 + k**8/560 + k**7/280 + k**6/360 - 71*k**3/6 - 7*k**2. Let y(t) be the first derivative of x(t). Factor y(j).
j**2*(j + 1)**3
Let t(x) = x**4 + x**3 - 5*x - 2. Let q(z) = -8*z**4 - 32*z**3 - z**2 + 2024*z - 5188. Let m(k) = 2*q(k) + 14*t(k). Find l such that m(l) = 0.
-17, 3, 6
Let y = 8484/5 - 1399858/825. Let i = 148/825 + y. Let i*s + 2/11*s**2 + 0 = 0. Calculate s.
-1, 0
Let x(k) = 3*k**3 + k + 1. Let m(n) = 2*n**3 - 1000*n**2 + n + 1. Let i(r) = 4*m(r) - 4*x(r). Determine u, given that i(u) = 0.
-1000, 0
Let r be (396/66)/(-3 + 14). Factor 6/11*u**2 - r*u + 0.
6*u*(u - 1)/11
Let q(l) = l**2 + 3123*l + 18704. Let m be q(-6). Factor 0 + 0*o**4 - 4/3*o**2 + 2/3*o**5 + 0*o - m*o**3.
2*o**2*(o - 2)*(o + 1)**2/3
Let q(u) be the third derivative of -1/80*u**6 + 0*u - 11/4*u**3 - 23/16*u**4 - 13/40*u**5 + 0 - 89*u**2. Factor q(b).
-3*(b + 1)**2*(b + 11)/2
Let x = -62 + 83. Suppose 2*s = 5*c - x, 5*c - 11 = s + 12. Solve 8*p**s + 8*p**3 - 20*p**2 - 214*p + 206*p = 0.
-1/2, 0, 2
Suppose -18 = c - 5*x, 0*c + 4*c + 5*x - 28 = 0