 4
Suppose -15*q = 131*q - 584. Let p(b) be the first derivative of 45/4*b**q + 25/6*b**6 + 3 + 10/3*b**3 + 0*b**2 + 12*b**5 + 0*b. Factor p(h).
5*h**2*(h + 1)**2*(5*h + 2)
Let v(y) = -y - 4. Let c be v(-7). Suppose 9*q - 42 = 2*q. Solve -4*f - f**c - 2*f**3 + f + q*f**2 = 0.
0, 1
Let l(g) be the first derivative of 5*g**8/336 + 47*g**7/504 + g**6/6 + g**5/18 + 2*g**3 - 22. Let y(m) be the third derivative of l(m). What is k in y(k) = 0?
-2, -1, -2/15, 0
Let x(c) be the first derivative of -76*c**5/35 - 117*c**4/14 - 82*c**3/7 - 47*c**2/7 - 6*c/7 + 1111. Let x(f) = 0. Calculate f.
-1, -3/38
Find a such that 4*a**3 - 21/2*a - 2 + 15*a**4 + 13/2*a**5 - 13*a**2 = 0.
-1, -4/13, 1
Suppose 0 = -5*l + 20, -2*a = 2*l - 76 + 62. Let g(z) be the third derivative of 12*z**2 + 1/3*z**4 + 1/15*z**5 + 2/3*z**a + 0*z + 0. Find h such that g(h) = 0.
-1
Let q(t) be the third derivative of -t**8/112 + 3*t**7/70 + 13*t**6/20 + 9*t**5/10 - 25*t**4/8 - 21*t**3/2 + 162*t**2 + 8*t. Let q(s) = 0. Calculate s.
-3, -1, 1, 7
Suppose -15*d - 27 = -25 - 107. Let j(x) be the second derivative of 3/14*x**d + 19/15*x**6 + 31/10*x**5 + 4*x**4 + 0 + 17*x + x**2 + 17/6*x**3. Factor j(g).
(g + 1)**4*(9*g + 2)
Suppose -a = 2*y - 3*a - 4, 0 = -5*y + 4*a + 13. Suppose -2*x = -2*u - 10, 4*u + 1 = -y*x - 19. Factor 6/17*f + 2/17*f**2 + x.
2*f*(f + 3)/17
Let t be (-160)/(-35) - (-4)/(-7). Let 6*w**3 - 35*w**2 + 3*w**3 + 30*w - t*w**3 = 0. Calculate w.
0, 1, 6
Factor 114/7*i**2 - 15/7*i**4 - 129/7*i + 3/7*i**5 + 45/7 - 18/7*i**3.
3*(i - 5)*(i - 1)**3*(i + 3)/7
Suppose -1/4*f**4 + 849/2*f**2 - 425*f + 567/4 - 141*f**3 = 0. Calculate f.
-567, 1
Let q(j) be the second derivative of j**5/4 + 125*j**4/12 - 5*j**3/6 - 125*j**2/2 - 25*j + 25. Factor q(w).
5*(w - 1)*(w + 1)*(w + 25)
Let t(c) = c**3 - 72*c**2 + 721*c - 12. Let i be t(12). Solve -2/5*q**4 + 2/5*q**2 + 2/5*q**5 + 4/5*q + i - 6/5*q**3 = 0.
-1, 0, 1, 2
Let k(i) be the second derivative of -i**5/20 + 19*i**4/4 + 10*i**3 - 58*i**2 + i - 476. Determine u, given that k(u) = 0.
-2, 1, 58
Determine y so that 0 - 108*y + 69/2*y**3 + 3/4*y**4 - 297/4*y**2 = 0.
-48, -1, 0, 3
Let l = 440544 - 440544. Factor l - 16/5*t + 2/5*t**3 - 4/5*t**2.
2*t*(t - 4)*(t + 2)/5
Solve 88/5*l**2 - 32/5*l + 58/5*l**3 + 1/5*l**5 + 13/5*l**4 - 128/5 = 0.
-4, -2, 1
Let b(g) be the first derivative of g**6/80 - 9*g**5/160 - g**4/32 + 3*g**3/16 + 286*g - 297. Let x(q) be the first derivative of b(q). Factor x(o).
3*o*(o - 3)*(o - 1)*(o + 1)/8
Let r = 12486/11 - 1134. Factor 2/11*v**3 - r*v + 16/11 - 6/11*v**2.
2*(v - 4)*(v - 1)*(v + 2)/11
Suppose -31*b + 116 = 23. Factor 23 + 5*l + l**5 - 26 - 6*l**b + 2*l**2 + 355*l**4 - 354*l**4.
(l - 1)**3*(l + 1)*(l + 3)
Let h(a) = -2*a**3 - 1198*a**2 + 9198*a - 7996. Let x(j) = -2*j**4 - 7*j**3 - 4791*j**2 + 36791*j - 31982. Let m(u) = 9*h(u) - 2*x(u). Factor m(y).
4*(y - 10)**2*(y - 1)*(y + 20)
Let h(c) be the third derivative of -c**5/180 + 16*c**4/3 - 382*c**3/9 - 647*c**2. Solve h(i) = 0.
2, 382
Let n(v) be the third derivative of v**5/12 + 440*v**4/3 + 309760*v**3/3 + 6965*v**2. Factor n(y).
5*(y + 352)**2
Let u(k) = -8*k**4 + 16*k**3 + 407*k**2 + 985*k + 625. Let h(i) = 2*i**4 - 4*i**3 - 102*i**2 - 246*i - 156. Let y(p) = 23*h(p) + 6*u(p). Factor y(q).
-2*(q - 9)*(q + 1)*(q + 3)**2
Let q(c) be the third derivative of -c**5/12 + 40*c**4/3 + 110*c**3 + 452*c**2. Find r such that q(r) = 0.
-2, 66
Let p(w) be the third derivative of 9*w**2 + 1/1500*w**6 + 0 - 2/375*w**5 + 0*w**3 + 1/100*w**4 + 0*w. Factor p(y).
2*y*(y - 3)*(y - 1)/25
Let h(m) = -m**3 - 18*m**2 + 20*m + 21. Let f be h(-19). Let u(l) = 2*l**3 + l**2 - 2*l + 8. Let j be u(f). Factor 12*g - 17 + 29 - 3*g**2 - j.
-3*(g - 2)**2
Suppose 5*r = d + 19, -3*r = 3303*d - 3301*d + 12. Solve 2/3*f**r - 1/3*f**3 + f + 0 = 0 for f.
-1, 0, 3
Factor -84 - 43/3*c - 1/3*c**2.
-(c + 7)*(c + 36)/3
Factor -3*a**4 + 48*a**3 + 48*a**2 - 6 + 6 - 93*a**3.
-3*a**2*(a - 1)*(a + 16)
Let j be 616/76 - 8 - 3525/456 - -8. Determine y, given that 3/2*y - 3/8*y**2 - j*y**3 + 3/2 = 0.
-2, -1, 2
Factor -26*q**2 - 1120/3 - 192*q - 1/3*q**3.
-(q + 4)**2*(q + 70)/3
Factor -4*p**3 + 7/2*p + 0 - 25/4*p**2.
-p*(p + 2)*(16*p - 7)/4
Suppose -s - 6*a + 5014 = -8*a, -2*s - 2*a = -10034. Let m be s/2970 + (-2)/15. Factor -2*k - 2/9*k**4 - 10/3*k**2 - m*k**3 + 0.
-2*k*(k + 1)*(k + 3)**2/9
Let c(n) = n**3 - 9*n**2 - 10*n + 2. Let v be c(10). Suppose 10*i = 18*i - 24. Find s, given that -s**v - 196*s**3 + 197*s**3 + i*s**2 = 0.
-2, 0
Factor 1/6*f**3 + 0 - 85/3*f**2 + 169/6*f.
f*(f - 169)*(f - 1)/6
Solve -18*f**3 + 1128/7*f**2 + 0 + 6/7*f**5 - 48/7*f**4 - 960/7*f = 0.
-5, 0, 1, 4, 8
Let b(v) be the second derivative of v**7/21 - v**5/10 + 14*v - 50. Determine p so that b(p) = 0.
-1, 0, 1
Determine w so that 1/11*w**2 + 142/11*w + 5041/11 = 0.
-71
Let m(l) = 11*l**2 + 20*l + 57. Let q(t) = -2*t**2 - t - 1. Let z(n) = -m(n) - 5*q(n). Let i be z(-7). Factor u**3 - 1/2*u**i - 1/2*u**2 + 0*u + 0.
-u**2*(u - 1)**2/2
Let k(c) = -c**3 - 21*c**2 - 5*c. Let y be 60/24*-3*(-2)/3. Let n(j) = -j**3 - 21*j**2 - 4*j. Let w(s) = y*n(s) - 4*k(s). Determine i so that w(i) = 0.
-21, 0
Factor 2/15*w**3 + 238048/15*w + 239432/15 - 1382/15*w**2.
2*(w - 346)**2*(w + 1)/15
Let x(v) be the third derivative of -841*v**7/630 - 2407*v**6/180 - 6193*v**5/180 + 83*v**4/3 - 8*v**3 - 2809*v**2. Suppose x(q) = 0. Calculate q.
-3, 4/29
Let p be (-16)/24*18/(-4). Let -19*a - 9*a**p - 31*a + 6*a**2 + 53*a = 0. What is a?
-1/3, 0, 1
Factor 0 + 0*a + 2/11*a**4 - 136/11*a**3 - 576/11*a**2.
2*a**2*(a - 72)*(a + 4)/11
Suppose 67*a - 63*a = 8. Suppose -5*f = 5*d - a*d - 11, -6 = -4*d + 2*f. Factor 8*z**2 + 162 - 36*z + 4*z**2 + 4*z**2 - 14*z**d.
2*(z - 9)**2
Let o(s) = 23*s**2 - 39*s. Let d(t) = 66*t**2 - 118*t. Let w = -355 + 372. Let y(i) = w*o(i) - 6*d(i). Factor y(n).
-5*n*(n - 9)
Let 118/13*c + 742/13*c**2 - 460/13 + 6/13*c**4 + 170/13*c**3 = 0. What is c?
-23, -5, -1, 2/3
Let o be (-4)/36*-6 + (-12)/(-9). Determine v so that -5*v - 396*v**3 - 4*v + 84*v**o + 68*v**2 + 159*v**4 - 7*v + 3*v**4 = 0.
0, 2/9, 2
Let x(w) be the second derivative of 1/3*w**4 + 5/6*w**3 - 88*w + 0 + 0*w**2. Factor x(b).
b*(4*b + 5)
Let j be 45*(3 - (-52)/(-20)). Suppose -3*m - 3*m = -j. Factor -h**5 + h**5 - 3*h**5 - m*h**4.
-3*h**4*(h + 1)
Let l(p) be the third derivative of -p**2 + 0*p + 0 + 7/32*p**4 + 1/20*p**5 + 1/480*p**6 - 1/2*p**3. Let u(o) be the first derivative of l(o). Factor u(t).
3*(t + 1)*(t + 7)/4
Let k = 1137699/331835 - -3/47405. Solve 4/7*l**3 + 24/7 + k*l**2 + 44/7*l = 0.
-3, -2, -1
Let g = 591977/18 + -295984/9. Let j be ((-3)/2)/(-1 - 5). Factor g*x**3 - 1/2*x - j*x**4 + x**2 - 3/4.
-(x - 3)*(x - 1)*(x + 1)**2/4
Let d(l) be the second derivative of l**4/30 - 32*l**3/3 - 161*l**2/5 - 2111*l. Suppose d(k) = 0. Calculate k.
-1, 161
Let f(l) = l**3 - 10*l**2 - 19*l - 56. Let p be f(12). Suppose p*s = 2*h + 8 + 2, 0 = -4*s + h + 5. What is g in 4/3 - 1/3*g**2 + s*g = 0?
-2, 2
Suppose 0 = -n - 5*o + 143 + 3, 0 = 5*o. Let s = 231 - n. Suppose s*m**2 + 40*m**2 + 4 + 16 - 100*m = 0. What is m?
2/5
Let t(b) be the second derivative of -7*b**4/18 - 16*b**3/9 - 4*b**2/3 - 554*b. Factor t(w).
-2*(w + 2)*(7*w + 2)/3
Let x(d) be the first derivative of 2*d**3/15 - 201*d**2 - 3137. Factor x(o).
2*o*(o - 1005)/5
Let o(n) be the first derivative of n**3/5 + 15*n**2/2 - 918*n/5 + 3665. Factor o(a).
3*(a - 9)*(a + 34)/5
Suppose 392*f = 402*f + 170. Let s(x) = -15*x - 255. Let k be s(f). Solve -1/5*b**4 + 0 + 2/5*b**3 + k*b + 0*b**2 = 0.
0, 2
Let q(h) be the first derivative of -49*h**6/48 + 91*h**5/4 + 6107*h**4/32 + 573*h**3/2 - 1377*h**2/4 + 108*h + 1533. Suppose q(w) = 0. What is w?
-3, 2/7, 24
Let a(b) be the third derivative of 4/3*b**4 + 0*b + 39*b**2 - 1/210*b**7 - 2/5*b**5 - 1/12*b**6 + 0 + 64/3*b**3. Factor a(i).
-(i - 2)*(i + 4)**3
Let w be (-1251470)/(-169554) - (-2)/(-42). Factor 4 + 8/3*k**2 + w*k - 2/3*k**3.
-2*(k - 6)*(k + 1)**2/3
Let g be 3 + (-130)/40 - (-39)/12. Let s(q) be the first derivative of 4/3*q**6 + 0*q**2 + g*q**4 + 18/5*q**5 + 0*q + 15 + 2/3*q**3. What is m in s(m) = 0?
-1, -1/4, 0
Factor 7/5*i**5 + 1287/5*i**3 - 186/5*i**4 + 0*i + 0 - 676/5*i**2.
i**2*(i - 13)**2*(7*i - 4)/5
Let h(c) be the first derivative of -c**6/6 - 9*c**5/5 - 1