*2/7
Let x(b) = -b**3 + 4*b**2 - 3*b. Let m be x(2). Factor 7 - 7 - 25 - 16*g - 7 - 2*g**m.
-2*(g + 4)**2
Let z(m) be the second derivative of 11*m**4/2 + 31*m**3/2 + 12*m**2 + 24*m - 2. Let p(f) = f**2 + f + 1. Let l(s) = 6*p(s) - z(s). Factor l(a).
-3*(4*a + 1)*(5*a + 6)
Let i be (8/28)/(131/917). Factor 30*y**3 + 72*y - 72*y**i - 9/2*y**4 - 24.
-3*(y - 2)**3*(3*y - 2)/2
Let n(z) be the first derivative of z**6/180 - 2*z**3/3 + 4. Let u(h) be the third derivative of n(h). Factor u(q).
2*q**2
Factor 16428*j - 1215672 + 1/9*j**3 - 74*j**2.
(j - 222)**3/9
Let u = -276 + 3313/12. Let c(v) be the third derivative of 8*v**2 + u*v**4 + 0*v - 1/60*v**6 + 0*v**3 + 0*v**5 + 0. Suppose c(t) = 0. Calculate t.
-1, 0, 1
Let f(d) be the second derivative of -d**7/840 + d**6/240 + 11*d**4/6 - 26*d. Let p(x) be the third derivative of f(x). Factor p(a).
-3*a*(a - 1)
Let a(t) be the first derivative of -t**3 + 24*t**2 - 3. Factor a(x).
-3*x*(x - 16)
Let -2/9*c**3 - 100/9*c**2 - 32/3 - 194/9*c = 0. What is c?
-48, -1
Let f = -29 - -34. Suppose -3*l = f*v - 0*v - 31, -4*v + 24 = 2*l. Factor 3 - 15 + u**l + 8.
(u - 2)*(u + 2)
Let l be (-2)/((2/(-10) + 0)*2). Solve 48*n**3 + 10*n**4 - 18*n**3 + 32*n**3 - 15*n**l - 2*n**3 - 40*n**2 = 0 for n.
-2, 0, 2/3, 2
Let v(h) = -2*h**2 + 22*h + 32. Let t(d) = 3*d**2 - 23*d - 33. Let u(j) = -4*t(j) - 5*v(j). Determine w so that u(w) = 0.
-7, -2
Let i(l) be the second derivative of -9*l**5/40 + 7*l**4/2 + 5*l**3 + l + 41. Factor i(v).
-3*v*(v - 10)*(3*v + 2)/2
Let s(r) be the second derivative of -r**7/21 - 2*r**6/15 + 3*r**5/5 + 4*r**4/3 - 5*r**3/3 - 6*r**2 + 54*r. Suppose s(d) = 0. What is d?
-3, -1, 1, 2
Suppose -223*f + 10 + 436 = 0. Find c, given that 2/3*c**2 + 0 + f*c = 0.
-3, 0
Suppose -3*j + 2*c - 2 = 0, 26 = 2*j + 5*j + 3*c. Find x, given that -22/13*x**j - 24/13*x - 6/13*x**3 - 8/13 = 0.
-2, -1, -2/3
Let g(r) be the second derivative of 0*r**2 + 15*r + 1/80*r**6 - 1/336*r**7 - 1/32*r**4 + 1/24*r**3 + 0 - 1/160*r**5. Determine w, given that g(w) = 0.
-1, 0, 1, 2
Let y(m) be the third derivative of -m**11/2827440 - m**10/1285200 + m**5/60 - 17*m**2. Let t(g) be the third derivative of y(g). Factor t(p).
-2*p**4*(p + 1)/17
Factor -5*g**2 + 15*g - 5*g + 40*g.
-5*g*(g - 10)
Solve 48*r + 81*r - 4*r**2 + 256 - 132*r + 51*r = 0.
-4, 16
Suppose 3*g - 5*g + 72 = z, 4*z - 260 = -g. Factor 7*h**3 + z*h**4 + 12*h**2 + 3*h**3 - 2*h**3 + 44*h**3 + 16*h**5.
4*h**2*(h + 3)*(2*h + 1)**2
Suppose -2*f + 89 = 85. Solve -16/17*n**3 + 6/17*n**f - 2/17 + 8/17*n**4 + 4/17*n = 0.
-1/2, 1/2, 1
Let i(l) = 4*l + 61. Let y be i(-14). Factor 3090 - 3090 + 2*r**4 + 2*r**y.
2*r**4*(r + 1)
Let r(z) = 92*z**3 - 5216*z**2 + 82220*z - 23064. Let k(q) = 61*q**3 - 3478*q**2 + 54813*q - 15376. Let j(f) = -8*k(f) + 5*r(f). Determine n so that j(n) = 0.
2/7, 31
Suppose 191 = -5*r - 29. Let u = -38 - r. Solve -u - 2*d**4 + 3*d**3 - 2*d**2 - 4*d**3 - 4*d + 10*d**2 + 5*d**3 = 0 for d.
-1, 1, 3
Let c(m) be the second derivative of -m**6/30 + 71*m**5/5 - 5041*m**4/2 + 715822*m**3/3 - 25411681*m**2/2 - 248*m. Determine k, given that c(k) = 0.
71
Let p = -6 + 6. Suppose 5*n - 8*n + 9 = p. Factor -7*x + x**3 + 2*x**3 - x**4 - n*x**2 + 7*x + x.
-x*(x - 1)**3
Let y = -23 - -26. Let u be (4 - y)*11*1. Factor -6 - 2*p**2 + p**2 + 5*p**2 + u*p**2 + 9*p.
3*(p + 1)*(5*p - 2)
Factor 11*n**3 - 48*n**2 + 8*n + 300 + 3*n**4 - 35*n**3 + n**4 - 7*n + 279*n.
4*(n - 5)**2*(n + 1)*(n + 3)
Let b(w) = 5*w**3 + 66*w**2 + 174*w + 6. Let v(h) = 30*h**3 + 395*h**2 + 1045*h + 35. Let m(c) = -35*b(c) + 6*v(c). Determine t, given that m(t) = 0.
-6, 0
Let n(c) = -2*c**2 + 5*c - 4. Let z(f) = f**2. Let v(q) = q**2 + 3. Let l be v(0). Let o(h) = l*n(h) + 3*z(h). Factor o(t).
-3*(t - 4)*(t - 1)
Let t(r) be the third derivative of -1/12*r**4 + 0 + 12*r**2 + 0*r**3 + 1/30*r**5 + 0*r. Factor t(l).
2*l*(l - 1)
Let b(t) be the third derivative of 0*t**3 + 0*t - 1/20*t**6 - 23*t**2 - 1/15*t**5 + 1/168*t**8 + 0*t**4 + 0*t**7 + 0. Determine r, given that b(r) = 0.
-1, 0, 2
Let q(y) be the second derivative of y**4/3 - 20*y**3/3 - 22*y**2 - 213*y. Factor q(n).
4*(n - 11)*(n + 1)
Let u(f) be the third derivative of -f**6/300 + 3*f**5/10 - 11*f**4/15 - f**2 - 265. Factor u(n).
-2*n*(n - 44)*(n - 1)/5
Let z(i) = 30*i**2 - 1528*i - 97. Let n be z(51). Factor 16/5 - 10*l**3 - 56/5*l - 2/5*l**n + 76/5*l**2 + 16/5*l**4.
-2*(l - 2)**3*(l - 1)**2/5
Determine q so that 5/2 + 19/2*q - 2*q**2 = 0.
-1/4, 5
Let j(c) be the first derivative of 0*c**2 - 1/72*c**4 - 10*c + 2 + 0*c**3. Let h(a) be the first derivative of j(a). Factor h(w).
-w**2/6
Let s = -1787 + 1789. Factor 9/7*v**3 + 0 + 6/7*v - 3/7*v**5 + 3/7*v**4 - 15/7*v**s.
-3*v*(v - 1)**3*(v + 2)/7
Suppose 0 = 4*j + 2*j - 78. Determine b so that j*b**3 + 5*b**3 - 15*b**3 + 12*b + 12*b**2 = 0.
-2, 0
Let o(f) be the second derivative of f**5/4 + 2*f**4/3 - f**3 - 15*f. Let q(g) = 14*g**3 + 23*g**2 - 17*g. Let i(w) = 17*o(w) - 6*q(w). Factor i(j).
j**2*(j - 2)
Let f(l) = -l**2 + 3*l. Let s(o) = -o + 1. Let q(t) = -f(t) + 4*s(t). Let n(w) = -w. Let x(h) = 3*n(h) - q(h). Factor x(j).
-(j - 2)**2
Suppose 4 = 3*c + 3*b - 17, 21 = 4*c - 3*b. Let m(p) be the second derivative of -1/8*p**4 + 0*p**5 + 0 + 0*p**3 + 0*p**2 + 3*p + 1/20*p**c. Factor m(q).
3*q**2*(q - 1)*(q + 1)/2
Let f(m) be the third derivative of 2*m**7/315 - 11*m**6/180 + 19*m**5/90 - 13*m**4/36 + m**3/3 - m**2 + 62. Suppose f(g) = 0. What is g?
1/2, 1, 3
Suppose -4*c - g = -12, -8 = 2*c + 6*g - 9*g. Factor 0 - p**3 + 0*p + 2/3*p**c + 1/3*p**4.
p**2*(p - 2)*(p - 1)/3
Let d = 94 + -94. Let x = 181/346 + -4/173. Let -x*f**2 + f + d = 0. Calculate f.
0, 2
Let i = 10 - -8. Let f = i + -14. Factor -6 + f*v - 2/3*v**2.
-2*(v - 3)**2/3
Determine r, given that -1/7*r**2 + 27/7 - 6/7*r = 0.
-9, 3
Let t(m) be the third derivative of -m**5/12 + 205*m**4/8 - 305*m**3/3 - 731*m**2. Solve t(h) = 0 for h.
1, 122
Let k = -76 - -78. Factor 1 + 4 + 4*z**2 - 4*z**k - 5*z**2.
-5*(z - 1)*(z + 1)
Let p(t) be the third derivative of 1/112*t**8 - 10*t**2 + 1/20*t**5 + 1/4*t**4 + 0*t**3 + 0*t - 1/70*t**7 - 3/40*t**6 + 0. Solve p(o) = 0.
-1, 0, 1, 2
Let y = 2 - -2. Suppose 0 = b + 5*s - 2*s + 7, 4*b = 4*s + 20. Solve -3*k**4 - k**5 + k**y - k**3 - 2*k**2 + b*k**2 = 0.
-1, 0
Let r be 1/(-2) - (-7)/10. Let t be (-5 - -5)/((-10)/(-2) + -6). Factor -2/5*x**3 + 1/5*x**4 + r*x**2 + t + 0*x.
x**2*(x - 1)**2/5
Let y(s) be the third derivative of -s**6/90 + 2*s**5/45 + 4*s**4/9 - 122*s**2. Factor y(i).
-4*i*(i - 4)*(i + 2)/3
Let p = 47514086/217 + -218960. Let m = 2/31 - p. Factor -2/7 - 8/7*r**3 - m*r - 2/7*r**4 - 12/7*r**2.
-2*(r + 1)**4/7
Let m(t) be the first derivative of 0*t**2 - 5*t**3 - 28 - 3/5*t**5 - 9/2*t**4 + 0*t. Factor m(q).
-3*q**2*(q + 1)*(q + 5)
Suppose -106 = -4*v + 3*f, 3*v - 2*f - 81 = f. Factor v*d + 9*d**2 + 2*d**3 - 39*d + 17*d - 4.
(d + 1)*(d + 4)*(2*d - 1)
Let n = -635 + 640. Factor 0 + 2/15*d**n - 2/15*d - 4/15*d**2 + 4/15*d**4 + 0*d**3.
2*d*(d - 1)*(d + 1)**3/15
Let k(p) be the third derivative of p**5/15 - 10*p**4/3 + 38*p**3/3 + 60*p**2. Let k(m) = 0. Calculate m.
1, 19
Let s(p) be the first derivative of p**6/51 + 4*p**5/85 - p**4/34 - 4*p**3/51 + 118. What is h in s(h) = 0?
-2, -1, 0, 1
Suppose 5*x = -5*f, -5*x + 3*f + 23 + 9 = 0. Solve -2/15 + 0*i**3 - 2/15*i**x + 4/15*i**2 + 0*i = 0.
-1, 1
Let q(y) = -3*y + 19. Let d be q(8). Let g = d + 11/2. Factor -1/2*h**3 + 0 + 0*h**2 + g*h.
-h*(h - 1)*(h + 1)/2
Let t(b) be the third derivative of 0*b**4 + 0*b + 0*b**3 + 1/45*b**5 + 9*b**2 + 1/315*b**7 - 1/60*b**6 + 0. Let t(c) = 0. What is c?
0, 1, 2
Determine d so that -1/6*d**2 - 13/3*d - 169/6 = 0.
-13
Let s(k) be the third derivative of 0*k + 1/42*k**7 + 5/336*k**8 + 8*k**2 + 0 + 0*k**5 + 0*k**3 + 0*k**4 - 1/12*k**6. Factor s(t).
5*t**3*(t - 1)*(t + 2)
Let f(w) = 9*w**3 + 99*w**2 - 69*w - 135. Let z(m) = -2*m**3 - 20*m**2 + 14*m + 27. Let s(k) = -5*f(k) - 24*z(k). Factor s(t).
3*(t - 3)**2*(t + 1)
Suppose -l - 4 + 6 = 0. Let q be 14*l*(-4)/(-28). Let -12*n**2 + 7*n**4 + q*n - 9*n**3 + 7 - 7 = 0. What is n?
-1, 0, 2/7, 2
Determine k so that 0 + 32/3*k + 2/3*k**2 = 0.
-16, 0
Suppose -6/7 - 2/7*d**3 - 2*d - 10/7*d**2 = 0. What is d?
-3, -1
Let j(q) be the first derivative of q**5/5 + 9*q**4/2 + 61*q**3/3 - 90*q**