3)*(p + 1)/6
Let l(t) be the first derivative of t**5/5 - t**4/2 + t**3/3 + 36. Determine b, given that l(b) = 0.
0, 1
Let r(a) be the third derivative of -a**8/336 + 2*a**7/105 - a**6/40 - a**5/15 + a**4/6 - 106*a**2. Factor r(q).
-q*(q - 2)**2*(q - 1)*(q + 1)
Let y(d) be the second derivative of -d**9/432 + d**8/336 + d**7/420 - d**3/3 + 15*d. Let z(g) be the second derivative of y(g). Factor z(v).
-v**3*(v - 1)*(7*v + 2)
Let j be (-138)/92*(1/(-3) - 1). Let d(y) be the third derivative of 0*y + y**j - 1/24*y**5 + 1/48*y**4 + 0 + 0*y**3. Let d(m) = 0. What is m?
0, 1/5
Find b such that -4/3*b**4 + 0*b - 2/15*b**3 + 0 + 4/3*b**2 + 2/15*b**5 = 0.
-1, 0, 1, 10
Let r(j) be the third derivative of -j**6/90 + 3*j**5/10 + 7*j**4/18 - 41*j**2 + j. Solve r(h) = 0.
-1/2, 0, 14
Factor 399/2*q + 41/2*q**2 - 441/2 + 1/2*q**3.
(q - 1)*(q + 21)**2/2
Let j(w) be the first derivative of 24*w**5/5 - 113*w**4/2 + 266*w**3/9 + 19*w**2/3 - 6*w + 246. Let j(v) = 0. What is v?
-1/4, 1/3, 9
Let t(s) = -72*s**2 + 5*s + 3. Let x be t(0). Let j(i) = -2*i. Let u be j(-1). Factor 6/5*h**u - 4/5*h + 0 + 4/5*h**x.
2*h*(h + 2)*(2*h - 1)/5
Suppose 2*j = 0, 33*j + 40 = 5*c + 28*j. Suppose -c*r + 11 = 2*v - 7*r, -r - 4 = -3*v. Factor 0*f**2 + 2/5*f + 0 - 2/5*f**v.
-2*f*(f - 1)*(f + 1)/5
Let 40/19 - 2/19*r**2 + 2/19*r = 0. What is r?
-4, 5
Let c(a) = -a**2 - a. Let x(o) = 6*o**2 + o - 8. Let s(z) = 35*c(z) + 5*x(z). Factor s(i).
-5*(i + 2)*(i + 4)
Suppose -8*p - 5*p = 26000. Let h be (p/63)/(-8) - 1/9. Let -h*y**2 + 33/7*y**3 + 3/7*y + 3/7 - 12/7*y**4 = 0. What is y?
-1/4, 1
Let s(p) be the second derivative of p**6/75 + 3*p**5/25 + 2*p**4/5 + 2*p**3/3 + 3*p**2/5 - 79*p. Find g, given that s(g) = 0.
-3, -1
Let x(g) be the second derivative of g**7/12600 + g**6/1800 - 5*g**4/12 - 5*g. Let j(r) be the third derivative of x(r). Factor j(f).
f*(f + 2)/5
Let n(s) be the second derivative of s**7/42 - 3*s**6/10 - 17*s**5/10 - 2*s**4 + 343*s + 1. What is q in n(q) = 0?
-2, -1, 0, 12
Let w(y) be the second derivative of 4*y**6/9 - 133*y**5/30 + 10*y**4 - 77*y**3/9 + 10*y**2/3 - y - 198. Let w(z) = 0. Calculate z.
1/4, 2/5, 1, 5
Let b(r) = 6*r**3 - 61*r**2 - 69*r. Let l(m) = m**3 - 12*m**2 - 14*m. Let a(z) = 2*b(z) - 11*l(z). Let y be a(-8). Suppose -3/2*x**2 - 3/2*x + y = 0. What is x?
-1, 0
Let -142 + 278 - 20*x**4 - 5*x**5 - 136 = 0. Calculate x.
-4, 0
Let v be (-126)/(-45) - (-1)/5. Let k be -12*(-1 - -2)*-4. Factor -4 - 48*x**2 + 16 - x**v + 123*x**2 + 58*x**3 + 21*x**4 + 3*x**5 + k*x.
3*(x + 1)**3*(x + 2)**2
Let o be 2/7 + -46*3/(-7). Let r be (-35)/o*(-4)/14. Determine m so that 1/2*m + m**4 - r*m**5 + 0 - m**2 + 0*m**3 = 0.
-1, 0, 1
Let p(c) be the first derivative of -c**3/9 - 4*c**2/3 - 7*c/3 + 46. Factor p(n).
-(n + 1)*(n + 7)/3
Let i be 7/(-140)*((-66)/18 + 2). Let x(d) be the first derivative of -3/8*d**2 - i*d**3 - 1/2*d - 13. Factor x(p).
-(p + 1)*(p + 2)/4
Let h(p) be the third derivative of -p**8/26880 - p**7/6720 + p**6/480 + 2*p**5/15 - p**2. Let u(i) be the third derivative of h(i). Let u(v) = 0. Calculate v.
-2, 1
Let y(x) be the first derivative of x**7/14 + x**6/2 + 27*x**5/20 + 7*x**4/4 + x**3 + 15*x + 18. Let u(p) be the first derivative of y(p). Factor u(n).
3*n*(n + 1)**3*(n + 2)
Let b(d) be the third derivative of 0 - 3/20*d**5 + 0*d + 1/4*d**4 + 0*d**3 - 11*d**2 + 1/40*d**6. Factor b(h).
3*h*(h - 2)*(h - 1)
Let y = 27 - 20. Solve -4*s - 5*s**2 - 13*s + y*s + 15 = 0 for s.
-3, 1
Suppose 2*l = 8 + 6. Factor 20*o**2 - 8 - 28*o + 8*o + 6*o**2 - l*o**3.
-(o - 2)**2*(7*o + 2)
Suppose -10*m + 16 - 66 = 0. Let x(b) = b - 1. Let a(f) = f**2 - 2*f + 5. Let z(y) = m*x(y) - a(y). Factor z(j).
-j*(j + 3)
Suppose 0*h + 28 = 4*h. Let w = 11 - h. What is n in n**5 + 16 - 3*n**w + 2*n - 2*n**5 + 2*n**2 - 2*n**3 + n - 15 = 0?
-1, 1
Let j = 14 - 8. Suppose -8*d + 22 = j. Factor 1/2*n**d + 0*n + 0.
n**2/2
Let g = -15/4 + 4. Suppose -75*b - 34 + 184 = 0. Factor -3/2*a + 9/4 + g*a**b.
(a - 3)**2/4
Let r be ((-12)/(-14))/(-20*(-21)/735). Solve 9/4*a**2 + 0 + r*a + 3/4*a**3 = 0.
-2, -1, 0
Suppose 0*n + 2*n = 11*n. Let i(m) be the third derivative of n - 1/40*m**6 - 7*m**2 + m**3 - 1/10*m**5 + 0*m + 1/8*m**4. Solve i(a) = 0 for a.
-2, -1, 1
Let d(o) be the first derivative of -4*o**3/3 + 30*o**2 + 64*o - 184. Let d(u) = 0. Calculate u.
-1, 16
Let o(c) be the third derivative of 0 + 11/6*c**7 - 73/12*c**5 - 20/3*c**4 + 13*c**2 - 17/24*c**6 + 35/48*c**8 - 10/3*c**3 + 0*c. Solve o(l) = 0.
-1, -2/7, 1
Let n(j) = j**3 - 15*j**2 + 39*j - 43. Let x(y) = -y**3 + 17*y**2 - 39*y + 42. Let a(f) = -6*n(f) - 4*x(f). Determine q, given that a(q) = 0.
3, 5
Let j(o) = -o**3 - 5*o**2 + 6*o + 13. Let h be j(-6). Find x, given that -h*x**2 - x**2 + 2*x**4 + 4*x + 8*x**2 = 0.
-2, 0, 1
Let q = 30937 + -30932. Suppose -12/5*a**q + 0*a**2 + 0 + 32/5*a**4 - 24/5*a**3 + 4/5*a = 0. Calculate a.
-1/3, 0, 1
Suppose 0 = 2*x + 2*f - 2, 3 = 3*f. Factor -2*o + 0*o - 2*o**2 - 4*o**3 + x*o**2 + 6*o + 2*o**4.
2*o*(o - 2)*(o - 1)*(o + 1)
Let m(r) be the second derivative of -r**7/77 + 2*r**6/55 + 9*r**5/22 + 2*r**4/11 - 20*r**3/11 - 9*r + 2. Find t such that m(t) = 0.
-2, 0, 1, 5
Let d(h) be the second derivative of h**7/3780 - h**6/360 + h**5/90 + h**4/6 - 8*h. Let s(w) be the third derivative of d(w). Determine b so that s(b) = 0.
1, 2
Let h be (12/36)/(-1 - (-4 + 2)). Factor 0*r**2 + 0 + 0*r - 3*r**3 + 2*r**4 - h*r**5.
-r**3*(r - 3)**2/3
Suppose 0 = 74*i - 68*i - 12. Factor 0 + 1/5*s**i - 1/5*s.
s*(s - 1)/5
Let p(w) be the second derivative of 3/16*w**4 - 1/4*w**3 + 0 + 9*w + 1/8*w**2 - 1/20*w**5. Factor p(g).
-(g - 1)**2*(4*g - 1)/4
Let k(i) be the first derivative of 2*i**3/3 + 14*i**2 + 26*i + 223. Factor k(u).
2*(u + 1)*(u + 13)
Let a(u) be the first derivative of -u**3 - 486*u**2 - 78732*u + 318. Factor a(d).
-3*(d + 162)**2
Let g be (-84)/(-294)*(-21)/(-2). Let d(p) be the second derivative of 0 - 5/12*p**4 + 15/2*p**2 + 5/3*p**g - 8*p. Factor d(a).
-5*(a - 3)*(a + 1)
Find w, given that 45 - 129/2*w + 6*w**2 = 0.
3/4, 10
Let a(f) be the third derivative of f**8/5880 - f**7/1470 - f**6/1260 + f**5/210 + 2*f**3 + 5*f**2. Let c(r) be the first derivative of a(r). Factor c(x).
2*x*(x - 2)*(x - 1)*(x + 1)/7
Let s(y) = -y**2 + 6*y - 6. Let o be s(4). Let m(z) = -z**3 - 5*z**2 - 5*z - 2. Let v be m(-4). Let -4 - 2*g - o + 0*g + v*g**2 - 2*g = 0. Calculate g.
-1, 3
Let a be (-12)/(-38)*(835/(-105) + 8). Let d = 522/665 + a. Factor 6/5*r + 2/5*r**2 + d.
2*(r + 1)*(r + 2)/5
Let r = -236 + 239. Suppose 3*b - q - 1 = 0, r*b + 2*q = 3 + 13. Determine h, given that 3*h**b - 9/5*h**3 + 0 + 6/5*h = 0.
-1/3, 0, 2
Factor -5*m + 17*m + m**4 - 7*m**2 - 4*m**2 - 2*m**2.
m*(m - 3)*(m - 1)*(m + 4)
Let w = -421 - -98. Let a be w/(-153) + (-2)/18. Factor 0 - 2/7*n**3 + 4/7*n**a - 2/7*n.
-2*n*(n - 1)**2/7
Let f(v) be the first derivative of v**5/5 + 9*v**4/4 - v**3/3 - 9*v**2/2 - 7. Determine o so that f(o) = 0.
-9, -1, 0, 1
Let b(w) be the second derivative of w**4/4 - 6*w**3 - 39*w**2/2 + 37*w. Factor b(s).
3*(s - 13)*(s + 1)
Let w(d) be the third derivative of -d**6/180 - 17*d**5/45 - 95*d**4/36 - 62*d**3/9 - 533*d**2. Let w(f) = 0. What is f?
-31, -2, -1
Let p be 5578/(-2670) + (4/(-3) - -1). Let k = -2/89 - p. Factor -2/5*i**2 - 18/5 + k*i.
-2*(i - 3)**2/5
Factor -5*u**5 - 366*u**2 + 65*u**4 - 3 + 121*u**2 - 175*u**3 + 3.
-5*u**2*(u - 7)**2*(u + 1)
Suppose -105*f + 109*f = 20. Let t(a) be the second derivative of 0*a**2 + 0*a**3 + 1/24*a**4 - 1/40*a**f + 0 - 2*a. What is c in t(c) = 0?
0, 1
Suppose -77 + 21 = -4*h. Suppose 4 = 9*v - h. Let 1/3*d**v + 1/3 + 2/3*d = 0. Calculate d.
-1
Let b(d) be the second derivative of -19*d - 8/27*d**3 + 0 + 1/45*d**5 - 8/9*d**2 + 1/27*d**4. Find a, given that b(a) = 0.
-2, -1, 2
Let b(d) be the first derivative of d**6/25 - d**5/10 + d**4/15 - 9*d - 10. Let l(r) be the first derivative of b(r). Suppose l(k) = 0. What is k?
0, 2/3, 1
Let g(w) be the second derivative of -2*w**2 - 1/3*w**4 - 4/3*w**3 + 0 - 13*w. Solve g(a) = 0.
-1
Let a = -4429/187 + 415/17. Factor 0 - 16/11*y**2 + a*y - 2/11*y**4 + 10/11*y**3.
-2*y*(y - 2)**2*(y - 1)/11
Let w(o) be the first derivative of o**5/20 - o**2/2 + 8. Let d(c) be the second derivative of w(c). What is k in d(k) = 0?
0
Let k(y) be the first derivat