 be the second derivative of z**8/336 - z**7/420 - z**6/120 + z**5/120 + 13*z**2 + 21*z. Let u(h) be the first derivative of v(h). Solve u(s) = 0 for s.
-1, 0, 1/2, 1
Factor 490 + 2/5*q**2 - 28*q.
2*(q - 35)**2/5
Let f = 4/7 - -2/21. Let i = 202/3 + -67. Suppose 1/3*c - i*c**2 + f = 0. What is c?
-1, 2
Let g be (-28)/8 - (11 + -16). Suppose -9/4*q + g + 3/4*q**2 = 0. Calculate q.
1, 2
Let z be ((-219)/(-66) - 82/(-451)) + 1/4. Determine o so that -33/4*o**3 + 0 - 3*o**4 - z*o**2 + 3/2*o = 0.
-2, -1, 0, 1/4
Suppose -5*y = 42 - 2. Let k be (-44)/y - 1/(-2). Factor -3 + 0*n**3 - 5 + k*n**3 - 6*n + 5 + 3*n**4.
3*(n - 1)*(n + 1)**3
Let m(a) be the first derivative of -1/42*a**4 - 5 - 2/7*a**3 - 9/7*a**2 - 3*a. Let j(w) be the first derivative of m(w). Factor j(o).
-2*(o + 3)**2/7
Let h(a) be the third derivative of -a**6/60 - 2*a**5/15 + a**4/3 + 16*a**3/3 - 90*a**2. Solve h(v) = 0 for v.
-4, -2, 2
Let r(v) be the third derivative of -4*v**8/63 - 16*v**7/315 + v**6/6 + 8*v**5/45 + v**4/18 - 4*v**2 - 27. Determine p so that r(p) = 0.
-1, -1/4, 0, 1
Let b(c) be the first derivative of 2*c + 1/8*c**4 - c**2 - 1/6*c**3 - 19. Determine k so that b(k) = 0.
-2, 1, 2
Let i(x) = -7*x + 5. Let p be i(0). Let n(s) be the first derivative of -2/35*s**p - 1/7*s**2 + 3 + 1/14*s**4 + 0*s + 2/21*s**3. Factor n(y).
-2*y*(y - 1)**2*(y + 1)/7
Factor -16/11*w**3 + 0 + 6/11*w**4 - 4/11*w + 14/11*w**2.
2*w*(w - 1)**2*(3*w - 2)/11
Let x(k) be the second derivative of -k**4/54 + 10*k**3/27 - 7*k**2/3 + 24*k. Factor x(a).
-2*(a - 7)*(a - 3)/9
Let o = 19 + -17. Find v, given that 31*v - 34*v + 0*v**o + 3*v**2 = 0.
0, 1
Let a(f) = 44*f**3 - 746*f**2 + 568*f - 115. Let h(p) = 178*p**3 - 2982*p**2 + 2272*p - 459. Let y(k) = -22*a(k) + 6*h(k). Factor y(m).
4*(m - 14)*(5*m - 2)**2
Suppose -21 = t - 0*k - 5*k, t - 4*k = -16. Find c such that 7*c**4 - t*c**4 + 0*c**5 - 4*c**3 + c**2 - c**5 + c**3 = 0.
0, 1
Let w = 37 + -35. Factor -q**2 + 16*q - 2*q**w + 2*q**2 - 17*q.
-q*(q + 1)
Suppose -4*h - 11 = -k, 3*h + 3 = 5*k - 18. Factor 4/5*d**4 - 2/5*d**5 + 0*d**k + 0 + 2/5*d - 4/5*d**2.
-2*d*(d - 1)**3*(d + 1)/5
Factor -6/7*g**2 + 3/7 - 3/7*g.
-3*(g + 1)*(2*g - 1)/7
Let t(q) = q**3 + q**2. Let j(r) = -9*r**3 + 3*r**2. Suppose 5*f = 2 + 3. Let u(a) = f*j(a) + 6*t(a). Suppose u(w) = 0. Calculate w.
0, 3
Let r(s) be the first derivative of 1/4*s**4 + 17 - 15*s**3 + 675/2*s**2 - 3375*s. Determine o, given that r(o) = 0.
15
Let o(t) = -45*t**2 + 235*t - 50. Let p(i) = 1. Let f(d) = o(d) - 6*p(d). Let z(j) = -1. Let r(w) = -f(w) + 6*z(w). Solve r(v) = 0.
2/9, 5
Let c be (21/6)/((-4)/8). Let q(m) = -10*m**2 - 6*m - 6. Let d(z) = -11*z**2 - 7*z - 7. Let t(w) = c*q(w) + 6*d(w). Suppose t(p) = 0. Calculate p.
0
Suppose -2*k = 2*s - 4, -5*s = -2*s - 4*k - 27. Suppose 2*t - 6 = j, -s*t + 10*t = 2*j + 15. Factor 3*n - 2*n**t - 2*n**2 + 2*n - 5*n.
-2*n**2*(n + 1)
Suppose -o + 15 = -21. Let w = o - 32. Factor v**3 - v**2 + 5*v + v**2 - 5*v**2 - 6*v**3 + 5*v**w.
5*v*(v - 1)**2*(v + 1)
Suppose k + 5*s = 151, 5 + 3 = -4*s. Let f be k/147*3 - (-3)/(-1). Determine t, given that -18/7 + 12/7*t - f*t**2 = 0.
3
Let h be -6*(354/54 + -7) + (-4)/6. Determine q so that -27/4*q**h + 195/4*q - 169/4 + 1/4*q**3 = 0.
1, 13
Let u(r) be the third derivative of r**8/784 - 3*r**6/140 - 2*r**5/35 - 3*r**4/56 - 141*r**2 + r. Solve u(t) = 0 for t.
-1, 0, 3
Let c(l) be the second derivative of -l**4/36 + 7*l**3/18 + 4*l**2/3 - 186*l. Suppose c(z) = 0. What is z?
-1, 8
Let l be ((-2)/7)/((-20)/56) - (-4)/(-30). Let 0*m**3 + 2/3*m**2 - 1/3*m + 0 - l*m**4 + 1/3*m**5 = 0. Calculate m.
-1, 0, 1
Let d(v) be the second derivative of -v**5/120 - v**4/12 + 8*v**2/3 - 122*v. Factor d(n).
-(n - 2)*(n + 4)**2/6
Let l(o) be the third derivative of 0 + 11/96*o**4 + 0*o + 13/80*o**5 - 1/4*o**3 - 7/240*o**6 - 3*o**2. What is v in l(v) = 0?
-1/2, 2/7, 3
Solve -225/2 + 3*w**2 + 3/4*w**3 - 105/4*w = 0 for w.
-5, 6
Suppose -1 + 29 = 2*p. Suppose -3*k + p = 2. Factor k + 3*u + 3*u - 4*u**3 + 2*u**3 + 0*u**3.
-2*(u - 2)*(u + 1)**2
Suppose 31*s = 1038 - 201. Let b be 15/s*(-456)/(-20). Find z such that 40/3*z + b*z**2 - 14/3*z**5 - 46/3*z**4 + 8/3 - 26/3*z**3 = 0.
-2, -1, -2/7, 1
Let m(y) = 8*y**2 - 96*y + 275. Let n(l) = 4*l**2 - 48*l + 138. Let g = -6 - -12. Let j(k) = g*m(k) - 13*n(k). What is w in j(w) = 0?
6
Let d(j) be the third derivative of -j**6/90 - 2*j**5/15 - 2*j**4/3 + j**3/3 + 4*j**2. Let b(a) be the first derivative of d(a). Find f such that b(f) = 0.
-2
Factor -6*m**2 - 897*m - 4*m**3 + 905*m - 6*m**2 + 8*m**3.
4*m*(m - 2)*(m - 1)
Let f(v) be the second derivative of -5*v**4/48 + 10*v**3/3 + 285*v**2/8 + 243*v. Factor f(y).
-5*(y - 19)*(y + 3)/4
Let m(o) = o**3 + o**2 + 4*o - 18. Let u(p) = 3*p**3 + 4*p**2 + 11*p - 54. Let j(k) = 11*m(k) - 4*u(k). Let y be j(-4). Factor 0*n + 2/3 - 2/3*n**y.
-2*(n - 1)*(n + 1)/3
Let y(x) = x**3 - 4*x**2 - 2*x + 24. Let u be y(5). Let i be -2 - 1 - (2 + (-201)/u). Solve 0 - 2/13*j**3 - i*j**5 + 0*j + 4/13*j**4 + 0*j**2 = 0 for j.
0, 1
Suppose 2*t + 3*g = -5, 0 = -40*t + 45*t + 3*g - 1. Factor 8/7*k + 10/7 - 2/7*k**t.
-2*(k - 5)*(k + 1)/7
Let s be 4 - 2 - 682/99. Let y = s + 326/63. Determine o so that -2/7*o - y + 24/7*o**2 = 0.
-1/4, 1/3
Suppose 4*d = -3*j + 14, 0 = -2*d - 7*j + 6*j + 6. Solve -2/23*w - 2/23*w**3 + 0 - 4/23*w**d = 0 for w.
-1, 0
Let g(x) be the second derivative of -5/2*x**2 + 1/24*x**4 + 0 - 1/180*x**5 - 1/9*x**3 + x. Let y(p) be the first derivative of g(p). Factor y(r).
-(r - 2)*(r - 1)/3
Factor 3*j**5 + 15*j**5 - 24*j**2 + 26*j**3 + 3*j + 5*j + 2*j**4 - 14*j**4 - 16*j**5.
2*j*(j - 2)**2*(j - 1)**2
Let z(f) be the second derivative of 25*f - 5/84*f**7 + 1/30*f**6 - 2/3*f**4 + 0*f**2 + 0 + 1/3*f**3 + 3/8*f**5. Suppose z(r) = 0. What is r?
-2, 0, 2/5, 1
Let 2*m**2 + m**4 + 8*m**3 + 24*m**3 - 3*m**4 - 38*m**3 + 6*m = 0. Calculate m.
-3, -1, 0, 1
Let l be 34*1 + 3/((-18)/24). Suppose 6*n - l + 18 = 0. Let -5/2*z**2 - 3/2*z + 3/2*z**3 + n*z**4 + 1/2 = 0. Calculate z.
-1, 1/4, 1
Let n(g) be the second derivative of g**8/26880 - g**7/1440 + g**4/3 - 11*g. Let r(b) be the third derivative of n(b). Let r(z) = 0. Calculate z.
0, 7
What is v in 59/4*v + v**2 - 15/4 = 0?
-15, 1/4
Let y(s) = -7*s**2 + 430*s - 24205. Let u(p) = -3*p**2 + 216*p - 12102. Let q(a) = -5*u(a) + 2*y(a). Factor q(b).
(b - 110)**2
Let d(w) = -w**3 + 4*w**2 + 26. Let n be d(5). Let p be n*(-5)/((-10)/4). Find v such that 2 - 2*v + 1/2*v**p = 0.
2
Let y(o) be the first derivative of 5*o**3/3 + 15*o**2/2 + 10*o - 15. Factor y(n).
5*(n + 1)*(n + 2)
Factor -1/3*w**3 - 147 - 161*w - 43/3*w**2.
-(w + 1)*(w + 21)**2/3
Suppose 21 = 5*m - 5*a - 19, 0 = 2*a + 10. Determine y so that -15*y**4 + 4*y**m + 3*y**2 + 12*y**5 - 7*y**3 + 3*y**4 = 0.
-1/2, 0, 1/2, 1
Let f(c) be the first derivative of -c**7/1785 + c**6/510 + 15*c**2/2 + 2*c - 3. Let s(i) be the second derivative of f(i). Suppose s(l) = 0. What is l?
0, 2
Let t(n) be the first derivative of -n**6/36 - n**5/5 - 7*n**4/12 - 8*n**3/9 - 3*n**2/4 - n/3 - 75. Factor t(v).
-(v + 1)**4*(v + 2)/6
Suppose 1/2*w**4 + 16*w**2 + 7*w**3 - 64*w + 0 = 0. What is w?
-8, 0, 2
Determine o, given that -14*o**2 - 66*o**3 + 42*o + 16*o**2 + 64*o**3 - 90 = 0.
-5, 3
Let v(n) be the second derivative of 0 - 15*n + 0*n**3 - 1/28*n**4 + 0*n**2. Factor v(f).
-3*f**2/7
Let n = 1217/9 - 135. Let c be 9 - (-7 - 426/(-27)). Let -c*t**2 + 2/9*t**4 + 0 + 2/9*t**3 - n*t = 0. Calculate t.
-1, 0, 1
Let x(s) = -4*s**3 - 12*s**2 - 12*s - 2. Let y be x(-1). Let 16/3 + 8/3*c + 1/3*c**y = 0. What is c?
-4
Let j = 24919/3 + -8477. Let b = j - -171. Determine o so that 0*o + 0 + 1/3*o**2 - b*o**4 + 0*o**3 = 0.
-1, 0, 1
Let c(m) be the first derivative of -16*m + 40*m**2 - 8 - 196/5*m**5 - 70*m**4 + 4*m**3. Find l such that c(l) = 0.
-1, 2/7
Suppose -4*a + 19 + 5 = 0. Suppose 2*n + 16 = 4*x, 2*n - 3*x + 2*x + 1 = 0. Factor a*w - 3*w**4 - 4*w**n + 15*w**2 - 6*w**3 - 8*w**2.
-3*w*(w - 1)*(w + 1)*(w + 2)
Let f(a) = 2*a**3 + 11*a**2 + 4*a. Let g be f(-6). Let p be (4/5)/((-216)/g). Suppose 0*x**4 - 4/9 + p*x**5 - 8/9*x**3 + 2/3*x + 4/9*x**2 = 0. What is x?
-2, -1, 1
Let p(s) = -4*s - 59. Let x be p(-16). Let b(j) be the third derivative of x*j**2 + 1/12*j**4 + 0 - 1/60*j**6 - 1/30*j**5 + 0*j + 1/3*j**3. Factor b