0
Let q(g) be the third derivative of -g**7/1470 - g**6/210 - g**5/84 - g**4/84 + 297*g**2 + 1. Suppose q(a) = 0. Calculate a.
-2, -1, 0
Let o = 6 + -2. Let h be 2/(-9) - (-145)/45. Solve -11*n**4 + 5*n + 11*n**o - 10*n**h + 5*n**5 = 0 for n.
-1, 0, 1
Let y be 720/270 - (2 - (-2 - -2)). Determine t so that 0 + y*t**2 + 4/3*t = 0.
-2, 0
Let a(p) = -30*p - 58. Let j be a(-2). Let n be 2/(-6)*(-12)/16. Suppose -n*c**j + 1 + 1/4*c**3 - c = 0. Calculate c.
-2, 1, 2
Let n(x) be the first derivative of -x**6/780 - 2*x**5/195 - x**4/39 + 10*x**2 - 27. Let d(o) be the second derivative of n(o). Determine z so that d(z) = 0.
-2, 0
Let v(n) be the second derivative of n**7/42 - n**6/8 + 5*n**4/6 - 3*n**2 + 6*n. Let m(g) be the first derivative of v(g). Factor m(o).
5*o*(o - 2)**2*(o + 1)
Let f(p) be the second derivative of -1/5*p**2 + 5*p - 1/225*p**6 + 2/9*p**3 - 2/15*p**4 + 1/25*p**5 + 0. Determine j so that f(j) = 0.
1, 3
Let v(r) = -r**2 - r + 1. Let h(j) = 3 - 5 + 7*j**3 - j - 4*j**3 - 6*j**2. Let x(i) = -3*h(i) - 6*v(i). Factor x(b).
-3*b*(b - 3)*(3*b + 1)
Factor 20/13 - 2/13*a**3 - 42/13*a + 24/13*a**2.
-2*(a - 10)*(a - 1)**2/13
What is z in -6/5 - 2/15*z**2 - 4/3*z = 0?
-9, -1
Let w(m) = -m**3 - 74*m**2 + 581*m - 3. Let v(z) = -4*z**3 - 368*z**2 + 2904*z - 14. Let q(k) = 6*v(k) - 28*w(k). Determine h so that q(h) = 0.
0, 17
Let 15*o**2 - 13 + 5*o**3 + 0 - 2*o**3 - 14 + 9*o = 0. What is o?
-3, 1
Factor 200*w + 5*w**2 + 280 + 65 + 71 - 15*w**2 + 6*w**2.
-4*(w - 52)*(w + 2)
Let o(a) = a**3 - 6*a**2 + 11*a. Let s(d) = -5*d**3 + 25*d**2 - 45*d. Let f = -61 + 36. Let z(g) = f*o(g) - 6*s(g). What is b in z(b) = 0?
-1, 0, 1
Let z = -23 + 27. Factor -79*t**2 - 9*t**z + 32*t**3 + 0*t**4 + 5*t**4 + 108 + 7*t**2.
-4*(t - 3)**3*(t + 1)
Let l(h) be the second derivative of h**6/105 - h**5/10 + 3*h**4/14 + h**3/3 - 10*h**2/7 + 554*h. Suppose l(m) = 0. What is m?
-1, 1, 2, 5
Let p be 12 + 476/(-70) - (-2)/(-10). Let 41/7*h**2 - 1/7*h**3 - 24/7*h + 4/7 + 25/7*h**p - 45/7*h**4 = 0. Calculate h.
-1, 2/5, 1
Let d = -2509 - -17567/7. Factor 0*o**3 + 4/7*o**4 - 2/7*o - d*o**2 + 0 + 2/7*o**5.
2*o*(o - 1)*(o + 1)**3/7
Let m(q) be the first derivative of 5*q**6/6 - 16*q**5 + 80*q**4 - 38. Factor m(w).
5*w**3*(w - 8)**2
Let w(p) be the second derivative of -p**6/120 + 3*p**5/40 - p**4/4 + 5*p**3/12 - 3*p**2/8 + p - 2. Suppose w(q) = 0. What is q?
1, 3
Let o(b) be the third derivative of 2*b**3 + b**4 - 9*b**2 + 1/40*b**6 + 0*b + 0 + 1/4*b**5. Factor o(n).
3*(n + 1)*(n + 2)**2
Let a(w) be the third derivative of 0 + 36*w**2 + 2/3*w**3 + 0*w**5 + 0*w + 1/4*w**4 - 1/60*w**6. Factor a(p).
-2*(p - 2)*(p + 1)**2
Let n be (22/(-99))/((-12)/9). Let o(u) be the third derivative of 1/30*u**5 + 2*u**2 + 0*u - 1/60*u**6 + 0*u**3 + n*u**4 + 0. Solve o(i) = 0 for i.
-1, 0, 2
Let u(o) = 3*o + 47. Let l be u(-14). Let m be (-93)/(-36)*2 - l. Find w such that -1/6*w**3 + m*w - 1/3 - 1/6*w**4 + 1/2*w**2 = 0.
-2, -1, 1
Let r(d) = 2*d**4 - 10*d**3 - 174*d**2 - 426*d - 270. Let h(a) = -2*a**4 + 11*a**3 + 175*a**2 + 427*a + 270. Let p(l) = -6*h(l) - 5*r(l). Solve p(j) = 0 for j.
-3, -1, 15
Let j(k) be the first derivative of -k**4/9 - 4*k**3/27 + 2*k**2 + 4*k + 24. Factor j(l).
-4*(l - 3)*(l + 1)*(l + 3)/9
Let p(f) = 40*f**2 + 249*f + 209. Let k(v) = -20*v**2 - 125*v - 105. Let b(x) = -7*k(x) - 3*p(x). Determine m, given that b(m) = 0.
-27/5, -1
Suppose 0 = -4*r + 5*c - 17, -1 - 2 = r - c. Solve 2*g**2 - 6*g + g**r + 6*g**2 - 3*g**4 = 0 for g.
-2, 0, 1
Let v(j) be the second derivative of j**6/30 + 2*j**5/5 + 5*j**4/12 - 7*j**3/3 + 232*j. Factor v(c).
c*(c - 1)*(c + 2)*(c + 7)
Let v(h) be the second derivative of -h**7/15120 - h**6/1080 - h**5/180 - h**4/6 - 12*h. Let x(d) be the third derivative of v(d). Suppose x(j) = 0. What is j?
-2
Let a = -81153 - -10712077/132. Let z = 13/12 + a. Let -z*w - 2/11*w**2 + 0 = 0. Calculate w.
-1, 0
Suppose -43*l - 20 = -4*a - 41*l, -2*a + 3*l + 22 = 0. Solve 1/4 + 7/2*t**a - 15/4*t**4 - 2*t + 2*t**3 = 0.
-1, 1/5, 1/3, 1
Let h be (8/10)/(14/(-105)). Let j = h - -8. What is p in 2*p**3 - 2*p**5 - 7*p**4 - 2*p**2 + j*p - 10*p**3 + 2 + 0*p**5 - 1 = 0?
-1, 1/2
Let y(l) be the first derivative of 4/35*l**5 + 0*l**3 - 6 - 1/14*l**4 - 1/21*l**6 + 0*l**2 + 0*l. Factor y(p).
-2*p**3*(p - 1)**2/7
Let m be 12*(392/(-6))/(-2). Suppose -7*h - 9 = -23. Let 16 + 564*g**2 - m*g**3 - 343*g**4 - 10*g - 60*g**h - 150*g = 0. Calculate g.
-2, 2/7
Let j(a) be the second derivative of 9*a**5/70 - 29*a**4/42 - 10*a**3/7 + 8*a**2/7 - 2*a. Determine u, given that j(u) = 0.
-1, 2/9, 4
Let b(m) be the third derivative of -m**7/1120 - m**6/192 - m**5/80 - 9*m**4/8 - 22*m**2. Let u(t) be the second derivative of b(t). What is w in u(w) = 0?
-1, -2/3
Solve 0 + 7/5*a**4 - 1/5*a**5 - 7/5*a**2 + 19/5*a**3 - 18/5*a = 0.
-2, -1, 0, 1, 9
Let j(u) = -6*u**2 + 6*u + 2. Suppose 11*p + 19 + 14 = 0. Let y(x) = -x**3 - 5*x**2 + 5*x + 3. Let m(s) = p*j(s) + 2*y(s). Suppose m(a) = 0. Calculate a.
0, 2
Let -1024/3 - 12*m**4 - 896/3*m**2 + 256/3*m**3 + 2/3*m**5 + 512*m = 0. What is m?
2, 4
Suppose -29*z**2 - 3*z**3 - 24*z**2 + 37*z**2 + 15*z - 8*z**2 + 45*z = 0. Calculate z.
-10, 0, 2
Let r(v) be the first derivative of v**5/5 + 61*v**4/4 - 341. Factor r(c).
c**3*(c + 61)
Let q be (-10 - (-144)/15)/(-48). Let f(m) be the third derivative of -1/24*m**3 + 0*m - q*m**5 - 7*m**2 + 1/32*m**4 + 0. Determine s, given that f(s) = 0.
1/2, 1
Let q = 111/16 + -99/16. Suppose 3/4*w - q*w**2 + 0 = 0. Calculate w.
0, 1
Let g(u) be the first derivative of 5*u**3/3 + 5*u**2/2 - 10*u - 15. Factor g(s).
5*(s - 1)*(s + 2)
Let -9*m**2 - 13/4*m**4 + 0 - 1/4*m**5 + 0*m - 12*m**3 = 0. Calculate m.
-6, -1, 0
Suppose 54 = -4*d + 13*d. Let q be -1 + 2/d - (-48)/54. Factor 4/9*h - 2/9*h**2 - q.
-2*(h - 1)**2/9
Let t be 16/((-144)/27) - -8. Factor 1/2*s**4 + 1/3*s**3 - 1/6 + 1/6*s**t - 1/3*s**2 - 1/2*s.
(s - 1)*(s + 1)**4/6
Let l be (1*(-3)/(-108))/((-8)/(-12)). Let o(x) be the third derivative of 0 + x**2 + 0*x - l*x**4 - 1/360*x**6 + 0*x**3 - 1/45*x**5. Factor o(q).
-q*(q + 1)*(q + 3)/3
Let t be (4/6)/((-78)/(-78)). Solve -16/3 - 4*a**2 + 8*a + t*a**3 = 0 for a.
2
Factor -64/5 + 64/5*n - 4*n**2 + 2/5*n**3.
2*(n - 4)**2*(n - 2)/5
Let n(p) be the first derivative of -22 + 2/21*p**3 - 4/35*p**5 + 0*p**2 - 1/14*p**4 + 0*p. Suppose n(m) = 0. Calculate m.
-1, 0, 1/2
Let 1369/11 + 74/11*p + 1/11*p**2 = 0. Calculate p.
-37
Let b(x) be the first derivative of -1/4*x**4 - 2/15*x**5 + 1/18*x**6 - 2/3*x**2 + 8/9*x**3 + 0*x - 14. Suppose b(k) = 0. What is k?
-2, 0, 1, 2
Factor 4*b**5 - 48*b**2 - 1 + 1 + 829*b**4 + 52*b**3 + 16*b - 853*b**4.
4*b*(b - 2)**2*(b - 1)**2
Let s(v) = -4*v**3 + 52*v**2 - 52*v - 16. Let o(l) = -12*l**3 + 156*l**2 - 155*l - 44. Let h(d) = -4*o(d) + 11*s(d). Factor h(x).
4*x*(x - 12)*(x - 1)
Let z(b) be the first derivative of -b**5/25 + 14*b**4/5 - 242*b**3/5 - 812*b**2/5 - 841*b/5 - 548. What is x in z(x) = 0?
-1, 29
Let b(z) be the third derivative of 0 + 0*z - 8/9*z**3 + 2/9*z**4 + 3*z**2 - 1/45*z**5. Factor b(h).
-4*(h - 2)**2/3
Let f = 581/230 + -118/115. Factor 1/2*p + 0*p**2 + 0 - f*p**3 - p**4.
-p*(p + 1)**2*(2*p - 1)/2
Let l(x) be the first derivative of -4*x**5/15 - 7*x**4/12 + 62*x**3/9 - 5*x**2/2 - 202. Suppose l(c) = 0. Calculate c.
-5, 0, 1/4, 3
Let z(k) = -8*k - 48. Let a be z(-8). Suppose -4 = 14*i - a*i. Factor 3/4*u + 1/2 + 1/4*u**i.
(u + 1)*(u + 2)/4
Let u be 1/((-21)/(-112)) - 15/3. Let n(f) be the first derivative of -5 + u*f**4 - 16/9*f**3 + 8/3*f**2 + 0*f. Factor n(j).
4*j*(j - 2)**2/3
Let o(l) be the third derivative of l**7/105 + l**6/15 - 8*l**5/15 - 16*l**4/3 - 5*l**2 - 9*l. Let o(j) = 0. What is j?
-4, 0, 4
Suppose 5*p + 6 - 6 = 0. Let x(b) be the second derivative of 1/2*b**3 - 1/10*b**6 + p*b**2 - 3/4*b**4 + 9/20*b**5 + 5*b + 0. Suppose x(c) = 0. Calculate c.
0, 1
Let b(s) be the second derivative of 0 + 1/10*s**5 - 2/45*s**6 + 0*s**2 + 0*s**3 - 8*s - 1/18*s**4. Factor b(y).
-2*y**2*(y - 1)*(2*y - 1)/3
Factor 125*v**2 - 76 - 2*v**2 - 54 + 6*v**3 - 9*v**3 + 3*v + 7.
-3*(v - 41)*(v - 1)*(v + 1)
Factor -6859/8 - 1083/8*s - 57/8*s**2 - 1/8*s**3.
-(s + 19)**3/8
Suppose -1 = -4*u - 3*u + 13. Factor 21/5*y**u - 6/5*y + 0.
3*y*(7*y - 2)/5
Factor -1/6*m**3 - 1/2*m + 0 + 2/3*m**2.
-m*(m - 3)*(