Calculate x.
-8, -1, 0
Let p(f) be the third derivative of -f**6/180 + f**5/90 + 5*f**4/36 + f**3/3 - 6*f**2 - 5*f. Factor p(a).
-2*(a - 3)*(a + 1)**2/3
Let l = 1073/2 + -520. Let w = l + -15. Let 0 + 1/2*q**4 - w*q**2 + 0*q**3 - q = 0. What is q?
-1, 0, 2
Let s = -29 + 71. Let v = s - 23. Find a, given that -6 + 8*a + v*a**2 - 4*a**2 + a = 0.
-1, 2/5
Let u(r) = -65*r**3 - 25*r**2 + 30*r + 60. Let d(s) = -11*s**3 - 4*s**2 + 5*s + 10. Let l(w) = 35*d(w) - 6*u(w). Let l(t) = 0. What is t?
-2, -1, 1
Let x be (20/(-12))/(2/(-6)). Suppose g**4 - 1021*g**x + 5*g**4 - 2 - 28*g**2 - 15*g - 14*g**3 + 1026*g**5 = 0. Calculate g.
-1, -1/5, 2
Let m(d) be the first derivative of d**4/22 + 16*d**3/33 + d**2 - 40*d/11 + 302. Factor m(a).
2*(a - 1)*(a + 4)*(a + 5)/11
Let r(u) = -5*u**5 + u**4 - u**3 + 5*u**2 - 6*u - 6. Suppose 2*g = -4*g - 36. Let d(y) = -y**4 + y**3 + y + 1. Let q(t) = g*d(t) - r(t). Factor q(v).
5*v**2*(v - 1)*(v + 1)**2
Let h(z) be the first derivative of -5*z**4/4 - 65*z**3/3 - 120*z**2 - 180*z + 21. Let h(v) = 0. What is v?
-6, -1
Let n(j) = 2*j. Let o(r) = r**2 - 4*r + 9. Let l(i) = -10*n(i) - 2*o(i). Factor l(g).
-2*(g + 3)**2
Let f(q) be the first derivative of 3*q**5/10 - 11*q**4/24 - 17*q**3/9 + 11*q**2/3 - 4*q/3 - 61. Suppose f(u) = 0. What is u?
-2, 2/9, 1, 2
Let t(i) = -i**3 + i**2 + i + 1. Let v be t(-1). Factor -4*s + s + s**2 + 4 - v*s.
(s - 4)*(s - 1)
Let n(k) = -2*k**3 - 9*k**2 + 32. Let z be n(-3). Factor 2/15*g**3 - 2/15*g**z - 2/15*g**2 + 0 + 2/15*g**4 + 0*g.
-2*g**2*(g - 1)**2*(g + 1)/15
Let i(s) be the third derivative of 1/210*s**6 + 0*s + 0*s**4 + 0*s**3 + 0 + 0*s**7 + 0*s**5 - 3*s**2 - 1/588*s**8. Let i(l) = 0. Calculate l.
-1, 0, 1
Determine b so that -24*b - 600 + 130*b + 193*b**2 + 192*b**2 + 109*b - 390*b**2 = 0.
3, 40
Let z be (-98)/(-12) + -8 + 82/12. Let t(v) be the second derivative of 1/2*v**4 + 1/14*v**z + 0 + 0*v**2 - 1/2*v**3 + 0*v**5 - v - 1/5*v**6. Factor t(f).
3*f*(f - 1)**3*(f + 1)
Let p(u) be the second derivative of -u**4/78 + 11*u**3/39 + 12*u**2/13 + 3*u + 35. Find g such that p(g) = 0.
-1, 12
Suppose 4*c + 7*q - 2*q + 95 = 0, -c = 5*q + 20. Let u = c + 31. Factor -38*r - r**2 - 2*r**2 + u + 35*r.
-3*(r - 1)*(r + 2)
Let n(z) be the first derivative of -5*z**4/4 + 155*z**3/3 - 1275*z**2/2 + 1125*z - 471. What is o in n(o) = 0?
1, 15
Let k(c) be the second derivative of c**6/3600 + c**5/240 + c**4/60 + 5*c**3/6 - 9*c. Let r(o) be the second derivative of k(o). Factor r(i).
(i + 1)*(i + 4)/10
Factor 0*t**5 - 48*t**3 + 10*t**2 + 1198*t**4 + 26*t**2 - 1185*t**4 - t**5.
-t**2*(t - 6)**2*(t - 1)
Let j(x) = 3*x + 10. Let g(h) = -5*h - 15. Let t(b) = -5*g(b) - 8*j(b). Let w be t(10). Factor -4*s**2 + 0 + 8*s + w - 3 - s.
-(s - 2)*(4*s + 1)
Suppose 6*d = 3*d - 384. Let c = d + 130. Factor c + 3/2*w**2 - 3*w - 1/4*w**3.
-(w - 2)**3/4
Let a(y) = -10*y - 58. Let f be a(-6). Let m(g) be the first derivative of g**4 + 2*g - 2*g**f + 1 + 0*g**3 - 2/5*g**5. Factor m(c).
-2*(c - 1)**3*(c + 1)
Let k be (27/9)/(3*2). Find a such that k*a**2 - 3/4*a - 1/2 = 0.
-1/2, 2
Suppose -10*y = -6*y - 12. Factor 3*v**4 + 0*v**3 - 7*v**3 - 2*v**y + 4*v**2 + 2*v**2.
3*v**2*(v - 2)*(v - 1)
Suppose 2 = 5*w - 3. Suppose -9 = -4*b - w. Factor -2*v - 3*v**3 + 2*v**2 - b*v**4 - 3*v**3 + 4*v**3 + 4*v.
-2*v*(v - 1)*(v + 1)**2
Let c(n) be the second derivative of n**7/14 + 3*n**6/2 + 177*n**5/20 + 97*n**4/4 + 36*n**3 + 30*n**2 - 6*n + 17. Suppose c(i) = 0. What is i?
-10, -2, -1
Suppose 2*r - 12 = 2*p, -5*r + 3*p = p - 21. Let m(b) = -b**3 - 2*b**2 + 3*b + 3. Let d be m(-3). Solve 2*w**2 - 3*w**d + 3*w**4 + 7*w**2 + r*w + 12*w**3 = 0.
-1, 0
Let i(r) = r**3 - 11*r**2 + 10*r - 3. Let f be i(10). Let h be (f + 9)/((-15)/(-16)). Factor -48/5*o - 2/5*o**3 + h + 18/5*o**2.
-2*(o - 4)**2*(o - 1)/5
Let w(y) = 20*y - 48. Let s = -8 - -30. Let f = -18 + s. Let l(v) = v**2 + 100*v - 239. Let m(n) = f*l(n) - 22*w(n). Determine c, given that m(c) = 0.
5
Let c(b) be the first derivative of b**4/26 - 2*b**3/3 + 3*b**2 - 54*b/13 - 160. Let c(f) = 0. What is f?
1, 3, 9
Let b(k) be the first derivative of -k**5/10 - k**4/2 + k**3/3 + 3*k**2 - 13*k - 4. Let h(m) be the first derivative of b(m). Suppose h(q) = 0. What is q?
-3, -1, 1
Let u(k) = -3*k + 17. Let b be u(5). Let -10 - b*v**2 + 2 + v**2 + 4 + 4*v = 0. Calculate v.
2
Let -360*h + 8*h**3 - 21*h**3 + 64 + 402*h**2 + 38*h**3 + 0 + 31*h**3 = 0. Calculate h.
-8, 1/4, 4/7
Let q(o) be the second derivative of o**6/5 - 23*o**5/10 + 55*o**4/6 - 11*o**3 - 18*o**2 + 4*o + 12. Factor q(t).
2*(t - 3)**2*(t - 2)*(3*t + 1)
Let k(v) = v**2 + 9*v + 4. Let l = -13 + 4. Let y be k(l). Determine c so that -4*c**2 - 237 + 243 + 2*c**2 + y*c = 0.
-1, 3
Suppose 1162*o = 1167*o. Let i(x) be the third derivative of 1/120*x**5 + 0 + 1/3*x**3 + o*x + 1/12*x**4 - 4*x**2. Factor i(w).
(w + 2)**2/2
Suppose 30*y = -y + 62. Let r(j) be the first derivative of 1/2*j**4 - 16*j + 12*j**y - 4*j**3 - 4. Determine w so that r(w) = 0.
2
Suppose 2*k = -5*q + 3, q + 2 + 11 = 3*k. Let s be k + -2*4/4. Factor -2*b**s - 2*b**4 + 3*b**3 + 1/2*b**5 + 1/2*b + 0.
b*(b - 1)**4/2
Let m(u) be the third derivative of -u**6/120 - u**5/30 + u**4/24 + u**3/3 + 69*u**2. Factor m(c).
-(c - 1)*(c + 1)*(c + 2)
Suppose 4*n + 144 = 160. Suppose 0 - 2/3*h - 9/2*h**3 + n*h**2 = 0. What is h?
0, 2/9, 2/3
Suppose -14 + 1/3*i**2 - 19/3*i = 0. What is i?
-2, 21
Let a(y) be the second derivative of -y**5/20 + 13*y**4/12 - 23*y**3/6 + 11*y**2/2 + 5*y. Factor a(n).
-(n - 11)*(n - 1)**2
Let h(r) be the second derivative of -r**7/210 - r**6/25 - 2*r**5/25 + r**4/30 + 3*r**3/10 + 2*r**2/5 + 150*r. Factor h(l).
-(l - 1)*(l + 1)**3*(l + 4)/5
Let j(r) = -2*r**2 - 16 - 11*r + 5*r**2 - 4*r**2 - 7*r. Let n be j(-10). Factor -24*q - n*q**3 - 2 - 56*q**2 - 72*q**4 + 36*q**4 - 2 - 8*q**5.
-4*(q + 1)**4*(2*q + 1)
Let g be 7 - (-480)/(-78) - 80/(-520). Suppose 0 = -6*x + 2*x + 8. Let -g + a**x - 3/2*a = 0. Calculate a.
-1/2, 2
Let t = 41 + -83. Let o = t + 44. Factor 3/5 + 3/5*a**o - 6/5*a.
3*(a - 1)**2/5
Let j(n) = 17*n**2 - 90*n - 140. Let f(o) = -6*o**2 + 30*o + 48. Let p(s) = 11*f(s) + 4*j(s). Find q such that p(q) = 0.
-1, 16
Let n(d) = 5 + d**2 - 18*d + 4 - 4. Let q be n(18). Factor -134 + q*l**2 + 16*l + 130 - 16*l**3 - l**2.
-4*(l - 1)*(l + 1)*(4*l - 1)
Let n = -26/69 - -24/23. Let y be (-12)/(-5) - 24/(-40). Factor -n*z**2 + 2/9*z - 2/9*z**y + 2/3.
-2*(z - 1)*(z + 1)*(z + 3)/9
Let r(h) be the third derivative of 0 + 1/1155*h**7 + 0*h**3 + 0*h + 1/66*h**4 - 1/110*h**5 + 14*h**2 + 0*h**6. Let r(u) = 0. What is u?
-2, 0, 1
Suppose -20 = -g + 6*g, -3*d + 4*g = -199. Suppose d - 61 + 5*q**2 + 5*q**4 - 10*q**3 = 0. What is q?
0, 1
Let j(h) be the first derivative of h**5/360 - h**4/36 - 5*h**3/36 + 10*h**2 + 7. Let s(b) be the second derivative of j(b). Find w, given that s(w) = 0.
-1, 5
Let n(j) be the second derivative of -1/15*j**6 + 0*j**3 + 9*j + 0*j**2 - 1/18*j**4 + 0 - 1/63*j**7 - 1/10*j**5. Determine g, given that n(g) = 0.
-1, 0
Let t(l) = -l**3 + l**2 - l + 1. Let i(d) = -41 + 24 + 3*d - 25*d**2 + 12*d + 5*d**3 + 22. Let z(f) = i(f) + 10*t(f). Suppose z(k) = 0. Calculate k.
-3, -1, 1
Find x such that -10 - 6*x**2 - 136*x - 6*x**2 - 25 - 9 = 0.
-11, -1/3
Let h(y) be the third derivative of -1/24*y**4 + 0*y**3 + 0*y + 0 + 0*y**5 + 1/120*y**6 - 4*y**2. Let h(w) = 0. Calculate w.
-1, 0, 1
Let a(s) be the third derivative of s**6/480 - s**5/48 - s**4/96 + 5*s**3/24 - 130*s**2. Find m, given that a(m) = 0.
-1, 1, 5
Factor -75 - 18*a**2 - 4*a**3 - 18*a**2 - 108*a - 33.
-4*(a + 3)**3
Let l(a) be the first derivative of -4*a**3/3 - 50*a**2 + 104*a + 55. Find o, given that l(o) = 0.
-26, 1
Let j = 70393/11 + -6399. Solve j*n**2 - 4/11*n**3 + 6/11*n + 2/11 - 6/11*n**4 - 2/11*n**5 = 0 for n.
-1, 1
Suppose -20 = 4*d, -2*h - 20 = 3*d - 5. Suppose 2*t - 8*t = h. Factor t*a + 1/3*a**5 + 0 + 2/3*a**4 + 0*a**3 + 0*a**2.
a**4*(a + 2)/3
Let z(m) be the second derivative of -1/6*m**4 - 5/3*m**3 - 3*m**2 + 1/10*m**5 + 0 + 5*m. Suppose z(l) = 0. What is l?
-1, 3
Let m(f) = -f**2 + 11*f - 8. Let p be m(12). Let k = p - -23. Factor -2*o**k - 42*o**4 - 3*o**2 + 43*o**4 + 2*o + 2*o**2.
o*(o - 2)*(o - 1)*(o + 1)
Find w such that -4*w**3 - 3*w**3 + 2*w**3 + 8*w - w**4 + 2*w**3 + 6*w**2 = 0.
-