 7*u**3 + 18 + 1/2*u**4.
(u + 1)*(u + 2)**2*(u + 9)/2
Let f = -3 - -6. Suppose i - 14 = -5*h, 0 = i - f*h + 6 - 4. Factor 2*d**2 - i*d**2 + 3*d**4 + d**5 - d - d**4.
d*(d - 1)*(d + 1)**3
Determine d, given that -4/7*d**4 - 80/7*d**2 + 12 - 88/7*d + 88/7*d**3 = 0.
-1, 1, 21
Let f(g) = g**2 - 6*g - 2. Let u be f(7). Suppose -t + u*t - 12 = 0. Factor 3*o**3 - 3*o**2 + t*o**4 - 5*o + 2*o + 0*o.
3*o*(o - 1)*(o + 1)**2
Let v be 222/226 + (6 - 9) - -2. Let y = v + 1021/226. Suppose y*t**2 + 3/2*t**3 + 9/2*t + 3/2 = 0. What is t?
-1
Let v = 8745/7 + -1249. Factor -2/7*g**3 + 0 + 2/7*g**2 + 2/7*g**5 + 0*g - v*g**4.
2*g**2*(g - 1)**2*(g + 1)/7
Factor 4*q**3 + 180*q**2 + 189*q**2 - 401*q**2 + 28*q.
4*q*(q - 7)*(q - 1)
Let k(m) be the second derivative of -m**7/4200 - m**6/900 + 13*m**3/6 + 13*m. Let p(o) be the second derivative of k(o). Factor p(a).
-a**2*(a + 2)/5
Suppose -2*d + 12 = -2*f, -7*d + 5*f = -4*d - 26. Solve 2/19*v**3 + 0 + 4/19*v**4 + 0*v + 2/19*v**5 + 0*v**d = 0.
-1, 0
Let k(w) be the second derivative of -w**4/34 - 4*w**3/51 - w**2/17 - 11*w - 2. Determine z, given that k(z) = 0.
-1, -1/3
Let s(d) = -2*d**3 + 9*d**2 - 9*d - 2. Let j(f) = 4*f**3 - 18*f**2 + 17*f + 6. Let g = 147 - 140. Let w(n) = g*s(n) + 3*j(n). Let w(t) = 0. Calculate t.
1/2, 2
Let r = -27 + 39. Suppose 0 = -4*h + 24 + r. Find j, given that h*j - 4 - j**2 - 8*j + 3*j = 0.
2
Let b(g) be the third derivative of g**6/120 - 7*g**5/60 + g**4/4 + 158*g**2. Factor b(k).
k*(k - 6)*(k - 1)
Suppose -12 = -4*s + 3*x, -6*s + s = 2*x - 15. Suppose -4 = 5*t + 4*g, 2*t + s*t + g = -1. Find b, given that -2/5*b**2 + t + 4/5*b = 0.
0, 2
Let u = 709/36342 - 2/2019. Let p(k) be the second derivative of 1/27*k**3 - u*k**4 + 0*k**2 + 0 - 5*k. Factor p(m).
-2*m*(m - 1)/9
Solve 419*j**3 - 704*j - 18*j**5 - 86*j**4 + 1 + 127 + 552*j**2 - 291*j**3 = 0 for j.
-4, 2/9, 1, 2
Let n(q) be the second derivative of q**4/8 - 77*q**3/4 - 117*q**2/2 + q - 37. Factor n(h).
3*(h - 78)*(h + 1)/2
Find y, given that 159*y**3 + 8*y**2 + 124*y**3 - 4*y**5 - 271*y**3 = 0.
-1, 0, 2
Factor -2*k**3 + 1/2*k**4 - k + 5/2*k**2 + 0.
k*(k - 2)*(k - 1)**2/2
Let n = -22 + 56. Let s = n - 27. Solve -4*m - s*m**2 + 4 + 2*m - 10*m = 0 for m.
-2, 2/7
Factor -1/2 - 1/4*z**2 - 3/4*z.
-(z + 1)*(z + 2)/4
Let j = -23 + 25. Find p, given that p**j + p**2 + p**2 - 28 - 6*p + 31 = 0.
1
Factor -45*w**2 + 5*w**5 - 5*w**2 - 30*w**4 - 34*w**3 + 94*w**3 - 332*w + 347*w.
5*w*(w - 3)*(w - 1)**3
Let y(q) be the third derivative of 0*q**3 - 1/70*q**7 + 0*q**4 + 0*q - 1 + 1/336*q**8 - 25*q**2 + 1/15*q**5 + 0*q**6. Determine s so that y(s) = 0.
-1, 0, 2
Suppose 0 = 8*a - 11*a + 6. Determine f so that 2/5*f**4 + 12/5*f**a - 8/5*f + 2/5 - 8/5*f**3 = 0.
1
Let z be (99/88)/(3/4). Let 3/4*v**2 + z - 9/4*v = 0. Calculate v.
1, 2
Suppose -25*n + 20*n + 15 = 0. Factor -5*l**3 + 3*l + 10*l**4 + 8 - 15*l**2 - n + 2*l.
5*(l - 1)**2*(l + 1)*(2*l + 1)
Let i(x) be the third derivative of -x**7/1470 + x**6/105 - 17*x**5/420 - x**4/84 + 4*x**3/7 - 28*x**2. Solve i(m) = 0 for m.
-1, 2, 3, 4
Let o(w) = w**3 - 7*w**2 - 7*w - 5. Let a be o(8). Suppose -12 = -j - 5*i, a*j - 5*i = -5 + 1. Factor -s**3 - 4 + j*s**2 - 3*s**2 - s**2 + 7*s + 0*s**2.
-(s - 1)**2*(s + 4)
Factor -2/9*b**5 + 2/9*b**4 + 2/9 + 4/9*b**3 - 2/9*b - 4/9*b**2.
-2*(b - 1)**3*(b + 1)**2/9
Let q(c) be the second derivative of 9*c**6/10 - 207*c**5/10 + 157*c**4/4 + 76*c**3 + 42*c**2 + 344*c. Let q(i) = 0. Calculate i.
-1/3, 2, 14
Suppose 5*c = q - 10, 5*c + 323 = 313. What is s in 0*s + 0 + q*s**2 + s**3 - 1/2*s**4 - 1/2*s**5 = 0?
-2, 0, 1
Let n(w) be the first derivative of 5*w**7/84 - w**6/4 + 3*w**5/8 - 5*w**4/24 + 13*w + 1. Let q(z) be the first derivative of n(z). Factor q(l).
5*l**2*(l - 1)**3/2
Let u be 2/19 + (60 - (-90220)/(-1520)). Let 7/4*r**5 + 0 + 0*r + u*r**3 + 3*r**4 - 1/2*r**2 = 0. Calculate r.
-1, 0, 2/7
Suppose -96 = 12*t - 9*t. Let q = t - -34. Let -1/4*c**4 - 1 - 3*c - 13/4*c**q - 3/2*c**3 = 0. Calculate c.
-2, -1
Let g(h) be the second derivative of -23/8*h**5 + 0 + 625/8*h**2 + 875/24*h**3 + 13/24*h**6 - 26*h - 25/24*h**4 - 5/168*h**7. Let g(x) = 0. What is x?
-1, 5
Let s(h) be the first derivative of -2*h**3/3 - 29*h**2 + 60*h + 421. Solve s(j) = 0.
-30, 1
Let b(o) be the second derivative of -o**7/231 + 7*o**6/165 + 17*o**5/110 + 3*o**4/22 - 2*o - 7. Solve b(x) = 0 for x.
-1, 0, 9
Let i = 136 + -130. Let o be (-4)/i - (-34)/17. Solve 1/3*u**3 + u**2 + 0*u - o = 0.
-2, 1
Let t be 168/585 + 29/(4350/(-20)). Let 2/13*k**3 + 0 + t*k + 4/13*k**2 = 0. Calculate k.
-1, 0
Let a(q) be the third derivative of 3*q**7/35 + q**6/8 - 5*q**5/4 - 5*q**4/2 + 2*q**3 + 57*q**2 + 7*q. Determine o, given that a(o) = 0.
-2, -1, 1/6, 2
Let t(h) be the second derivative of -h**6/45 + 14*h**5/15 - 11*h**4/2 + 8*h**3 - 114*h. Determine z so that t(z) = 0.
0, 1, 3, 24
Let c(i) be the second derivative of 0 + 0*i**3 - 1/78*i**4 + 1/13*i**2 - 18*i. Solve c(o) = 0.
-1, 1
Let s(v) = 6*v**3 + 6*v**2 - 6*v + 2. Let g(k) = -5*k**3 - 5*k**2 + 5*k - 1. Let z be (-10)/(-3)*6/5. Let a(r) = z*g(r) + 3*s(r). Factor a(l).
-2*(l - 1)*(l + 1)**2
Let b(k) be the first derivative of -2*k**3/27 - 12*k**2 - 648*k - 196. Suppose b(w) = 0. Calculate w.
-54
Let u(c) be the second derivative of -c**6/900 + c**5/75 - 25*c**3/6 + 30*c. Let t(d) be the second derivative of u(d). Factor t(k).
-2*k*(k - 4)/5
Let t(h) = 3*h**4 + 21*h**3 + 15*h**2. Let b(z) = -z**3 - z**2. Suppose r - 2*r = 1. Let j(w) = r*t(w) - 15*b(w). Determine n, given that j(n) = 0.
-2, 0
Let o(q) be the first derivative of -1/70*q**5 + 5/21*q**3 - 3/7*q**2 + 1 - 1/42*q**4 - 4*q. Let s(w) be the first derivative of o(w). What is r in s(r) = 0?
-3, 1
Let l(p) = -7*p - 20. Let a be l(-4). Let j be (2/5)/(a/5). Factor j*y**2 + 0*y - 1/4.
(y - 1)*(y + 1)/4
Let w(t) be the third derivative of t**6/90 + t**5/15 + t**4/6 + 8*t**3/3 + 9*t**2. Let a(y) be the first derivative of w(y). Factor a(p).
4*(p + 1)**2
Let p be 2 - (-4)/(-8) - (-3)/2. Let v(k) be the first derivative of -1 + 3/8*k**4 - 3/2*k**p + 3/2*k**2 + 0*k. Determine b so that v(b) = 0.
0, 1, 2
Let d(s) = s**5 - 19*s**4 - 7*s**3 + 19*s**2 - 6*s + 12. Let y(g) = g**5 - 18*g**4 - 6*g**3 + 18*g**2 - 5*g + 10. Let w(n) = 5*d(n) - 6*y(n). Factor w(x).
-x**2*(x - 13)*(x - 1)*(x + 1)
Let s(w) be the third derivative of w**9/3024 - w**8/1344 - 11*w**4/12 + 17*w**2. Let o(d) be the second derivative of s(d). Let o(t) = 0. What is t?
0, 1
Let s be 6/(-9) - (-10)/15. Suppose -3*k + s*k = -9. Factor -3*y + 2*y**2 + 7*y**3 - y**2 - 4*y**2 + k - 4*y**3.
3*(y - 1)**2*(y + 1)
Suppose 0 = 2*l - j - 2 + 3, -4*l + 3 = 3*j. Let o = -3867/7 - -553. Solve 2/7*a**3 + 0*a + l + 2/7*a**5 + 0*a**2 - o*a**4 = 0 for a.
0, 1
Let d(p) = -9*p**3 + p**2 - 3*p - 2. Let m be d(2). Let o be (m/20 - -4)*4. Solve o - 2*j**3 + 6/5*j + 4/5*j**5 + 6/5*j**4 - 2*j**2 = 0 for j.
-2, -1, -1/2, 1
Let b be ((8/6)/(-1))/((-8)/12). Let q be -1*(-8)/b - (4 - 0). Factor 1/5*m**2 + 2/5*m + q.
m*(m + 2)/5
Let x(w) be the second derivative of -w**6/10 + 2*w**5/3 - w**4/2 + 4*w**2 + 15*w. Let g(s) be the first derivative of x(s). Let g(c) = 0. Calculate c.
0, 1/3, 3
Let w(v) be the first derivative of 1/3*v**3 + 9*v + 3*v**2 + 2. Factor w(k).
(k + 3)**2
Let s(m) = 6*m**2 + 16*m. Let y(p) = 6*p**2 + 16*p + 2. Let l(o) = -4*s(o) + 5*y(o). Factor l(b).
2*(b + 1)*(3*b + 5)
Let a(l) = -l + 13. Let b be a(10). Suppose 3*c**5 - 2*c + 5*c**4 - c + 3 - 2*c**4 + 6*c - 6*c**2 - 6*c**b = 0. What is c?
-1, 1
Let f be 30 + -24 - ((-994)/24)/(-7). Let i(s) be the second derivative of 1/12*s**4 + f*s**3 + 1/40*s**5 + 0 - 12*s + 0*s**2. Factor i(w).
w*(w + 1)**2/2
Let w = 77380796303/312078619708 + 2/79856351. Let h = 2/977 + w. Factor 3/4*d - 1/4*d**2 + 1/2 - 3/4*d**3 - h*d**4.
-(d - 1)*(d + 1)**2*(d + 2)/4
Let o(u) be the second derivative of u**7/7560 - u**5/360 - 17*u**4/6 - 11*u. Let r(n) be the third derivative of o(n). Factor r(a).
(a - 1)*(a + 1)/3
Suppose 41 = 4*q + 5*h, -2*q - 18 = -4*q - 2*h. Factor 116*o**q - 2*o**3 - 3*o**3 - 121*o**4.
-5*o**3*(o + 1)
Let i(t) = 17*t**2 + 153*t + 411. Let l(c) = 9*c**2 + 76*c + 207. Let r(p) = -4*i(p) + 7*l(p). Determine v so that r(v) = 0.
-13, -3
Let z(v) be the third derivative of -v**8/2240 - v**7/840 + v**6/60 + v**5/10 - 