 76*h/5 + 126. Find f, given that k(f) = 0.
-38, -1
Let u = 657 + -1970/3. Determine q, given that 0 + 2/3*q**2 - 1/3*q**4 + u*q**3 + 0*q = 0.
-1, 0, 2
Let b(h) be the third derivative of h**5/60 - h**4/3 - 3*h**3/2 + 24*h**2. Factor b(g).
(g - 9)*(g + 1)
Let g(r) = 2*r**2 - 22*r. Let z(v) = 5*v**2 - 45*v. Let d(h) = -14*g(h) + 6*z(h). Factor d(s).
2*s*(s + 19)
Factor 9/2*b**2 + 15/4*b + 3/4*b**3 + 0.
3*b*(b + 1)*(b + 5)/4
Let i(o) be the first derivative of o**6/9 - 38*o**5/15 - 137*o**4/6 - 626*o**3/9 - 296*o**2/3 - 200*o/3 + 176. Let i(m) = 0. What is m?
-2, -1, 25
Let r be (-4)/16 - 39/(-12). Suppose 0 = -r*p + 2*p + 3. Let -14*l**3 + 30*l**3 + 3*l**4 - 13*l**p = 0. What is l?
-1, 0
Let a = -53 + 55. Factor 361*i**3 - 5*i**a + 5*i - 16*i**2 - 366*i**3 + 20*i**4 + i**2.
5*i*(i - 1)*(i + 1)*(4*i - 1)
Let k(u) be the first derivative of -3*u**5/40 + u**4/8 + u**3 - 3*u**2 - 16*u + 7. Let r(p) be the first derivative of k(p). Factor r(o).
-3*(o - 2)*(o - 1)*(o + 2)/2
Let s(y) = -y**2 + 102*y + 2601. Let b(j) = 2*j**2 - 102*j - 2601. Let g(k) = -4*b(k) - 6*s(k). Let g(a) = 0. Calculate a.
-51
Let s = -2/869 - 22584/4345. Let f = 88/15 + s. Solve 0 - 2/3*y - f*y**2 = 0 for y.
-1, 0
Let g(f) be the first derivative of -2*f**6/105 - 3*f**5/35 + 8*f**3/21 + 16*f - 26. Let j(l) be the first derivative of g(l). Factor j(h).
-4*h*(h - 1)*(h + 2)**2/7
Let r = 208 + -14975/72. Let q(z) be the third derivative of -z**2 + r*z**4 + 1/180*z**5 - 1/252*z**8 - 1/40*z**6 + 0 + 0*z**3 + 11/630*z**7 + 0*z. Factor q(c).
-c*(c - 1)**3*(4*c + 1)/3
Let c(v) = -1403*v + 14032. Let r be c(10). Factor 3/2*z**r + 1/4*z**3 + 1 + 9/4*z.
(z + 1)**2*(z + 4)/4
Factor 177*w**3 + w**4 + 5*w**5 - 6*w**5 - 175*w**3.
-w**3*(w - 2)*(w + 1)
Suppose 3*q = -y + 6, q + 2*y + 4 = 1. Let d be (1/(2 - q))/(-3). Factor d*w + 1/3*w**4 - w**2 - 1/3*w**3 + 2/3.
(w - 2)*(w - 1)*(w + 1)**2/3
What is i in 1635*i + 443*i**2 - 655*i**2 - 2*i**3 - 510 + 9*i**3 + 60 = 0?
2/7, 15
Solve 18*w**3 - 5*w**3 + 3*w - 10*w**3 - 6*w**3 = 0 for w.
-1, 0, 1
Let m(h) be the first derivative of 0*h + 0*h**2 + 39 - 7/5*h**3 - 3/20*h**4. Factor m(o).
-3*o**2*(o + 7)/5
Let l(d) be the second derivative of 0 - 12*d + 0*d**2 + 1/2*d**5 - 5/12*d**4 - 5/3*d**3 + 1/6*d**6. Factor l(i).
5*i*(i - 1)*(i + 1)*(i + 2)
Let a be (1 + 5 + -10)/(1/(-47)). Let z = a + -188. Let z*q**2 - 4/9*q**4 + 2/9*q**5 + 0 + 0*q + 2/9*q**3 = 0. What is q?
0, 1
Let h(f) be the third derivative of -5/24*f**4 + 3/40*f**6 + 0*f + f**2 + 0 - 1/6*f**3 - 1/20*f**5. Factor h(u).
(u - 1)*(3*u + 1)**2
Factor -8/7*f + 8/7*f**2 - 2/7*f**5 + 6/7*f**3 + 0 - 4/7*f**4.
-2*f*(f - 1)**2*(f + 2)**2/7
Let n = -34405 - -34407. Factor -7/4*u**n - 19/4*u + 3/2.
-(u + 3)*(7*u - 2)/4
Let a(h) = -47*h + 17. Let j be a(-3). Let f = 792/5 - j. Factor -f*l - 1/5*l**2 + 0.
-l*(l + 2)/5
Suppose 5*w = 4*t + 12, 2*w + w - 12 = 0. Find b such that b**t - 16*b - 3 - 1 + 16 + 3*b**2 = 0.
1, 3
Suppose 0*t = 4*t - 2*f - 2, 0 = 2*t + 2*f - 10. Factor -3092 - 15*o**t - 20*o + 5*o**3 + 3092.
5*o*(o - 4)*(o + 1)
Let n(h) be the third derivative of 5/24*h**4 - 13*h**2 + 1/36*h**6 + 0*h**7 + 0 - 1/1008*h**8 - 2/9*h**3 - 1/9*h**5 + 0*h. Let n(c) = 0. What is c?
-4, 1
Let o(c) be the third derivative of -4*c**2 + 1/8*c**4 + 0*c**3 + 0 + 0*c + 1/20*c**5. Let o(u) = 0. Calculate u.
-1, 0
Let l(b) be the first derivative of 3/8*b**2 + 1/2*b**3 + 10 - 3/4*b. Find p, given that l(p) = 0.
-1, 1/2
Find u, given that 26*u**3 + 943*u**5 - 20*u**2 - 4*u**4 - 467*u**5 - 478*u**5 = 0.
-5, 0, 1, 2
Let p(f) be the first derivative of f**6/6 + 3*f**5/5 + f**4/4 - f**3 - f**2 + 39. Suppose p(w) = 0. What is w?
-2, -1, 0, 1
Let z(g) = -g**3 + 22*g**2 + 23*g + 9. Let k be z(23). Let u = k - 9. Find y such that -2/5*y**2 + 0 + u*y = 0.
0
Let w(n) = -2*n**3 + 3*n**2 + n + 1. Let f(t) = -55*t**3 + 1005*t**2 + 41430*t - 42290. Let i(z) = f(z) - 30*w(z). Find a such that i(a) = 0.
-92, 1
Let f = -9/638 + 7719/4466. Let 48/7*r + 57/7*r**3 + 3*r**4 + f + 3/7*r**5 + 75/7*r**2 = 0. Calculate r.
-2, -1
Suppose -2*p - 2 = v, -2*v - 6 = -4*p - 34. Suppose 2*o - o**2 + v*o - 9*o + 2*o**2 = 0. What is o?
0, 1
Let k be 92/9 + -6 - 5 - -1. Factor 0 - k*w**2 + 8/9*w.
-2*w*(w - 4)/9
Let x(h) = -h**2 - 13*h - 2. Let y(i) = -10*i**2 - 155*i - 25. Let d(o) = 25*x(o) - 2*y(o). Factor d(w).
-5*w*(w + 3)
Factor -6*d**4 + 32 + 36*d**2 + 7*d**4 + 10*d**3 - 26*d + 68*d + 14*d.
(d + 2)**3*(d + 4)
Let m(k) be the third derivative of 0*k**3 - 1/270*k**6 + 0 + 0*k - 1/270*k**5 - 1/945*k**7 + 0*k**4 + 17*k**2. Find s such that m(s) = 0.
-1, 0
Solve y + 0 + 3/2*y**2 - 1/2*y**3 - 1/2*y**5 - 3/2*y**4 = 0 for y.
-2, -1, 0, 1
Factor -2030*o + 253*o**3 + 1000 - 2070*o - 681*o**3 + 540*o**2 + 1680*o**2 + 28*o**4.
4*(o - 5)**3*(7*o - 2)
Let t(v) be the third derivative of v**8/560 + v**7/350 - v**6/50 - v**5/25 + 154*v**2. Determine o so that t(o) = 0.
-2, -1, 0, 2
Suppose 20 = 5*m + 5. Suppose 1 = -2*c - m, -4*a + 16 = -2*c. Suppose a*f**3 - 4*f + 0*f**3 + f = 0. What is f?
-1, 0, 1
Let h(c) be the second derivative of 1/12*c**4 + 6*c + 0 - 1/3*c**3 + 3/2*c**2. Let f(a) = -4*a**2 + 7*a - 12. Let r(x) = -2*f(x) - 9*h(x). Solve r(m) = 0.
1, 3
Suppose -a + 4*m - 16 = 0, 0 = a + 3*a + 3*m - 31. Suppose 6*f - a + 1 - 4*f**2 - f**2 + 2*f**2 = 0. What is f?
1
Let b(o) = -36*o + 2. Let a be b(0). Let j(z) be the third derivative of 4*z**a - 1/360*z**6 + 0*z**4 + 1/90*z**5 + 0*z**3 + 0*z + 0. Let j(d) = 0. What is d?
0, 2
Let y(k) = -3*k + 35. Let w be y(10). Let p be ((-40)/50)/((-1)/w) - 2. Factor 0 + 2/3*f**4 + 0*f + 2/3*f**3 + 0*f**p.
2*f**3*(f + 1)/3
Let f(v) = -4*v**3 + 3*v**3 + 4*v**2 - 54*v + 52*v. Let a be f(3). Factor 3*z - 3/2*z**4 - 3*z**a + 0*z**2 + 3/2.
-3*(z - 1)*(z + 1)**3/2
Let l(d) be the third derivative of d**6/60 - d**5/5 - d**4/12 + 2*d**3 - 225*d**2. Determine p so that l(p) = 0.
-1, 1, 6
Let b be (-2582)/(-14) + (9 - 6). Let x be (704/(-6))/(14/(-24)). Factor b*q**3 - x*q**4 - 4/7 + 10*q - 456/7*q**2.
-2*(4*q - 1)**3*(11*q - 2)/7
Let p = -56 + 62. Let c(g) = -7*g + 42. Let s be c(p). Solve 3/7*f - 9/7*f**2 - 3/7*f**4 + 9/7*f**3 + s = 0 for f.
0, 1
Let a(n) be the third derivative of -n**7/1470 + 3*n**6/70 - 11*n**5/35 + 16*n**4/21 - 303*n**2. Let a(q) = 0. Calculate q.
0, 2, 32
Let h(j) be the second derivative of -j**4/12 + 19*j**3/6 + 21*j**2 + 1002*j. Factor h(o).
-(o - 21)*(o + 2)
Let f be (4 - (-16)/4) + -2. Factor f*a**2 - 4*a + 2*a**2 + 0*a**2 + 0*a**2 - 4*a**3.
-4*a*(a - 1)**2
Let b(w) be the second derivative of w**5/35 - 11*w**4/21 - 8*w**3/7 - 2*w + 60. Factor b(y).
4*y*(y - 12)*(y + 1)/7
Let g(l) be the third derivative of l**6/180 + 2*l**5/45 + 5*l**4/36 + 2*l**3/9 - l**2 + 5. Factor g(i).
2*(i + 1)**2*(i + 2)/3
Factor 25*t**2 + 0*t**2 + 20*t**3 + 1029*t + 5*t**4 - 1019*t.
5*t*(t + 1)**2*(t + 2)
Let v = 25 + -18. Suppose -2*h = -v*h + 40. What is s in 6*s**5 + h*s**4 - 3*s**4 + 3*s**4 - 3*s**2 + s**4 = 0?
-1, 0, 1/2
Let a be (-8)/10*(-360)/432. Let v = -119/4 - -373/12. Factor 0*m - v*m**3 + a - 2*m**2.
-2*(m + 1)**2*(2*m - 1)/3
Let d be 4/(-14)*175/(-100). Let q(s) be the first derivative of -7/16*s**4 + 4/3*s**3 + 0*s - 5 - d*s**2. Factor q(y).
-y*(y - 2)*(7*y - 2)/4
What is a in 15*a**3 - 97*a**3 - 12*a**4 - 4*a**5 + 74*a**3 = 0?
-2, -1, 0
Let l(r) be the third derivative of -r**8/1008 + 9*r**7/70 - 243*r**6/40 + 2187*r**5/20 - 94*r**2. Find a, given that l(a) = 0.
0, 27
Let d(n) be the second derivative of 0*n**2 + 0 - 9*n - 1/2*n**5 + 1/3*n**4 - 1/21*n**7 + 4/15*n**6 + 0*n**3. Factor d(m).
-2*m**2*(m - 2)*(m - 1)**2
Let a(x) be the second derivative of x**5/510 + 13*x**2/2 + 9*x. Let f(o) be the first derivative of a(o). Factor f(c).
2*c**2/17
Suppose -1561*v + 1552*v = -18. Let l(p) be the second derivative of -3/5*p**5 + 4/15*p**6 - 1/3*p**4 + 7*p + 0 - 2*p**v + 2*p**3. Solve l(y) = 0.
-1, 1/2, 1
Let f(r) = 15*r**2 - 26*r - 41. Suppose 14 - 3 = n. Let p be 3/((-54)/(-63))*4/(-7). Let l(z) = 3*z**2 - 5*z - 8. Let u(y) = n*l(y) + p*f(y). Factor u(o).
3*(o - 2)*(o + 1)
Let s(i) be the third derivative of i**5/72 + 5*i**4/18 + 5*i**3/3 - 39*i**2. Find p such that s(p) = 0.
-6, -2
Let w(l) be the first derivative of l**3/3 - 17*l**2 + 289*l - 65. Let w(o) = 0. Calculate o.
17
Let t be 17/4 - (5/4 + -1). Suppo