21))/15. Suppose 24/7 - 36/7*w + c*w**2 - 3/7*w**3 = 0. Calculate w.
2
Let c(u) be the third derivative of -u**5/15 + 25*u**2. Suppose c(r) = 0. Calculate r.
0
Let r(z) = -319*z + 322. Let d be r(1). Suppose 10/9*y**d + 2*y**2 + 2/3*y - 2/9 = 0. What is y?
-1, 1/5
Let b be ((-15)/63)/((-55)/30 + 2). Let d = 32/7 + b. Suppose -18/7*h**2 - 4/7 + d*h = 0. Calculate h.
2/9, 1
Let i(p) be the second derivative of 3*p**5/100 + 123*p**4/10 + 10086*p**3/5 + 827052*p**2/5 + 13*p - 12. Suppose i(v) = 0. Calculate v.
-82
Let b(a) be the third derivative of 13*a**6/600 + a**5/75 - 2*a**2 - 31*a. Suppose b(o) = 0. Calculate o.
-4/13, 0
Let p(i) be the first derivative of -5*i**4/12 + i**3/3 + 5*i**2/6 - i - 26. Factor p(v).
-(v - 1)*(v + 1)*(5*v - 3)/3
Let v(l) be the first derivative of 4*l**5/5 + l**4 - 8*l**3/3 - 124. Factor v(b).
4*b**2*(b - 1)*(b + 2)
Let x(l) = 3*l**2 - 2*l + 5. Let z be -2*(-4 + 9/6). Let j(k) = -2 + 3*k**2 - 2*k**2 + k - 2*k**2. Let q(w) = z*j(w) + 2*x(w). Factor q(t).
t*(t + 1)
Let p(l) be the first derivative of -3*l**4/8 - 345*l**3/2 - 119025*l**2/4 - 4562625*l/2 + 376. Factor p(d).
-3*(d + 115)**3/2
Solve 21/8*r**2 + 0 - 9/4*r + 39/8*r**3 = 0.
-1, 0, 6/13
Let o(m) be the second derivative of 0 + 35/3*m**3 - 5/4*m**4 + 47*m - 20*m**2. Factor o(x).
-5*(x - 4)*(3*x - 2)
Let r(j) be the second derivative of j**9/7560 - j**7/420 + j**6/180 + j**4/3 + 12*j. Let p(s) be the third derivative of r(s). Factor p(g).
2*g*(g - 1)**2*(g + 2)
Let u = -33 + 35. Let q be 5 - 15/10 - u. Factor -q + 3/2*d**3 - 9/2*d**2 + 9/2*d.
3*(d - 1)**3/2
Let u(c) be the second derivative of 1/6*c**3 + 1/60*c**5 + 0 + 0*c**2 - 8*c - 1/9*c**4. Solve u(m) = 0 for m.
0, 1, 3
Let h be (3/(-2))/(17 + -6 + (-103)/8). Let 2/5*b**2 - h*b + 0 = 0. Calculate b.
0, 2
Factor 12/5*i + 2/5*i**2 + 18/5.
2*(i + 3)**2/5
Let s = -12751 - -12755. Factor 1/3*v**s + 3*v**2 + 0 + 0*v - 2*v**3.
v**2*(v - 3)**2/3
Let g(m) be the second derivative of 7*m**4/16 - 3*m**3/2 + 15*m**2/8 - m + 19. Find s such that g(s) = 0.
5/7, 1
Let g(c) be the first derivative of 0*c**2 + 0*c - 1/18*c**3 - 13. Factor g(o).
-o**2/6
Let b(l) = -5*l**5 - 3*l**4 - 9*l**3 - 3. Let p(a) = 8*a**5 + 5*a**4 + 18*a**3 + 5. Let t(g) = 5*b(g) + 3*p(g). Suppose t(x) = 0. What is x?
-3, 0, 3
Let o(i) be the first derivative of i**6/3 - 6*i**5/5 - 9*i**4/2 - 10*i**3/3 - 66. Factor o(y).
2*y**2*(y - 5)*(y + 1)**2
Let h be 2 + (0 + -1)/(-1). Suppose -2*v + v = -5. Let 3 - 27/2*r**v - 6*r**2 - 27/2*r + 27*r**3 + h*r**4 = 0. What is r?
-1, 2/9, 1
Let o(u) be the third derivative of -u**5/180 - u**4/24 + u**2 - 80. Suppose o(v) = 0. What is v?
-3, 0
Let d(q) = -9*q**3 - 2*q + 4. Let r be d(2). Let k be r/39*(-3)/6. Factor 2/13*y**2 - k*y + 18/13.
2*(y - 3)**2/13
Let k(h) be the third derivative of -h**9/3360 - h**8/4480 + h**7/420 + h**4/8 - 5*h**2. Let r(g) be the second derivative of k(g). Find q such that r(q) = 0.
-4/3, 0, 1
Let x(u) = 9*u**3 - 458*u**2 - 901*u - 469. Let d(z) = -7*z**3 + 459*z**2 + 903*z + 467. Let t(s) = 7*d(s) + 6*x(s). Factor t(h).
5*(h + 1)**2*(h + 91)
Suppose -2*x = 3*t - 16, -t - x = -2*x - 7. Let z be (-44)/(-10) - ((-6)/2 + t). Let 1/5*y**3 + 3/5 + z*y + y**2 = 0. What is y?
-3, -1
Let o(b) be the second derivative of 0*b**2 - 1/4*b**4 - 1/42*b**7 + 18*b - 11/90*b**6 - 1/9*b**3 + 0 - 1/4*b**5. Factor o(r).
-r*(r + 1)**3*(3*r + 2)/3
Let a(r) be the first derivative of r**7/1960 - r**6/140 - r**3/3 - 2. Let h(g) be the third derivative of a(g). Factor h(x).
3*x**2*(x - 6)/7
Let y(n) be the third derivative of -5*n**8/336 - n**7/6 - 3*n**6/4 - 5*n**5/3 - 5*n**4/3 + 225*n**2. Factor y(b).
-5*b*(b + 1)*(b + 2)**3
Let d(f) be the second derivative of f**5/50 - 13*f**4/30 - 3*f**3/5 + 81*f**2 + 854*f. What is b in d(b) = 0?
-5, 9
Let g(x) = 2*x**2 + 15*x - 17. Let v(s) = -3*s**2 - 15*s + 18. Let u = -39 - -34. Let q(r) = u*v(r) - 6*g(r). Factor q(m).
3*(m - 4)*(m - 1)
Let d(r) be the first derivative of 3*r**4/8 - 5*r**3/2 - 9*r**2/2 - 96. Find k, given that d(k) = 0.
-1, 0, 6
Let d be 95/(-380) + (-115)/(-4). Solve -d*m**3 + 21/2*m**4 + 12*m**2 + 0 + 6*m = 0 for m.
-2/7, 0, 1, 2
Determine k so that -6/7*k**2 - 12/7 + 18/7*k = 0.
1, 2
Let v(r) = -3 - 9*r + 0 + 2*r**2 - 1 + 2. Let x(z) = 2*z**2 - 8*z - 1. Let k(g) = -3*v(g) + 4*x(g). Determine j so that k(j) = 0.
1/2, 2
Let t(y) = y**2 + 7*y. Let s(w) = 4*w**2 + 22*w - 1. Let p(i) = 2*s(i) - 7*t(i). Let v be p(6). Factor 66*h**2 - 34*h + 5 - 40*h**3 - 1 + v*h.
-2*(h - 1)*(4*h - 1)*(5*h - 2)
Let n(i) = i**3 - 8*i**2 + 10*i + 19. Let c be n(3). Factor 3/2*y - 27/4*y**2 + 0 + 9*y**3 - 15/4*y**c.
-3*y*(y - 1)**2*(5*y - 2)/4
Let p be 1*6/36*6*0. Factor -10/9*r**4 + 0*r + p - 2/9*r**3 + 2/9*r**2 - 2/3*r**5.
-2*r**2*(r + 1)**2*(3*r - 1)/9
Let j be 4/(36 + -1 + 10 + -10). Let s(m) be the first derivative of j*m**5 - 5 - 4/21*m**3 + 0*m**4 + 0*m + 1/21*m**6 - 1/7*m**2. Factor s(d).
2*d*(d - 1)*(d + 1)**3/7
Factor 1575*n + 35*n**2 - 1605*n - 3*n**4 - 2*n**4.
-5*n*(n - 2)*(n - 1)*(n + 3)
Suppose 7*a + 32 = 5*a. Let w(m) = 6*m**3 + 34*m**2 - 30*m - 90. Let r(s) = -s**3 - 7*s**2 + 6*s + 18. Let x(l) = a*r(l) - 3*w(l). Factor x(k).
-2*(k - 3)**2*(k + 1)
Let f(h) be the first derivative of -h**5/10 + h**4 - 19*h**3/6 + 3*h**2 + 550. Find x such that f(x) = 0.
0, 1, 3, 4
Suppose 136*c = 146*c. Find s such that c + s + 1/4*s**5 + 13/4*s**3 - 3*s**2 - 3/2*s**4 = 0.
0, 1, 2
Let o(n) be the third derivative of -5/8*n**4 - 5/6*n**3 + 0*n + 9*n**2 - 1/24*n**6 + 0 - 1/4*n**5. Find b, given that o(b) = 0.
-1
Let w = -4215 + 4218. Solve 2/17 - 2/17*d**4 - 4/17*d**w + 4/17*d + 0*d**2 = 0.
-1, 1
Factor -8/5*f**2 - 2*f + 0 + 2/5*f**3.
2*f*(f - 5)*(f + 1)/5
Let d = -56278/5 + 11256. Suppose 0 + 0*g + d*g**2 = 0. What is g?
0
Let v(a) be the second derivative of 5*a**9/189 - a**8/42 + a**7/168 - 4*a**3/3 - 4*a. Let o(j) be the second derivative of v(j). Factor o(z).
5*z**3*(4*z - 1)**2
Let i(n) = n**3 - 21*n**2 - n + 21. Let q be i(21). Let 35*u + 0 - 5*u**2 + q = 0. Calculate u.
0, 7
Let z(m) be the first derivative of 3*m + 3/4*m**2 + 25 - 27/8*m**4 - 9*m**3. Determine x so that z(x) = 0.
-2, -1/3, 1/3
Let q(z) be the first derivative of 25/4*z**4 - 15*z**3 + 35/2*z**2 - 10*z - z**5 - 53. Factor q(k).
-5*(k - 2)*(k - 1)**3
Suppose 4*g - 10 = 3*g - 4*p, 0 = -5*g + 2*p + 6. Let j(d) = 4*d**2 - 20*d + 50. Let q(l) = -l**2. Let w(h) = g*q(h) + j(h). Solve w(v) = 0.
5
Let u(w) be the third derivative of 7*w**2 + 0*w + 0 + 1/15*w**5 + 2/3*w**3 - 1/3*w**4. Let u(j) = 0. Calculate j.
1
Let v be (9 + (-546)/56)/(1/(-4)). Let u(h) be the third derivative of -1/3*h**v + 0 + 8*h**2 + 1/4*h**4 + 0*h + 2/15*h**5. Let u(p) = 0. Calculate p.
-1, 1/4
Let q(o) = -o**3 + o**2 + o. Let z(x) = 15*x**3 + 5*x**2 - 15*x - 8. Let n(g) = -g**2 - 10*g - 10. Let l be n(-9). Let k(s) = l*z(s) - 3*q(s). Factor k(y).
-4*(y - 1)*(y + 1)*(3*y + 2)
Let i(b) = -b**3 + 11*b**2 + b + 21. Let a be i(11). Suppose 0 = -a*s + 30*s + 4. What is k in 9/8*k**3 + 3/8*k**s + 0 - 1/4*k = 0?
-2/3, 0, 1/3
Let x(q) be the second derivative of 1/42*q**7 + 0*q**2 + 1/30*q**6 + 0*q**3 + 0 + 26*q + 1/4*q**4 - 1/4*q**5. Factor x(u).
u**2*(u - 1)**2*(u + 3)
Factor -47*h**2 - 5*h**3 + 30*h + 4*h**2 - 55*h - 48 - 7*h - 72*h.
-(h + 4)**2*(5*h + 3)
Let g(q) be the third derivative of -5/3*q**3 + 6*q**2 + 1/24*q**5 + 0*q + 0*q**4 + 0. Factor g(h).
5*(h - 2)*(h + 2)/2
Find h, given that -128/7 - 52/7*h**2 + 184/7*h - 4/7*h**3 = 0.
-16, 1, 2
Let v be (-36)/(-20)*(-20)/(-6). Let w(m) = -10*m**3 - 30*m**2 - 65*m - 40. Let h(u) = -11*u**3 - 30*u**2 - 66*u - 40. Let b(q) = v*w(q) - 5*h(q). Factor b(z).
-5*(z + 2)**3
Let y be 8/(-14) + (-10)/7. Let k(v) = v**3 - v. Let d(p) = -5*p**3 - 6*p**2 - 3*p - 2. Let g(b) = y*d(b) - 6*k(b). Determine h so that g(h) = 0.
-1
Let b(n) be the first derivative of -n**4/14 + 22*n**3/21 + 12*n**2/7 - 657. Suppose b(k) = 0. Calculate k.
-1, 0, 12
Factor -93*p**2 - 955*p**2 + 873 - 112*p**3 - 2*p**4 + 963*p - 4659*p - 5229 - 2*p**4.
-4*(p + 3)**2*(p + 11)**2
Let v(b) be the second derivative of b**5/10 - 7*b**4 + 55*b**3/4 - 41*b**2/4 + 8*b - 4. Find a such that v(a) = 0.
1/2, 41
Let t(q) be the first derivative of -44 + 20/3*q**3 + 0*q + 23*q**4 + 76/5*q**5 + 8/3*q**6 - 6*q**2. Find i, given that t(i) = 0.
