 18
Let t(j) be the second derivative of j**3/3 - j**2/2 - 5*j. Let f be t(2). Factor 4*y**2 + y**2 + 21*y**f + y**2.
3*y**2*(7*y + 2)
Let x(w) be the first derivative of 0*w + 35/18*w**3 + 1/30*w**5 - 11/24*w**4 + 25 - 25/12*w**2. Let x(z) = 0. Calculate z.
0, 1, 5
Let q be ((-950)/570)/(15/(-36) - 0). Factor 0 + 4/9*a**2 + 0*a**q - 2/3*a**3 + 2/9*a**5 + 0*a.
2*a**2*(a - 1)**2*(a + 2)/9
Suppose -3*j = 4*j - 14. Suppose 2*u = -l + 36, -4*u + 2*l + 58 = j. Factor -u*h**2 - 10 - 20*h + 5 - 3 - 4*h**3.
-4*(h + 1)**2*(h + 2)
Let r(z) be the second derivative of -5/12*z**4 - 25/3*z**3 - 4*z + 0 - 125/2*z**2. Let r(x) = 0. Calculate x.
-5
Let g = 4906 + -53964/11. Factor -g*o**3 + 8/11*o + 0*o**2 + 0.
-2*o*(o - 2)*(o + 2)/11
Let z(o) be the first derivative of -o**5/20 + o**3/12 + 332. Solve z(g) = 0 for g.
-1, 0, 1
What is k in -1539*k**2 + 7*k**3 + 13*k**3 + k**4 + 1639*k**2 = 0?
-10, 0
Determine w, given that 12*w**2 + 8*w**3 - 4*w**3 + 13*w**2 + 3*w**2 = 0.
-7, 0
Let z = -50 + 68. Determine o, given that -4 - 17*o - o**4 + 7*o**3 - z*o**2 - 4 + 61*o - 24*o = 0.
1, 2
Let v(y) be the third derivative of -y**7/4410 - y**6/630 + y**5/70 + 17*y**4/24 + 14*y**2. Let h(t) be the second derivative of v(t). Solve h(z) = 0.
-3, 1
Factor -28*s + 3*s**4 - 34*s**3 - 39*s**2 + 25*s**3 - 35*s - 36*s**2.
3*s*(s - 7)*(s + 1)*(s + 3)
Let l(k) be the third derivative of k**8/896 - k**6/320 - 11*k**2. Let l(v) = 0. What is v?
-1, 0, 1
Let s = 11 - 15. Let f(i) = i**2 + 2*i - 3. Let j be f(s). Let 200*b**3 + 82*b + 95*b**4 - 176*b**2 - 50*b + 61*b**4 - 252*b**j = 0. Calculate b.
-1, 0, 2/7, 2/3
Let u(a) = -2*a - 1. Let k be u(-1). Suppose 6 = -5*v + k, 0 = -5*g + 3*v + 13. Factor -2/3*x**g - 20/3*x - 50/3.
-2*(x + 5)**2/3
Suppose 8*d = 5*d + 3. Let b = 3 - d. Suppose -1 - 10*u + 10*u + 3 + b*u**4 - 4*u**2 = 0. Calculate u.
-1, 1
Let c(x) = -x**3 + 8*x**2 - 2*x + 7. Let j be c(8). Let k be (j/((-450)/32))/(2/5). Let -k*u - 2/5*u**3 + 0 - 8/5*u**2 = 0. What is u?
-2, 0
Let c(f) = -f**3 + f + 2. Let x be c(0). Let u(h) be the second derivative of 0 + 5*h - 1/4*h**4 + 3*h**x + 1/2*h**3. Suppose u(j) = 0. Calculate j.
-1, 2
Let c(m) = -m**3 + 19*m**2 + 21*m - 18. Let k be c(20). Factor 9*h**k - 10*h + 5*h**2 - 6*h**2 - 3*h**2.
5*h*(h - 2)
Let p(c) be the second derivative of c**5/20 - 5*c**4/6 + 8*c**3/3 + 6*c. Determine n, given that p(n) = 0.
0, 2, 8
Factor -4*n**3 - 2 - 38 - 653*n - 727*n + 0 + 1432*n - 8*n**2.
-4*(n - 2)*(n - 1)*(n + 5)
Suppose 0*g - 8 = -4*g + 4*t, 0 = -t - 4. Let w(a) = -5*a**2 - 16*a - 29. Let k(h) = -16*h**2 - 47*h - 88. Let q(u) = g*k(u) + 7*w(u). Factor q(x).
-3*(x + 3)**2
Suppose -16 + 58*o**2 + 21*o + 6*o + 201*o = 0. Calculate o.
-4, 2/29
Let c = 19328 + -19326. Determine p, given that 0 - 2/15*p**4 - 4/15*p**3 + 4/15*p + 2/15*p**c = 0.
-2, -1, 0, 1
Let i(t) be the third derivative of -9*t**7/140 - 3*t**6/20 + t**5/20 + t**4/4 - t**3/4 - 6*t**2. Solve i(d) = 0 for d.
-1, 1/3
Let j(b) = -122*b**2 + 1649*b + 691. Let h(g) = 24*g**2 - 330*g - 138. Let d(v) = 11*h(v) + 2*j(v). Factor d(a).
4*(a - 17)*(5*a + 2)
Let z(h) be the second derivative of -5*h**7/42 + 7*h**6/3 - 23*h**5/2 + 80*h**4/3 - 205*h**3/6 + 25*h**2 - 49*h. Factor z(o).
-5*(o - 10)*(o - 1)**4
Let w(i) be the first derivative of -i**4/4 - i**3/3 - 3. Let f(j) = 12*j**3 + 4*j**2 + 15*j - 9. Let s(k) = -4*f(k) - 44*w(k). Factor s(m).
-4*(m - 3)**2*(m - 1)
Let g(s) be the first derivative of -s**5/15 - 41*s**4/12 + s**3/9 + 41*s**2/6 + 432. Factor g(w).
-w*(w - 1)*(w + 1)*(w + 41)/3
Let t(l) = -l**2 - 8*l - 12. Let s be t(-5). Suppose 0*h - 3*h**3 + 5*h + 9*h**2 - 6*h - 8*h + s = 0. What is h?
1
Let k(x) be the second derivative of 1/28*x**4 + 0 + 27/14*x**2 - 27*x - 5/7*x**3. Solve k(i) = 0 for i.
1, 9
Let -6*o + 1/2*o**2 + 27/2 = 0. What is o?
3, 9
Let v(u) be the third derivative of -5*u**3 + 19/8*u**4 - 1/40*u**6 - 4 + 0*u - 2/5*u**5 - 2*u**2. Factor v(k).
-3*(k - 1)**2*(k + 10)
Let n(o) be the third derivative of -o**8/2688 + o**7/336 - 3*o**6/320 + 7*o**5/480 - o**4/96 - o**2 - 29. Suppose n(l) = 0. What is l?
0, 1, 2
Let -v**4 + 31*v**2 + 0*v**4 - 15*v**2 - 4*v**4 - v**4 + 20*v**3 = 0. Calculate v.
-2/3, 0, 4
Let t(q) = -2*q**4 + 9*q**3 + 12*q**2. Let d(f) = f**4 - f**3 - f**2. Let o(n) = 12*d(n) + 4*t(n). Factor o(s).
4*s**2*(s + 3)**2
Factor -5/4 + 5/4*c**2 + 0*c.
5*(c - 1)*(c + 1)/4
Let -16/5*g**3 + 16/5*g - 14/5 + 12/5*g**2 + 2/5*g**4 = 0. What is g?
-1, 1, 7
Let p(k) be the first derivative of -k**8/84 + 2*k**7/105 + 10*k**2 + 28. Let g(w) be the second derivative of p(w). Factor g(v).
-4*v**4*(v - 1)
Suppose -4 = -2*c - 0. Factor c*u**2 - 9 + u - 5*u**2 - u - 12*u.
-3*(u + 1)*(u + 3)
Determine w so that 1/10*w**5 + 19/10*w**3 + 2/5 + 5/2*w**2 + 7/10*w**4 + 8/5*w = 0.
-2, -1
Let y be -2*9/24 + 1. Suppose 58 + 30 = 44*a. Factor -3/4*f**3 + y*f**4 + 3/4*f**a - 1/4*f + 0.
f*(f - 1)**3/4
Let x be 0 + 2 + 0 - (-20)/4. Suppose 3*a + 12 = x*a. Suppose -4/5 - 2*c - 8/5*c**2 - 2/5*c**a = 0. What is c?
-2, -1
Let o(q) be the third derivative of -q**6/105 - 13*q**5/210 - q**4/28 + 141*q**2. Factor o(j).
-2*j*(j + 3)*(4*j + 1)/7
Let t(s) be the second derivative of 2*s**6/15 - 18*s**5/5 - 61*s**4/3 - 28*s**3 - 82*s. Factor t(u).
4*u*(u - 21)*(u + 1)*(u + 2)
Factor 2/3*s**2 - 28/3 - 26/3*s.
2*(s - 14)*(s + 1)/3
Let h(y) = -2*y**2 + 3*y - 1. Let q(x) = -x**2 + x. Let a be 23/2 + 2/(-4). Suppose -a*f + 6*f = -10. Let m(j) = f*q(j) - 2*h(j). Factor m(l).
2*(l - 1)**2
Let w(b) = -64*b**4 + 125*b**3 - 62*b**2 + 13*b + 6. Let j(u) = 130*u**4 - 250*u**3 + 125*u**2 - 25*u - 10. Let y(n) = 3*j(n) + 5*w(n). What is h in y(h) = 0?
0, 2/7, 1/2, 1
Factor -1/2*b**4 + 100 - 30*b - 21/2*b**3 - 59*b**2.
-(b - 1)*(b + 2)*(b + 10)**2/2
Let x(m) = -31*m**2 - 241*m + 120. Let s(l) = -16*l**2 - 121*l + 60. Let o(g) = -11*s(g) + 6*x(g). Factor o(b).
-5*(b + 12)*(2*b - 1)
Let k(j) = 4*j - 7. Let g be k(5). Factor -2*x**2 - 21*x + 48 + g*x - 16*x + 5*x**2.
3*(x - 4)**2
Let p(o) be the second derivative of -o**6/12 + 5*o**5/12 - 5*o**4/6 + 5*o**3/6 + 43*o**2/2 - 16*o. Let r(w) be the first derivative of p(w). Factor r(f).
-5*(f - 1)**2*(2*f - 1)
Let g(u) be the third derivative of u**11/554400 - u**10/126000 + u**9/100800 - 11*u**5/60 - 31*u**2. Let h(o) be the third derivative of g(o). Factor h(i).
3*i**3*(i - 1)**2/5
Find f such that -1/9*f**4 - 2/9*f**3 + 4/9*f**2 + 2/9*f - 1/3 = 0.
-3, -1, 1
Suppose 12*p - 6 = 18*p. Let u(d) = -2*d**3 - 2*d**2 - d + 1. Let q be u(p). Factor 16/9*f + 2/3*f**3 - 8/9 + 22/9*f**q.
2*(f + 2)**2*(3*f - 1)/9
Let d(y) = 66*y**4 + 780*y**3 + 5643*y**2 + 16848*y + 16821. Let x(r) = 5*r**4 + 60*r**3 + 434*r**2 + 1296*r + 1294. Let s(p) = 2*d(p) - 27*x(p). Factor s(u).
-3*(u + 2)*(u + 6)**3
Find p, given that -72/5 + 34/5*p**2 - 42/5*p + 2/5*p**3 - 2/5*p**4 = 0.
-4, -1, 3
Let j be ((-1)/2)/((-7)/98). Let l = j - 3. Factor 5 - l + 3*f**2 + f**3 - 7*f**2 + 3*f**2 - f.
(f - 1)**2*(f + 1)
Factor 16 + 14*t + 3/2*t**3 - 14*t**2.
(t - 8)*(t - 2)*(3*t + 2)/2
What is v in 30*v + 70*v**2 - 41*v**2 - 27*v**2 = 0?
-15, 0
Factor -1/12*y**4 + 3/4*y**2 - 1 + 0*y**3 - 1/3*y.
-(y - 2)**2*(y + 1)*(y + 3)/12
Let o be (-27)/84 + 2*2/7. What is u in -3/4 + o*u**2 - 1/2*u = 0?
-1, 3
Let b(t) be the second derivative of -t**6/96 - t**5/12 - 5*t**4/24 - 9*t**2 - 9*t. Let s(x) be the first derivative of b(x). Factor s(m).
-5*m*(m + 2)**2/4
Let h(k) be the first derivative of 2*k**6/3 + 36*k**5/5 + 30*k**4 + 184*k**3/3 + 66*k**2 + 36*k - 68. Determine a, given that h(a) = 0.
-3, -1
Let w be 670/25 - 2/(-10). Factor 3*g**4 + 0*g**2 + 33*g - 6*g**3 - 3*g**2 - w*g.
3*g*(g - 2)*(g - 1)*(g + 1)
Let z = 1213 + -1211. Let j(t) be the first derivative of 1/3*t - 1/6*t**z - 1/9*t**3 + 1/12*t**4 - 5. Determine w, given that j(w) = 0.
-1, 1
Let o(j) be the second derivative of j**7/3360 + j**6/480 + j**5/160 - 11*j**4/6 + 17*j. Let b(g) be the third derivative of o(g). Factor b(x).
3*(x + 1)**2/4
Let f(w) be the first derivative of -w**6/18 - 11*w**5/15 - 13*w**4/6 - 16*w**3/9 - 301. Determine l, given that f(l) = 0.
-8, -2, -1, 0
Let p be 24/16*4/12. Factor -2*n**2 + 1/2*n**3 - 1/4*n**5 + p*n**4 + 7/4*n - 1/2.
-(n - 1)**4*(n + 2)/4
Let c = 2/64145 - -513122/1218755. Suppose -10/19 - c*z + 2/19*z**2 = 0. Calculate z.