3
Let n(v) be the first derivative of -v**4/6 - 2*v**3/9 - 20. Factor n(y).
-2*y**2*(y + 1)/3
Let d(t) be the first derivative of 2*t**3/9 + 4*t**2/3 + 2*t - 6. Factor d(m).
2*(m + 1)*(m + 3)/3
Let k be (-26)/(-42) + (-2)/7. Let b(t) be the second derivative of k*t**3 - t**2 - t - 1/10*t**5 + 0 + 1/6*t**4. Solve b(p) = 0 for p.
-1, 1
Factor -12/5*l**5 - 4*l**3 + 4/5*l**2 + 0*l + 28/5*l**4 + 0.
-4*l**2*(l - 1)**2*(3*l - 1)/5
Find n, given that -2/3*n**3 + 0 + 2/15*n**2 + 0*n = 0.
0, 1/5
Suppose -4*i = -0*i - 8. Factor -a**3 + 0*a**i + 1/2*a**4 + a - 1/2.
(a - 1)**3*(a + 1)/2
Suppose 0 = -b + 6*b - 25. Factor -3*u**5 + 2*u**5 - b*u - 24*u**3 + 16*u**4 - 3*u**5 + 16*u**2 + u.
-4*u*(u - 1)**4
Let p(i) be the second derivative of i**6/90 + i**5/10 - 5*i**4/12 + 4*i**3/9 + 41*i. Factor p(n).
n*(n - 1)**2*(n + 8)/3
Suppose -4*d = -12, 3*l - 8*l + 5*d = 25. Let a be (1 - l) + 6/(-4). Solve -1 - 5/2*s - a*s**2 = 0 for s.
-1, -2/3
Suppose -q = 3*r - 4 + 13, -3*q - r + 5 = 0. Let -3*v - 1 + 3*v**4 + 4*v**q + 4 + 2*v**3 - 6*v**2 - 3*v**5 = 0. Calculate v.
-1, 1
Let v(c) be the third derivative of c**6/420 - c**5/105 - c**2. Factor v(i).
2*i**2*(i - 2)/7
Let w = 13/54 - 2/27. Find l, given that -1/3*l + 1/6 + w*l**2 = 0.
1
Factor 4/7*o**2 + 144/7 + 48/7*o.
4*(o + 6)**2/7
Let a(j) be the third derivative of j**7/105 + j**6/30 - j**4/6 - j**3/3 - 9*j**2. What is w in a(w) = 0?
-1, 1
Let o(j) = j - 1. Let h(x) = 5*x**2 - 30*x + 25. Let r(s) = -h(s) - 25*o(s). Factor r(t).
-5*t*(t - 1)
Let x(f) be the second derivative of f**6/50 + 3*f**5/50 + f**4/20 + 55*f. Suppose x(w) = 0. What is w?
-1, 0
Let c = -24 - -40. Suppose 8*h + 0*h**2 + c + 0*h**4 - 8*h**2 - 2*h**4 - 10*h**3 - 4*h**2 = 0. Calculate h.
-2, 1
Let b(z) be the first derivative of 0*z + 0*z**5 - 2*z**4 + 2/3*z**6 + 2*z**2 + 0*z**3 + 5. Suppose b(f) = 0. What is f?
-1, 0, 1
Let k(x) = -x**3 - 3*x**2 + 5*x + 6. Let u be k(-4). Solve -7*z**2 - z + 3*z + 0*z - z**u = 0 for z.
0, 1/4
Find a such that 1/2*a - a**2 + 1 - 1/2*a**3 = 0.
-2, -1, 1
Let g(m) be the second derivative of 3*m**5/20 + m**4/4 - 8*m. Factor g(j).
3*j**2*(j + 1)
Let r(m) be the third derivative of 2/105*m**6 + 0*m**3 + 1/42*m**4 - 4*m**2 + 0 + 1/30*m**5 + 1/245*m**7 + 0*m. Factor r(l).
2*l*(l + 1)**2*(3*l + 2)/7
Let i(s) = -2*s**5 - 2*s**4 + 8*s**3 + 2*s**2 + 6. Let y(n) = 4*n**5 + 4*n**4 - 15*n**3 - 4*n**2 - 11. Let v(k) = -11*i(k) - 6*y(k). Factor v(h).
-2*h**2*(h - 1)*(h + 1)**2
Let n(g) = 8*g**2 + 6*g - 2. Let f(r) = -15*r**2 - 11*r + 4. Let y(x) = -6*f(x) - 11*n(x). Factor y(v).
2*(v - 1)*(v + 1)
Suppose -7*r + 16 = -2*o - 3*r, -o = 5*r - 20. Factor 2 - 4*k**2 + o + 0*k**4 + 2*k**4.
2*(k - 1)**2*(k + 1)**2
Let c(x) = -7*x**4 + 4*x**3 + 7*x**2 + x + 5. Let l(p) = -6*p**4 + 4*p**3 + 6*p**2 + 4. Let a(k) = -4*c(k) + 5*l(k). Determine m, given that a(m) = 0.
-1, 0, 1, 2
Let j(r) = -r**3 - 6*r**2 - 6*r - 5. Let f be j(-4). Let z = f - -15. Factor -4/3 - 1/3*c**z - 4/3*c.
-(c + 2)**2/3
Let d(j) = -j - 21. Let o be d(-21). Factor 0*b + o - 1/2*b**2 - b**3 - 1/2*b**4.
-b**2*(b + 1)**2/2
Let s(z) be the third derivative of -z**6/1260 + z**4/84 - 2*z**3/63 - 6*z**2. Factor s(h).
-2*(h - 1)**2*(h + 2)/21
What is j in 10/3*j + 25/3 + 1/3*j**2 = 0?
-5
Let -2/9*f**2 - 4/9 - 2/3*f = 0. Calculate f.
-2, -1
Let n(x) be the third derivative of -3/8*x**4 + 0*x**5 - 4*x**2 + 0 + 1/40*x**6 - x**3 + 0*x. Determine z so that n(z) = 0.
-1, 2
Let h(u) be the first derivative of u**6/3 + 2*u**5/5 - u**4/2 - 2*u**3/3 - 5. Factor h(l).
2*l**2*(l - 1)*(l + 1)**2
Let j = 11 - 11. Factor 4/5*w**4 + 2/5*w**5 - 2/5*w + 0*w**3 + j - 4/5*w**2.
2*w*(w - 1)*(w + 1)**3/5
Let l(c) be the second derivative of -3*c + 0 + 0*c**3 + 0*c**2 + 1/24*c**4. Factor l(k).
k**2/2
Let x(y) be the third derivative of 0*y**3 - 1/40*y**5 - y**2 + 0 + 1/24*y**4 + 0*y**6 + 1/420*y**7 + 0*y. Factor x(z).
z*(z - 1)**2*(z + 2)/2
Let i(w) = 3*w + 1 - w - 3*w + 0. Let l(d) = d**2 + 3*d - 4. Suppose -3*k + 0 = 6. Let u(h) = k*i(h) - l(h). Suppose u(s) = 0. Calculate s.
-2, 1
Let c(v) be the second derivative of -v**4/48 - v**3/4 - 9*v**2/8 - 4*v. Let c(f) = 0. Calculate f.
-3
Factor -7 - 14*n**4 + 92*n**2 + 57 + 4*n**3 - n**5 - 379*n - n**5 + 249*n.
-2*(n - 1)**3*(n + 5)**2
Let 2*c**2 + 4/9 + 10/9*c**3 + 14/9*c + 2/9*c**4 = 0. What is c?
-2, -1
Let l(y) = -63*y**4 + 89*y**3 - 26*y**2 - 8*y - 8. Let x(b) = 21*b**4 - 30*b**3 + 9*b**2 + 3*b + 3. Let s(n) = -3*l(n) - 8*x(n). Find i, given that s(i) = 0.
0, 2/7, 1
Let g = 109/18 - 50/9. Let q = -3 - -5. Let j + 0 - g*j**q = 0. Calculate j.
0, 2
Suppose -6*g - 10 = -34. Solve 2*y + 5*y**4 + 6*y**2 + 6*y**3 + y**4 - 2*y**4 - 2*y**g = 0.
-1, 0
Let h(f) be the third derivative of -f**10/105840 + f**8/11760 - f**6/2520 - f**4/12 - f**2. Let m(s) be the second derivative of h(s). Factor m(l).
-2*l*(l - 1)**2*(l + 1)**2/7
Let q be 17/29 + 24/(-40). Let k = 296/435 + q. Determine f so that 4/3 - k*f**2 + 2/3*f = 0.
-1, 2
Let j be -1 - 2/(-1 + 2). Let a be j/(-30)*-6 + 1. What is q in -4/5*q + 2/5*q**3 + 0 + a*q**2 = 0?
-2, 0, 1
Let q(u) = 2*u + 1. Let m be q(4). Let f be (-16)/m - (-5 + 3). Factor 2/9*d**2 + 0 - f*d.
2*d*(d - 1)/9
Let c(z) be the second derivative of -1/8*z**2 - 1/80*z**5 + 0 - z + 1/48*z**4 + 1/24*z**3. Determine x, given that c(x) = 0.
-1, 1
Let v(x) be the first derivative of -x**4/12 + x**2/6 - 13. Factor v(i).
-i*(i - 1)*(i + 1)/3
Let n(a) = 6*a**4 + 6*a**3 + 7. Let r(o) = -o**4 - o**3 - 1. Let z(u) = 4*n(u) + 28*r(u). Factor z(f).
-4*f**3*(f + 1)
Suppose -2*p = 5*b + 19, 2 = -5*p + 2*b + 27. Let d(j) be the second derivative of -j**2 + 0 - 1/18*j**4 - 3*j - 4/9*j**p. Find k such that d(k) = 0.
-3, -1
What is p in -4/3*p**4 + 4*p**2 - 4/3*p - 8/3 + 4/3*p**3 = 0?
-1, 1, 2
Factor 0 + 0*q**3 - 2/9*q**5 + 0*q**2 + 0*q + 0*q**4.
-2*q**5/9
Let y be 1 - 5 - (-1 - 0). Let t be (-1 + (-16)/(-18))*y. Factor t - 2/3*l + 1/3*l**2.
(l - 1)**2/3
Let o(f) = f**2 - 5*f + 2. Let z be o(6). Let l(q) = -q**2 + 9*q - 8. Let m be l(z). Let 1/4*c**4 - 1/4*c**3 + m*c + 0 + 0*c**2 = 0. Calculate c.
0, 1
Let v be 2 - (247/(-7) + -3). Let g = -40 + v. Factor -4/7*i**3 + g*i + 0*i**2 + 2/7*i**5 + 0*i**4 + 0.
2*i*(i - 1)**2*(i + 1)**2/7
Let r(f) be the first derivative of 0*f - 3/10*f**5 - 1/6*f**3 + 0*f**2 - 3 + 3/8*f**4 + 1/12*f**6. Factor r(l).
l**2*(l - 1)**3/2
Let w = -2/7 + 19/42. Solve -1/3*i + 1/6*i**2 + w = 0 for i.
1
Let i be (-1)/(-1*4/16) - 4. Factor 2/9*l + i*l**2 - 2/9*l**3 + 0.
-2*l*(l - 1)*(l + 1)/9
Let i = 2 + 3. Let d(b) be the second derivative of 0*b**2 + 0*b**3 + 1/80*b**i - 1/120*b**6 + 2*b + 0*b**4 + 0. Find l such that d(l) = 0.
0, 1
Let d(m) be the first derivative of -m**4/18 - 10*m**3/27 - 8*m**2/9 - 8*m/9 - 4. Factor d(v).
-2*(v + 1)*(v + 2)**2/9
Let g(r) be the third derivative of r**5/12 + 5*r**4/3 + 40*r**3/3 + 4*r**2. Factor g(o).
5*(o + 4)**2
Let w(f) be the third derivative of 1/450*f**5 + 1/90*f**4 + 0 + 4*f**2 + 0*f + 0*f**3. What is q in w(q) = 0?
-2, 0
Let j(a) = a**3 + 8*a**2 + 6*a - 5. Let v be j(-7). Let q(i) be the first derivative of i**v + 0*i - 2/3*i**3 + 1. Factor q(b).
-2*b*(b - 1)
Let s(o) be the first derivative of 3*o**4/8 - 3*o**3/2 + 6*o - 18. Suppose s(f) = 0. What is f?
-1, 2
Suppose -15 = 3*r - 6, 2*b - 3*r = 25. Let z = -7 + 10. What is i in 4*i**3 + 6*i**4 + 3*i - 7*i + 0*i**z - b*i**2 + 2 = 0?
-1, 1/3, 1
Suppose 3*j + 3/2*j**2 - 9/2 = 0. Calculate j.
-3, 1
Let y(v) be the second derivative of v**8/3360 - v**7/630 + v**6/360 - 2*v**4/3 - 2*v. Let c(x) be the third derivative of y(x). Factor c(j).
2*j*(j - 1)**2
Let q(p) = -3*p - 10. Let x be q(-5). Let h be 6/2 - (x + -7). Factor 0 - 3/5*n**h + 0*n**3 + 0*n**2 + 1/5*n**4 + 0*n.
-n**4*(3*n - 1)/5
Suppose 4*k - 2*s = 3*k, -2*k = s - 5. Factor 2/7*m + 8/7*m**k + 0.
2*m*(4*m + 1)/7
Let t(k) = -k**2 + 6*k. Let x be t(6). Factor 27*d**3 - 28*d**3 + x*d - 3*d + 3*d**2 + 1.
-(d - 1)**3
Let b(v) = -v**2 + v - 1. Suppose -4*u - 24 = -0*u. Let k(c) = 4*c**2 - 6*c + 6. Let x(h) = u*b(h) - k(h). Find f, given that x(f) = 0.
0
Let f(j) = -j**4 + 6*j**3 + 9*j**2 + 5*j. Let b(h) = -h**4 + h**2 + h. Let w(r) = 6*b(r) - 2*f(r). Factor w(t).
-4*t*(t + 1)**3
Let -8*r**2 - 3*r + 13*r**2 - 2*r = 0. What is r?
0, 1
Let w = 600 - 548. What is n in w*n**3 + 8/11 + 104/11*n + 