h**3/5
Let i(f) be the third derivative of -f**9/60480 - f**5/30 - 2*f**2. Let y(s) be the third derivative of i(s). Factor y(u).
-u**3
Let d(p) be the first derivative of -p**3/6 - 7. Let d(w) = 0. What is w?
0
Suppose -34 = -5*n + 11. Factor -2*f**5 + 7*f**5 - 21*f**4 + 4*f**5 + 3*f**3 + n*f**4.
3*f**3*(f - 1)*(3*f - 1)
Let l be (9/(-30))/(48/(-40)). Find d, given that 1/4*d**3 - l*d**2 + 1/4 - 1/4*d = 0.
-1, 1
Suppose -2*p = 0, -p = 4*f - 6*p - 8. Factor -8*w**3 + 11*w**3 - w - f*w.
3*w*(w - 1)*(w + 1)
Let d(g) be the first derivative of -2/9*g**3 + 0*g + 2/15*g**5 - 2/3*g**2 + 1/3*g**4 + 3. Factor d(n).
2*n*(n - 1)*(n + 1)*(n + 2)/3
Suppose -m - 2 = 2*p, -3*m - 3*p = m - 2. Factor f**m + 1/3 - 1/3*f**3 - f.
-(f - 1)**3/3
Let g(x) be the first derivative of 1/16*x**4 - 1/3*x**3 + 0*x**2 - 6 + 0*x. What is y in g(y) = 0?
0, 4
Determine w, given that -5*w**3 - 11*w + 35*w**2 + 18*w - 20*w - 37*w = 0.
0, 2, 5
Let m(i) be the third derivative of 3*i**2 + 0*i**3 + 1/224*i**8 + 2/105*i**7 + 1/60*i**5 + 7/240*i**6 + 0 + 0*i + 0*i**4. What is h in m(h) = 0?
-1, -2/3, 0
Let p be (1 - 2)/(1/(-2)). Suppose s - p*x + x = -2, 4*s = 2*x. Factor -z**2 + 2*z + 3 - 2*z**3 - z**s + 2*z**4 - 3.
2*z*(z - 1)**2*(z + 1)
Let r(g) be the second derivative of 0 - 1/15*g**4 - 1/15*g**3 + g + 0*g**2 - 1/50*g**5. Find a such that r(a) = 0.
-1, 0
Let f(x) = x - 1. Let g(b) = 3*b**2 + 39*b + 33. Let c(d) = -15*f(d) + g(d). Find p such that c(p) = 0.
-4
Suppose 22 = 3*j + 4*x, -2*j + 2*x - 6 = -j. Let u(s) be the first derivative of 0*s**2 - 1/15*s**6 - 3/10*s**4 - 6/25*s**5 - 2/15*s**3 + 0*s + j. Factor u(w).
-2*w**2*(w + 1)**3/5
Let m(v) be the third derivative of v**6/660 - v**5/110 + 4*v**3/33 + 12*v**2. Factor m(j).
2*(j - 2)**2*(j + 1)/11
Suppose -h + 3 = i, 4*h - 3*h - 4*i - 28 = 0. Let o(s) be the first derivative of 4*s**2 - 2 - h*s - 2/3*s**3. Factor o(j).
-2*(j - 2)**2
Let z(v) be the second derivative of 1/84*v**7 + 3*v - 1/20*v**5 + 0*v**4 + 0*v**6 + 1/12*v**3 + 0*v**2 + 0. Factor z(u).
u*(u - 1)**2*(u + 1)**2/2
Let a(t) = -114*t**3 + 9*t**2 + 12*t - 6. Let o be (-8)/12*(-6)/(-4). Let x(s) = s**3 - s**2 - s + 1. Let d(q) = o*a(q) - 6*x(q). Solve d(b) = 0.
-2/9, 0, 1/4
Let b(t) be the second derivative of t**2 + 2*t - 3/20*t**5 + 1/6*t**3 - 1/3*t**4 + 0. Factor b(d).
-(d + 1)**2*(3*d - 2)
Let t(o) be the first derivative of -2/3*o + 7/24*o**4 - 7 + 2/3*o**2 + 19/18*o**3. Factor t(l).
(l + 1)*(l + 2)*(7*l - 2)/6
Let d = 11 + -6. Let h(u) be the third derivative of -2*u**2 + 0 + 1/8*u**4 - 1/336*u**8 - 1/6*u**3 - 1/30*u**d - 1/60*u**6 + 0*u + 1/70*u**7. Factor h(o).
-(o - 1)**4*(o + 1)
Factor 4/11*z + 2/11 + 2/11*z**2.
2*(z + 1)**2/11
Let o(q) be the second derivative of -1/10*q**5 - 1/9*q**3 - 7*q + 1/6*q**4 + 0*q**2 + 1/45*q**6 + 0. Suppose o(p) = 0. What is p?
0, 1
Find y, given that 14*y**5 - 8*y**3 + 16*y**4 + 0*y**3 - 4*y**5 = 0.
-2, 0, 2/5
What is h in -h**2 - 3*h**2 - h**2 - 6 + 26 = 0?
-2, 2
Let j(x) be the first derivative of -2*x**3/3 - x**2 + 4*x + 12. What is r in j(r) = 0?
-2, 1
Suppose 15 = 5*t + 5*o, 0 = 3*t + 3*o - 4*o + 3. Factor t + 0*c + 2/3*c**4 + 1/3*c**3 + 0*c**2.
c**3*(2*c + 1)/3
Let b = 2 - -3. Determine k, given that -2*k**3 + 1 + b*k**3 - 3*k - 1 = 0.
-1, 0, 1
Let d be 8/6*1/6. Factor -d*x**3 - 16/9*x + 10/9*x**2 + 8/9.
-2*(x - 2)**2*(x - 1)/9
Let o = 39 - 37. Let x(l) be the first derivative of -1/4*l**4 - 3 - l**3 + 0*l - l**o. Factor x(v).
-v*(v + 1)*(v + 2)
Let h(x) be the first derivative of -3*x**5/20 - 3*x**4/4 - 5*x**3/4 - 3*x**2/4 - 9. Find b such that h(b) = 0.
-2, -1, 0
Let w(s) be the first derivative of 2*s**5/5 + s**4/2 - 4*s**3/3 - 2. Factor w(x).
2*x**2*(x - 1)*(x + 2)
Let i(h) be the second derivative of h**7/105 + h**6/120 - h**5/60 - h**2 - 3*h. Let k(q) be the first derivative of i(q). Suppose k(g) = 0. What is g?
-1, 0, 1/2
Let c(f) be the third derivative of -f**5/60 - f**4/4 - 3*f**3/2 + 34*f**2. Suppose c(j) = 0. Calculate j.
-3
Suppose 3*p = -5*j + 1, -3*j + 0*j - 9 = -3*p. Let o(i) be the first derivative of -1/6*i**4 + 0*i + 2 + 0*i**p + 0*i**3. Find y, given that o(y) = 0.
0
Let k be (-12)/(-54) - 176/9. Let w = -19 - k. Determine h, given that 1/3 - w*h**2 + 0*h = 0.
-1, 1
Let l(z) be the first derivative of 6*z**5/5 + 5*z**4/2 + 4*z**3/3 + 14. Let l(p) = 0. What is p?
-1, -2/3, 0
Let m = 9 + -6. Factor l**2 + 6*l**2 + 8*l - 4 + 4*l**2 + 3*l**m.
(l + 2)**2*(3*l - 1)
Let g be 40/(-2)*(-16)/10. Let c be g/24*6/4. Let -i**2 + 2*i**c - 10*i + 4*i + 6 + 3 = 0. What is i?
3
Factor -1/9*h**2 + 0*h + 4/9.
-(h - 2)*(h + 2)/9
Let q(m) be the third derivative of -1/300*m**6 + 0*m**5 + 1/20*m**4 + 2/15*m**3 + 0 + 0*m - 6*m**2. Determine r, given that q(r) = 0.
-1, 2
Solve -27*f**3 - 8 + 21*f**2 + 33*f**4 + 27*f - 16 - 30*f**4 = 0.
-1, 1, 8
Suppose -5*j - 1 + 6 = 0. Suppose -3*f = -j - 8. Factor -2*q**5 + q**f - q**5 - q**5 + 3*q**5.
-q**3*(q - 1)*(q + 1)
Find u such that -128 + 71/4*u**3 + 138*u**2 + 336*u + 3/4*u**4 = 0.
-8, 1/3
Let 3/2 - 1/2*h**2 + h = 0. Calculate h.
-1, 3
Let g be (1/(-3))/(5/(-60)). Suppose 4*f - 10 = -f. Factor -2*t**3 + t**f - 2*t**4 + t**g + 2*t**4.
t**2*(t - 1)**2
Let j(s) = -4*s**3 + 21*s**2 - 16. Let n(z) = -z**3 + 5*z**2 - 4. Let k(p) = -4*j(p) + 18*n(p). Let k(y) = 0. What is y?
-1, 2
Let g(w) be the first derivative of -1/12*w**6 + 2/5*w**5 + 2/3*w**3 + 0*w - 3 - 1/4*w**2 - 3/4*w**4. Factor g(v).
-v*(v - 1)**4/2
Let r(f) be the second derivative of -1/25*f**5 + 0*f**6 + 1/15*f**3 + 0 + 1/105*f**7 + 0*f**4 + 0*f**2 - 3*f. Factor r(v).
2*v*(v - 1)**2*(v + 1)**2/5
Factor 11/3*c + 26/3*c**3 - 2/3 + c**5 - 8*c**2 - 14/3*c**4.
(c - 1)**4*(3*c - 2)/3
Suppose -20 = -4*p - 4*a, 2*p + 1 = a + 5. Suppose p*f = 2*r + 14, -2*r - 19 = -2*f - 7. Factor -2*s**2 - f*s - 2/3*s**3 - 2/3.
-2*(s + 1)**3/3
Let k(z) = -3*z**2 - 7*z - 4. Let m(u) = -u**2 - 3*u - 2. Let d(g) = 2*k(g) - 5*m(g). Solve d(t) = 0.
-1, 2
Let n(s) be the first derivative of 0*s + 2 - 1/4*s**4 - 3/20*s**5 - 1/6*s**3 - 1/2*s**2. Let v(r) be the second derivative of n(r). Solve v(h) = 0.
-1/3
Solve m**2 - 18*m**3 - 4*m**2 - 9*m**4 - 3*m**5 + 9*m**3 = 0.
-1, 0
Let t(i) be the second derivative of -i**6/900 + i**4/60 + i**3/2 + i. Let q(j) be the second derivative of t(j). Determine o, given that q(o) = 0.
-1, 1
Let g be (2/(-60))/((-42)/35). Let f(j) be the second derivative of 0 - 1/9*j**3 - 3*j + g*j**4 + 1/6*j**2. Find a, given that f(a) = 0.
1
Let v(p) = -8*p**2 + 5*p + 3. Let w(r) = -3*r**2 - 5*r + 4. Let k(x) = 4*x**2 + 6*x - 5. Let q(m) = 4*k(m) + 5*w(m). Let z(l) = -5*q(l) - v(l). Factor z(d).
3*(d - 1)*(d + 1)
Find m, given that 0*m**2 + 2/11*m**5 + 0 + 0*m - 2/11*m**3 + 0*m**4 = 0.
-1, 0, 1
Let x(q) = 24*q**2 + 4*q - 24. Let t(r) = -r**2 + r - 1. Let z(n) = -4*t(n) - x(n). Factor z(a).
-4*(a - 1)*(5*a + 7)
Let j(h) = -8*h - 44. Let u be j(-6). Let c(k) be the third derivative of -4/3*k**3 + 2*k**2 - 1/30*k**5 + 1/3*k**u + 0*k + 0. What is w in c(w) = 0?
2
Let w(p) = 4*p**5 - 12*p**4 - 26*p**3 - 24*p**2 - 8*p + 6. Let g(t) = -4*t**5 - 4*t**5 - 1 + 7*t**5. Let c(r) = -6*g(r) - w(r). Solve c(l) = 0.
-2, -1, 0
Find s, given that 0 - 2/5*s**2 + 2/5*s - 2/5*s**3 + 2/5*s**4 = 0.
-1, 0, 1
Let a = 225 + -1574/7. Suppose 3/7 - 3/7*p**2 + a*p - 1/7*p**3 = 0. Calculate p.
-3, -1, 1
Suppose 20 = 6*x - 2*x. Let p = x + -2. Suppose 3*g**2 - g**2 + 9*g**4 + 6*g**p - 5*g**4 = 0. What is g?
-1, -1/2, 0
Let w(m) = -75*m**3 + 137*m**2 - 70*m + 10. Let j(f) = -f**2 - f + 1. Let k(t) = -2*j(t) - w(t). Factor k(u).
3*(u - 1)*(5*u - 2)**2
Let l = 8 - 6. Find k such that -32955*k**4 - 4566*k**l + 85683*k**5 - 4251*k**2 - 1200*k - 2103*k**2 - 40560*k**3 - 48 = 0.
-2/13, 1
Let c = -217499 + 23924497/110. Let d = 27/22 - c. Suppose 8/5 + 2*u**2 - d*u = 0. What is u?
2/5, 2
Let s(i) = -2*i - 3. Let h be s(-3). Suppose -h*k + 3 = -2*k. Suppose -8 + 5*y + 6*y**2 + 34*y**k - 98*y**4 + 42*y**3 + 64*y**3 - 45*y = 0. What is y?
-2/7, 1
Suppose d - 8 = -5*s, -2*s = -3*d - s + 8. Let 3*q**3 + q**2 - 3*q**2 - d*q**4 + 3*q**3 - q**2 = 0. Calculate q.
0, 1
Suppose -5*d - 124 = 4*q, 0*d - 53 = 2*d + 5*q. Let b be (0 + -1)/(6/d). Factor -y**2 + y**b + 2*y**2 - 4*y**4 - 2*y**3.
-y**2*(y + 1)*(3*y - 1)
Suppose 4*f = -f - 10. Let a be 2/f*(-80)/28. Let a*q**2 - 18/7*q 