et t(v) be the second derivative of f(v). What is m in t(m) = 0?
-1, 0
Factor -12*f - 8*f + 8*f**3 + 4*f**4 + 7*f**3 + f**4.
5*f*(f - 1)*(f + 2)**2
Factor 1/4*d**3 - 1/4*d**5 + 0 + 0*d**4 + 0*d**2 + 0*d.
-d**3*(d - 1)*(d + 1)/4
Let x(z) be the third derivative of z**5/30 - z**4/12 - 13*z**2. Find h, given that x(h) = 0.
0, 1
Suppose d**3 - 5*d - 3*d**2 + 4*d + 0*d + 4*d**2 - d**4 = 0. What is d?
-1, 0, 1
Let b = 7 + -3. Suppose -5*v + b*q = -12, 0 + 6 = 2*v - q. What is m in 3*m**4 + m - m**4 - v*m**4 - m**5 + 2*m**2 = 0?
-1, 0, 1
Let h(q) be the third derivative of q**8/560 + q**7/140 - q**6/120 - q**5/20 - 7*q**3/6 + 7*q**2. Let n(c) be the first derivative of h(c). Factor n(z).
3*z*(z - 1)*(z + 1)*(z + 2)
Let g = 1352/9 + -150. Suppose -u + 10 = 4*u. Factor g*b - 2/9*b**3 + 0 - 2/9*b**4 + 2/9*b**u.
-2*b*(b - 1)*(b + 1)**2/9
Let t(f) = -f**3 + 5*f**2 - 5*f - 2. Let i(m) = 2*m**3 - 6*m**2 + 6*m + 2. Let l(g) = 3*i(g) + 4*t(g). Suppose l(x) = 0. What is x?
-1, 1
Suppose -5*m + 9*m - k - 13 = 0, 0 = -2*m - 5*k - 21. Let -m - 1/2*w**2 - 2*w = 0. Calculate w.
-2
Let l(b) be the first derivative of -15*b**4/4 - 5*b**3/3 + 5*b**2 - 62. Factor l(w).
-5*w*(w + 1)*(3*w - 2)
Let x(r) be the first derivative of -1/16*r**4 + 1/8*r**2 - 2 - 1/4*r + 1/12*r**3. Determine l so that x(l) = 0.
-1, 1
Let y(d) = 5*d**4 + 2*d**3 - 3*d**2 - 6. Let f(x) = -9*x**4 - 3*x**3 + 6*x**2 + 11. Let v(g) = 6*f(g) + 11*y(g). Suppose v(a) = 0. Calculate a.
-3, -1, 0
Factor 5184/7*l + 108/7*l**3 + 3/7*l**4 + 0 + 1296/7*l**2.
3*l*(l + 12)**3/7
Solve p**3 + 2*p**3 - 2*p**5 - 2*p + 0*p**3 + p**3 = 0 for p.
-1, 0, 1
Let h(c) = c**2 - 9*c + 10. Let q = -13 - -21. Let d be h(q). Determine g so that 1/4*g**d + g + 1 = 0.
-2
Let m be (-6)/9 - (-11)/3. Suppose 7 = d + p, d + 2*d - m*p = -9. Factor -7*j + 8 + 3*j + 2*j**d - 4*j.
2*(j - 2)**2
Suppose -5*u = -41 + 16. Suppose 0 = v - u + 3. Solve 0*y + 1/3*y**3 + 0 + 0*y**v = 0.
0
Let a(c) = c**2 - 8*c - 1. Let x be a(9). Suppose -13*q = -x*q. Solve 2/9*k**3 + 0*k + q*k**2 + 0 = 0.
0
Let i(z) = -z**3 + 10*z**2 + 2*z - 17. Let w be i(10). Factor -3/2*l**2 - 2 + w*l + 1/4*l**3.
(l - 2)**3/4
Suppose 6*o + 15*o = 17*o. Factor 3/2*t**5 + 0 + 0*t**4 + 3/2*t + o*t**2 - 3*t**3.
3*t*(t - 1)**2*(t + 1)**2/2
Let f(q) = q**2 - 5*q + 4. Let x(b) = -b**2 + 6*b - 5. Let l(c) = 5*f(c) + 4*x(c). Factor l(p).
p*(p - 1)
Let k be (-2 - 4 - 31/(-3)) + -4. Factor -k*h - 1/6*h**2 + 0.
-h*(h + 2)/6
Let s = 120 - 118. Let r(m) be the third derivative of -1/90*m**5 + 0 + 0*m**4 - s*m**2 + 1/9*m**3 + 0*m. Factor r(g).
-2*(g - 1)*(g + 1)/3
Let t(i) be the first derivative of 0*i**2 + 0*i + 1 + 3/2*i**4 - 4/3*i**3 - 2/5*i**5. Factor t(v).
-2*v**2*(v - 2)*(v - 1)
Let p(f) be the second derivative of -f**7/168 - f**6/120 + 3*f**5/80 + 5*f**4/48 + f**3/12 - 5*f. Factor p(h).
-h*(h - 2)*(h + 1)**3/4
Let g(k) be the first derivative of -6 + 0*k - 15/4*k**4 + 3*k**2 + 3*k**3. Solve g(t) = 0.
-2/5, 0, 1
Let q(x) be the first derivative of -3*x**5/5 + x**4/4 + 2*x**3/3 - 59. Factor q(s).
-s**2*(s - 1)*(3*s + 2)
Let z(q) = -q**2 + 3*q. Let o be z(2). Find d such that -o - d**4 - 8*d - d**4 - 12*d**2 - 8*d**3 + 0*d**4 = 0.
-1
Let s(f) be the second derivative of -7*f**7/240 + 7*f**6/120 - f**5/20 + f**4/4 + 3*f. Let n(l) be the third derivative of s(l). Factor n(p).
-3*(7*p - 2)**2/2
Let f(q) = q**2 + 2*q - 2. Let m be f(-6). Factor 8 - 10*h**2 + m*h**2 + 27*h - 2.
3*(h + 2)*(4*h + 1)
Factor 30*u**2 - 22*u**2 + 4*u + 31*u + 5*u**3 + 32*u**2.
5*u*(u + 1)*(u + 7)
Let m(u) = u + 5. Let y be m(-5). Suppose 5*v - 11*v + 12 = 0. Factor y - 4/9*h**v + 2/9*h + 2/9*h**3.
2*h*(h - 1)**2/9
Suppose -9 + 4 = f. Let d(b) = -b**2 - 4*b. Suppose 2*h = 5 - 19. Let r(t) = t**2 + 6*t. Let x(q) = f*r(q) + h*d(q). Let x(u) = 0. Calculate u.
0, 1
Let s(g) be the first derivative of g**6/360 + 2*g**3 - 9. Let c(w) be the third derivative of s(w). Find j such that c(j) = 0.
0
Let w(b) be the second derivative of 3*b**5/20 + 9*b**4/4 + 4*b**3 + b + 3. Find o, given that w(o) = 0.
-8, -1, 0
Let q be (-2 + 44/16)/(-5 - -35). Let x(z) be the second derivative of -1/40*z**6 + 3*z + 0*z**4 + q*z**5 + 0*z**3 + 0*z**2 + 0. Factor x(p).
-p**3*(3*p - 2)/4
Suppose 0 = -5*p - 4 - 1. Let f(r) = -r**5 - r**4 + r**2 + 1. Let g(h) = 4*h**5 + 4*h**4 - 2*h**3 - 4*h**2 - 2. Let c(y) = p*g(y) - 2*f(y). Factor c(n).
-2*n**2*(n - 1)*(n + 1)**2
Let z(o) be the first derivative of 2*o**3/3 - 5*o**2 + 8*o + 3. Factor z(b).
2*(b - 4)*(b - 1)
Factor 5*b**3 + b**2 + 5*b**2 + 3*b - 2*b**3.
3*b*(b + 1)**2
Let t = -13 - -25. Suppose 2*q + 4*m = 16, 0*q - 3*q = 2*m - t. Factor 3/5*b + 0 - 3/5*b**q + 3/5*b**4 - 3/5*b**3.
3*b*(b - 1)**2*(b + 1)/5
Suppose 0 = 3*z - 4*i + 3*i + 45, -4*z - 60 = -5*i. Let w = -11 - z. Factor 0 + 0*q - 2/3*q**w - 2*q**3 - 4/3*q**2.
-2*q**2*(q + 1)*(q + 2)/3
Let g(y) be the third derivative of -y**5/270 - y**4/9 - 11*y**3/27 + 34*y**2. Factor g(j).
-2*(j + 1)*(j + 11)/9
Suppose 0 = 3*f - 3*s - 6, 3*f = 4*f - 5*s + 2. Solve -1/2*t - 1/2*t**f + 0 - t**2 = 0 for t.
-1, 0
Suppose -9 = 3*z - 3*w, 0 = 2*z + z - 5*w + 19. Suppose -8 = -5*l + z. Factor 0*y**l + 4*y**2 + 2*y - 6*y**2.
-2*y*(y - 1)
Let b(p) be the second derivative of -p**6/420 + p**5/210 + p**4/84 - p**3/21 + p**2 - 3*p. Let w(j) be the first derivative of b(j). Solve w(n) = 0.
-1, 1
Let f(y) be the first derivative of -2*y**4 + 8*y**3/3 - 3*y**2/4 + 16. Factor f(l).
-l*(4*l - 3)*(4*l - 1)/2
Let s(t) be the third derivative of 2/35*t**7 + 0*t - 1/8*t**6 + 1/10*t**5 + 6*t**2 + 0*t**3 - 1/112*t**8 + 0*t**4 + 0. Suppose s(c) = 0. What is c?
0, 1, 2
Let r(z) be the third derivative of -z**5/240 + z**4/16 - 3*z**3/8 - 5*z**2. Factor r(g).
-(g - 3)**2/4
Let a(r) = 4*r**5 + 4*r**4 + r**3 + r**2 - 5*r. Let t(z) = 2*z**5 + 2*z**4 + z**3 + z**2 - 3*z. Let j(m) = 6*a(m) - 10*t(m). Let j(f) = 0. What is f?
-1, 0, 1
Suppose -2*g + 5*g - 3 = 3*r, -g - r + 3 = 0. Let k(c) be the second derivative of 3*c + 1/4*c**g - 7/48*c**4 + 5/24*c**3 + 0. Suppose k(f) = 0. Calculate f.
-2/7, 1
Let n(x) be the second derivative of -x**5/40 + x**4/12 - x**3/12 - 10*x. Factor n(b).
-b*(b - 1)**2/2
Let p be (-8)/(-40) + (-2 - 27/(-15)). Factor 2/3*v**2 + 0*v + p.
2*v**2/3
Suppose 3*i - i - 3*a = 17, -i - 3*a = 5. Suppose i + 9*q**3 - 6*q**2 - 2*q - 4 + 3*q = 0. Calculate q.
0, 1/3
Let d(j) be the first derivative of j**6/12 - j**4/8 - 5. Let d(y) = 0. What is y?
-1, 0, 1
Let z(j) be the second derivative of j**4/12 + 5*j**3/6 - 3*j**2/2 + j. Let d be z(-6). Suppose 0*v**d - v**3 + 3*v**3 - 2*v = 0. Calculate v.
-1, 0, 1
Factor 128*w**2 - 140*w + 28*w**4 + 103*w**2 + 5*w**2 + 21 + 3 - 148*w**3.
4*(w - 3)*(w - 1)**2*(7*w - 2)
Let d(h) be the first derivative of 12*h**5/5 - 11*h**4/3 + 8*h**3/9 + 7. Factor d(x).
4*x**2*(x - 1)*(9*x - 2)/3
Let s(o) = 11*o**2 - o + 3. Let r(x) = 56*x**2 - 6*x + 14. Let m(b) = 6*r(b) - 28*s(b). Let m(j) = 0. Calculate j.
0, 2/7
Let f(n) be the third derivative of n**5/15 + 2*n**4/3 - 8*n**3 - 7*n**2. Factor f(i).
4*(i - 2)*(i + 6)
Suppose -3*u + 15 = 3*c - 6, -4*c + u + 18 = 0. Let o(q) be the third derivative of 0 - 2/15*q**3 - 1/60*q**4 + 0*q - q**2 + 1/150*q**c. What is s in o(s) = 0?
-1, 2
What is o in 2/5*o - 1/5*o**2 + 3/5 = 0?
-1, 3
Let m(x) be the first derivative of -4*x**3/15 - 2*x**2/5 + 8*x/5 - 14. What is i in m(i) = 0?
-2, 1
Let i(y) = 3*y**5 - y**4 + 2*y**3 - 9*y**2 - 5. Let s(z) = 4*z**5 - z**4 + 3*z**3 - 13*z**2 - 7. Let f(x) = 7*i(x) - 5*s(x). Let f(k) = 0. Calculate k.
-1, 0, 1, 2
Let p(k) = 10*k**2 + k + 11. Let c(s) = 2*s**2 + 2. Let t(q) = -22*c(q) + 4*p(q). Factor t(v).
-4*v*(v - 1)
Let q(s) = 3*s. Let w be q(-2). Let g be ((-2)/w)/(2/12). Factor -9 - 32*h**2 - 3*h**5 - 15*h + 6 - 30*h**3 + 2*h**g - 15*h**4.
-3*(h + 1)**5
Let p = -565/7 - -81. Solve p*u**3 + 2/7*u**2 - 2/7 - 2/7*u = 0.
-1, 1
Suppose 4*k + 4*b = 9*b + 41, -3*b - 27 = -3*k. Factor -4/7*i**5 + 0 + 0*i + 0*i**2 - 4/7*i**3 - 8/7*i**k.
-4*i**3*(i + 1)**2/7
Let s(i) be the third derivative of -i**5/60 + i**4/2 - 6*i**3 + 12*i**2. Factor s(f).
-(f - 6)**2
Let c(l) be the third derivative of l**8/840 - l**7/525 - l**6/150 - 7*l**2 - 2. Suppose c(s) = 0. What is s?
-1, 0, 2
Let l(v) be the third derivative of v**5/240 + v**4/96 - v**3/12 + 20*v**2. Solve l(b) = 0.
-2,