- 3*s**4 + 2*s**3 + 0*s**4 - 6*s.
-3*(s - 1)**3*(s + 1)
Let g(z) be the first derivative of z**4/6 - 4*z**3/3 + 3*z**2 - 8*z/3 + 6. Suppose g(c) = 0. What is c?
1, 4
Let n(i) be the third derivative of -i**6/140 - i**5/30 + 4*i**3/21 + i**2. Determine g, given that n(g) = 0.
-2, -1, 2/3
Let f(h) be the second derivative of -25/24*h**4 - h**2 + 4/3*h**3 + h - 7/60*h**6 + 0 + 1/84*h**7 + 19/40*h**5. Suppose f(a) = 0. What is a?
1, 2
Let i(h) be the third derivative of h**5/15 + h**4/2 + 6*h**2. Determine c so that i(c) = 0.
-3, 0
Let w(x) be the third derivative of x**8/280 + x**7/420 - x**6/90 + x**3/2 + 2*x**2. Let b(g) be the first derivative of w(g). Suppose b(o) = 0. Calculate o.
-1, 0, 2/3
Determine h, given that 3 - 3*h**2 - 3/2*h**3 + 3/2*h = 0.
-2, -1, 1
Let a be 632/60 - 4/(-30). Find c such that 4/3 + a*c**2 + 4/3*c**3 - 22/3*c + 6*c**5 - 12*c**4 = 0.
-1, 1/3, 2/3, 1
Let c = -3 + 8. Let n = 0 + 2. Find a, given that 4*a**4 - c*a**4 + a**n - a + 2*a - a**3 = 0.
-1, 0, 1
Let g = 22 - 20. Suppose 3*r + 2*o - 8 = -g, 8 = 4*r + o. Factor -7/3*i - 3*i**3 + 1/3 + 5*i**r.
-(i - 1)*(3*i - 1)**2/3
Let n = -188 - -190. Suppose 12 = 3*o - 0. Factor -4/11*x**n + 0*x**3 + 0 - 2/11*x + 4/11*x**o + 2/11*x**5.
2*x*(x - 1)*(x + 1)**3/11
Let d(q) be the second derivative of -q**6/40 - q**5/10 - q**4/8 - q**2/2 + 2*q. Let b(n) be the first derivative of d(n). Suppose b(r) = 0. Calculate r.
-1, 0
Let n be -4*1 + (-6)/2. Let k = n + 12. Find v, given that 0 + 0*v**2 - 1/2*v**4 + 0*v**3 + 0*v + 1/2*v**k = 0.
0, 1
Let f(c) be the third derivative of 0*c + 0*c**5 + 1/360*c**6 + 2*c**2 + 0*c**4 + 0 + 0*c**3. Factor f(l).
l**3/3
Suppose 2*k = -2*k + 8. Factor 2 + 3 + 10*s - 3 + k + 6*s**2.
2*(s + 1)*(3*s + 2)
Suppose k + 3*d + 1 = 0, -k + 5 = -4*d - 8. Let s(p) be the third derivative of -1/18*p**4 + 0*p + p**2 + 1/180*p**k + 2/9*p**3 + 0. Factor s(o).
(o - 2)**2/3
Suppose -254 = -4*u - 82. Find w, given that 4*w**3 - u*w**2 + 41*w**2 - 3*w**4 + w**4 = 0.
0, 1
Let h(s) be the third derivative of s**5/80 - s**4/32 - 3*s**2 - 3*s. Find d such that h(d) = 0.
0, 1
Let f(n) be the third derivative of n**5/15 - n**4/3 + 11*n**2. Factor f(d).
4*d*(d - 2)
Let l(w) be the second derivative of -w**7/3360 - w**6/1440 - w**3/2 + 4*w. Let f(n) be the second derivative of l(n). Factor f(o).
-o**2*(o + 1)/4
Factor 4*b**3 - 63/4*b**2 - 4*b + 16 - 1/4*b**4.
-(b - 8)**2*(b - 1)*(b + 1)/4
Let d = -138 + 72. Let z = d - -135/2. Let 3*n + z + 3/2*n**2 = 0. What is n?
-1
Suppose -7*s = -2*s. Let a(h) = h. Let r be a(3). Solve 18/7*z**5 + s*z - 30/7*z**2 - 10/7*z**r + 30/7*z**4 + 8/7 = 0 for z.
-1, 2/3
Let x be (3/12*0)/3. Let y(d) be the second derivative of -3/40*d**5 + d + 1/42*d**7 - 1/60*d**6 + 1/24*d**4 + x*d**2 + 1/12*d**3 + 0. Solve y(u) = 0 for u.
-1, -1/2, 0, 1
Suppose -4*q + q = 0. Let g(j) be the first derivative of q*j + 1/2*j**2 - 3 + 1/3*j**3. Find h such that g(h) = 0.
-1, 0
Let o(g) = -g**3 - 6*g**2 - g - 4. Let c be o(-6). Suppose -c*q = 5*s, -12 = -s + q + q. Suppose 0*i**s + 2*i**2 - 3*i + 5*i - 3*i**2 = 0. What is i?
0, 2
Let i(u) be the first derivative of -5/3*u**3 - 9/4*u**4 + 7/5*u**5 - 2*u + 1 + 9/2*u**2. What is j in i(j) = 0?
-1, 2/7, 1
Let k(h) be the third derivative of -h**5/150 + h**4/30 - h**3/15 + 5*h**2. Solve k(d) = 0.
1
Let v(h) be the second derivative of -h**6/270 + h**5/90 + h**4/108 - h**3/27 - 17*h. What is i in v(i) = 0?
-1, 0, 1, 2
Let p(d) be the third derivative of d**5/150 + d**4/15 + 9*d**2. Factor p(v).
2*v*(v + 4)/5
Let n = 76 - -64. Let l be 4 + (n/(-6))/7. Determine h, given that 1/3*h + l*h**2 + 1/3*h**3 + 0 = 0.
-1, 0
Factor 0 + 1/2*h**4 + 1/2*h**5 - 1/2*h**3 - 1/2*h**2 + 0*h.
h**2*(h - 1)*(h + 1)**2/2
Let y(d) = 5*d**5 - 22*d**4 + 23*d**3 - 12*d**2 + 2. Let a(l) = -l**4 - l**3 - l**2 + 1. Let i(h) = 2*a(h) - y(h). Find z such that i(z) = 0.
0, 1, 2
Let m(f) = -f - 3. Let g(v) = -v**3 - 9*v**2 + 10*v - 5. Let d be g(-10). Let c be m(d). Factor 5*t**c - 25/2*t**3 + 0 - 1/2*t.
-t*(5*t - 1)**2/2
What is b in 1653*b - 1656*b + 5*b**2 - 3*b**4 - 2*b**2 + 3*b**3 = 0?
-1, 0, 1
Find u such that 2/11*u**2 + 0 + 0*u + 6/11*u**3 + 4/11*u**4 = 0.
-1, -1/2, 0
Let z(o) be the first derivative of 0*o**4 - 2 + 1/120*o**5 + 0*o + 1/360*o**6 + 0*o**2 - 1/3*o**3. Let v(u) be the third derivative of z(u). Factor v(y).
y*(y + 1)
Factor -1/3 - p**4 + 7/3*p**3 - 8/3*p**2 + 1/6*p**5 + 3/2*p.
(p - 2)*(p - 1)**4/6
Let o(z) be the second derivative of 2/195*z**6 - 1/273*z**7 - z + 0*z**2 + 1/130*z**5 - 1/39*z**4 + 0*z**3 + 0. Solve o(r) = 0.
-1, 0, 1, 2
Let p(z) = -z**3 - z**2 - z. Let m(g) = -7*g**3 + g**2 - 11*g + 2. Suppose -4 = -2*o - 6. Let i(t) = o*m(t) + 5*p(t). Factor i(v).
2*(v - 1)**3
Let x(s) be the first derivative of -2*s**2 - 2*s - 2. Let w be x(-3). Factor -r**3 - w*r + 0*r**3 + 4 + 8*r**2 - r**3.
-2*(r - 2)*(r - 1)**2
Let m(r) be the second derivative of 1/10*r**6 + 6*r + 0*r**3 + 0 + 3/50*r**5 + 0*r**4 + 0*r**2 + 3/70*r**7. Let m(d) = 0. Calculate d.
-1, -2/3, 0
Suppose 9*i = 4*i. Suppose 0*d = -d + 2, 2*o - d - 2 = i. Find q, given that -13 + 4*q**3 + 10*q**o + 13 + 4*q = 0.
-2, -1/2, 0
Let s(p) = -p + 7. Let v be s(8). Let c(a) = -5*a - 1. Let o be c(v). Factor 11*z**3 - 2*z**3 + 7*z**4 + 6*z**2 - o*z**2.
z**2*(z + 1)*(7*z + 2)
Determine b, given that 36*b**2 + 4*b**5 + 181*b**3 - 13*b**4 - 121*b**3 + 41*b**4 = 0.
-3, -1, 0
Let t(c) be the first derivative of 0*c**3 - 3/5*c**5 + 0*c**2 + 0*c + 1/4*c**4 - 2/3*c**6 - 4. Factor t(j).
-j**3*(j + 1)*(4*j - 1)
Let y = -13/120 - -5/24. Let r(i) be the second derivative of y*i**5 - 5/12*i**4 + 0 + 0*i**2 + 2*i - 1/3*i**3 + 1/6*i**6. Factor r(w).
w*(w - 1)*(w + 1)*(5*w + 2)
Let p(h) = h + 21. Let z be p(-17). Find f, given that -3/2*f**z + 3/2*f + 1/2 - 1/2*f**5 - f**3 + f**2 = 0.
-1, 1
Let o(z) be the third derivative of -z**8/840 - z**7/525 + z**6/100 + z**5/30 + z**4/30 + 8*z**2. Factor o(r).
-2*r*(r - 2)*(r + 1)**3/5
Let i(h) = -h**2 - 6*h + 0*h + 3 - 2*h. Let q be i(-8). Factor -2*l - 3*l**2 + q*l**3 + 4*l**4 - 3*l**2 + 2 - l**3.
2*(l - 1)*(l + 1)**2*(2*l - 1)
Let z = -17/2 + 9. Let s be -3 - (-3 + (-1)/2). Solve -z*r**3 + s - 3/2*r + 3/2*r**2 = 0 for r.
1
Let w = 28 - 28. Let n(g) be the second derivative of w - 2*g + 1/2*g**2 - 1/6*g**4 + 1/42*g**7 - 1/10*g**5 + 1/6*g**3 + 1/30*g**6. Solve n(x) = 0.
-1, 1
Solve 5/2*u**3 + 0*u - u**2 + 0 + 3/2*u**4 = 0.
-2, 0, 1/3
Let a = -2070/13 + 15114/91. Factor -a*c**3 + 18/7*c**2 - 32*c**4 + 0 + 4/7*c.
-2*c*(4*c + 1)**2*(7*c - 2)/7
Let w = 1 - 2. Let m = w - -5. Factor 0 + 0 - 5*b + m*b + b**3.
b*(b - 1)*(b + 1)
Let z(d) = 5*d**4 + 11*d**3 - 10*d**2 + 6*d + 6. Let l(u) = -5*u**4 - 10*u**3 + 10*u**2 - 5*u - 5. Let b(r) = 6*l(r) + 5*z(r). Solve b(f) = 0 for f.
-2, 0, 1
Let p = -5 + 7. Let f be (3/(-9))/(p/(-24)). Determine g so that 0*g + 0 - 1/3*g**f + 1/3*g**3 + 0*g**2 = 0.
0, 1
Let w(i) = -3*i**2 + 8*i + 5. Let d(g) = 2*g**2 - 4*g - 2. Let n(y) = 5*d(y) + 2*w(y). What is r in n(r) = 0?
0, 1
Let o be (-165)/(-9) + 2/(-6). Suppose 4*j + 21 = b, 2*j = -2*b + 32 - 0. Factor -15 + 6*v + b - o*v + 18*v**2 - 8*v**3.
-2*(v - 1)**2*(4*v - 1)
Let s(n) be the second derivative of -2*n**7/7 + n**6 - 51*n**5/80 + n**4/8 + 3*n. Determine y so that s(y) = 0.
0, 1/4, 2
Suppose 0 = -5*v + 20, -l + 1 + 13 = 3*v. Let x(a) be the second derivative of 0 - 1/11*a**l - 1/33*a**4 - 1/11*a**3 - 3*a. Factor x(m).
-2*(m + 1)*(2*m + 1)/11
Suppose -14 = -2*j + j. Suppose 4*x - 8 = 5*n, -5*x = 5*n + 4 - j. Factor 2/7*s**x + 0 + 4/7*s.
2*s*(s + 2)/7
Let s = -2537 - -433775/171. Let x = 10/19 + s. Solve 2/9*m**2 + 0 - x*m = 0 for m.
0, 1
Let l(n) be the third derivative of n**8/560 + n**7/70 - n**6/40 - 9*n**5/20 + 54*n**3/5 + n**2 + 6. Suppose l(f) = 0. Calculate f.
-3, 2
Let y(v) be the first derivative of 16*v**6/9 + 176*v**5/15 + 137*v**4/6 + 106*v**3/9 + 2*v**2 + 20. Suppose y(o) = 0. What is o?
-3, -2, -1/4, 0
Let m(y) = y**4 + 4*y**3 - 12*y**2 + 12*y - 1. Let h(p) = -p**4 + p**3 - p - 1. Let o(d) = -2*h(d) - m(d). Factor o(l).
(l - 3)*(l - 1)**3
What is t in -1/8*t**3 + 0*t + 0 + 3/8*t**2 = 0?
0, 3
Let z(y) be the third derivative of y**5/360 - y**4/72 - 21*y**2. Factor z(p).
p*(p - 2)/6
Let c(l) be the first derivative of l - 1/18*l**4 + 2/9*l**3 - 1/3*l**2 - 1. Let u(h