*s**3*(s - 1)/9
Suppose 2*k = 7*k + 2*t - 8, -5*t - 3 = k. Find s, given that 0*s + 0 - 1/4*s**k + 1/2*s**3 - 1/4*s**4 = 0.
0, 1
Find q, given that 16/5*q + 4/5*q**3 + 42/5*q**2 - 14/5*q**4 - 8/5 = 0.
-1, 2/7, 2
Suppose -4*h - p - 3*p = 12, h + 2*p = -8. Factor -5*g**2 - 2*g + 6*g**h + 3*g - 2.
(g - 1)*(g + 2)
Let l(r) be the second derivative of r**5/5 - 7*r**4/3 - 2*r**3/3 + 14*r**2 + 4*r - 3. Factor l(u).
4*(u - 7)*(u - 1)*(u + 1)
Let g(p) be the first derivative of -1/3*p + 1/9*p**3 - 1/6*p**2 + 5 + 1/12*p**4. Factor g(y).
(y - 1)*(y + 1)**2/3
Factor 3/5*s**3 + 9*s + 27/5*s**2 + 21/5.
3*(s + 1)**2*(s + 7)/5
Let y(f) be the third derivative of -f**7/75 + f**6/25 - f**5/50 - f**4/30 + 7*f**2. Suppose y(a) = 0. Calculate a.
-2/7, 0, 1
Let j be 6/1*(-2)/(-18). Let g(f) be the second derivative of -j*f**3 - 1/2*f**4 - 2*f - 1/3*f**2 + 0 - 2/15*f**5. Factor g(c).
-2*(c + 1)**2*(4*c + 1)/3
Let m be (-6)/4*8/(-18). Let -2/3*a**2 - 7/3*a**3 + 7/3*a + m = 0. Calculate a.
-1, -2/7, 1
Suppose -8/7*z**2 - 1/7*z**3 + 0 + 9/7*z = 0. What is z?
-9, 0, 1
Let m(j) be the third derivative of -j**7/70 - j**6/10 - 3*j**5/20 + j**4/2 + 2*j**3 - 15*j**2. Factor m(f).
-3*(f - 1)*(f + 1)*(f + 2)**2
Let c(s) = -10*s**4 + 29*s**3 + 4*s**2 - 29*s + 19. Let v(m) = -5*m**4 + 14*m**3 + 2*m**2 - 14*m + 9. Let u(z) = -6*c(z) + 13*v(z). Let u(w) = 0. What is w?
-1, 3/5, 1
Let u(s) be the first derivative of -2*s**3/27 + 4*s**2/9 - 20. Factor u(w).
-2*w*(w - 4)/9
Let m(l) be the second derivative of l**6/10 - 9*l**5/20 - l**4/4 + 3*l**3/2 - 22*l. What is s in m(s) = 0?
-1, 0, 1, 3
Let p(k) be the third derivative of k**8/50400 - k**7/12600 - k**6/900 - 7*k**5/60 - 6*k**2. Let v(q) be the third derivative of p(q). Factor v(j).
2*(j - 2)*(j + 1)/5
Suppose 20 = 7*v + 6. Factor 1/2 - 1/2*h**5 - 1/2*h + h**3 + 1/2*h**4 - h**v.
-(h - 1)**3*(h + 1)**2/2
Let q(d) be the first derivative of -d**4/15 - d**3/5 - d**2/5 - 2*d - 4. Let m(u) be the first derivative of q(u). Let m(a) = 0. What is a?
-1, -1/2
Let b(j) be the first derivative of -j**5/35 + j**3/7 - j**2/7 - 18. Suppose b(p) = 0. What is p?
-2, 0, 1
Let p(l) be the third derivative of l**6/120 - l**5/60 - l**4/6 + 2*l**3/3 - 25*l**2. Factor p(a).
(a - 2)*(a - 1)*(a + 2)
Let g(o) = -142*o**3 + 2*o**2 - 1. Let y be g(1). Let v = y + 712/5. Factor v*p**4 - 1/5 - 8/5*p**3 + 2/5*p + 2/5*p**2 - 2/5*p**5.
-(p - 1)**4*(2*p + 1)/5
Factor 20*y**2 - 18*y - 5*y**3 + 10 - 2*y - 13*y + 8*y.
-5*(y - 2)*(y - 1)**2
Let s(a) = -a**2 + a. Let x be (-9)/3 - (1 + -3). Let y(k) = 5*k**2 - 2*k. Let p(d) = x*y(d) - 4*s(d). Factor p(j).
-j*(j + 2)
Factor 12*f**3 + f**3 + 15*f**2 + 7*f**3 + 5*f**4.
5*f**2*(f + 1)*(f + 3)
Let f(p) = 6*p**2 + 6*p - 2. Let o(a) = 5*a**2 + 5*a - 2. Let z(u) = 4*f(u) - 5*o(u). What is j in z(j) = 0?
-2, 1
Suppose -2/5*c**3 + 8/15*c**5 + 0 - 2/15*c - 2/3*c**4 + 2/3*c**2 = 0. Calculate c.
-1, 0, 1/4, 1
Factor -4/7*c**2 + 5/7*c - 2/7 + 1/7*c**3.
(c - 2)*(c - 1)**2/7
Let k(h) be the third derivative of h**7/15 - 23*h**6/60 + 2*h**5/3 - h**4/3 - 16*h**2. Factor k(r).
2*r*(r - 2)*(r - 1)*(7*r - 2)
Suppose -p**2 + 2*p - 4*p**3 + 2*p + 3*p**2 + 2*p**3 = 0. Calculate p.
-1, 0, 2
Let g(y) be the third derivative of 0*y**4 + 0*y - 1/15*y**3 - 3*y**2 + 1/150*y**5 + 0. Factor g(b).
2*(b - 1)*(b + 1)/5
Suppose 0*x + 8 = 4*x. Let u be (8/1 - 3) + -1. Factor -u*a + a - 1 - a**x + a.
-(a + 1)**2
Let d = -156 + 158. Factor 0*c - 2/9 + 2/9*c**d.
2*(c - 1)*(c + 1)/9
Suppose -2*y = -10, 3*x + 3*y - 51 = -x. Let i be x + -7 + (-1 - -3). Factor 0*s + 2/5*s**i + 0 + 2/5*s**2 + 4/5*s**3.
2*s**2*(s + 1)**2/5
What is z in -28*z**2 - 10*z**3 + 2*z**2 + 6*z**2 - 6*z**2 - 8*z + 8 = 0?
-2, -1, 2/5
Let s be (3/(-5) - -1)*5. Let -7*p**2 - 8*p**2 + 12*p**s = 0. What is p?
0
Suppose -4*b + 20 = 0, 3*i - 12 - 57 = 3*b. Suppose -4*a + i*a**3 + 2*a - 20*a**3 = 0. What is a?
-1/2, 0, 1/2
Let r = -186/7 + 958/35. Find x, given that 0 + 0*x - 2/5*x**4 - 2/5*x**2 + r*x**3 = 0.
0, 1
Let g be (-2 + 4 - 3)*-3. Factor 1 + g*m - m**2 - m + 2*m**2.
(m + 1)**2
Find c, given that 9*c**3 - 2*c**3 - 40*c**3 + 3*c**4 = 0.
0, 11
Let a be 2/(-5) - 3370/(-50). Solve 12*p + 71*p**3 + 4*p**2 + 12*p**2 - a*p**3 = 0 for p.
-3, -1, 0
Let l = 53 + -49. Let b(i) be the third derivative of -1/12*i**l + 2*i**2 + 0*i + 0*i**7 + 0*i**5 + 0*i**3 + 0 + 1/30*i**6 - 1/168*i**8. Factor b(r).
-2*r*(r - 1)**2*(r + 1)**2
Let j(z) be the third derivative of z**6/300 + z**5/150 + 2*z**2. Factor j(a).
2*a**2*(a + 1)/5
Suppose -s - 2 = -4. Suppose -5*y + 3 = 4*v + 1, -4*v = -5*y + 18. Factor 2*j - j**s - y*j.
-j**2
Let i(x) be the second derivative of 0*x**2 + 0 + 0*x**3 - x - 1/20*x**5 + 1/60*x**6 + 1/24*x**4. Suppose i(y) = 0. What is y?
0, 1
Let o(l) be the third derivative of l**6/480 - l**5/120 + l**4/96 + 5*l**2. Suppose o(h) = 0. What is h?
0, 1
Suppose -2*x + b + 9 = 6, -2*x - 2*b - 6 = 0. Let r(n) be the first derivative of 0*n + 1 + 0*n**2 + 1/10*n**5 + 1/8*n**4 + x*n**3. Factor r(t).
t**3*(t + 1)/2
Let u(t) = 2*t**2 - 10*t + 12. Let r(b) = -b + 1. Suppose 3*v - 6 = -42. Let l = 24 - 23. Let z(p) = l*u(p) + v*r(p). Factor z(w).
2*w*(w + 1)
Let 2*i**3 - 8*i**2 + 1 + 3*i**2 + i**5 + 7*i**2 - 3*i - 3*i**4 = 0. What is i?
-1, 1
Let p be (-7 + 17 + 0)/(1 + 1). Let v(w) be the second derivative of 0*w**2 + 0*w**3 + 1/24*w**4 + 0 - 1/60*w**6 - 3*w + 0*w**p. Let v(m) = 0. Calculate m.
-1, 0, 1
Let o(t) = -t**2 + 5*t - 12. Let v(d) = 1. Let w(f) = 3*o(f) + 24*v(f). Factor w(x).
-3*(x - 4)*(x - 1)
Let f(s) be the first derivative of s**4/18 - 16*s**3/27 + 16*s**2/9 + 3. Factor f(k).
2*k*(k - 4)**2/9
Let r(l) = -17*l**3 - 16*l**2 - 29*l - 13. Let g(d) = 4*d**3 + 4*d**2 + 7*d + 3. Let m(i) = 26*g(i) + 6*r(i). Factor m(z).
2*z*(z + 2)**2
Let 3*o**4 + 20*o**3 - 24*o**3 - 2*o**2 - o**4 + 4*o = 0. What is o?
-1, 0, 1, 2
Let y(r) = r**3 - 2*r**2 + 2. Let i be y(2). Suppose 0 = -i*u - 2*u. Let 3/2*l**3 + 1/2*l - 1/2*l**4 - 3/2*l**2 + u = 0. Calculate l.
0, 1
Let f(m) = -4*m - 21. Let u be f(-6). Let g(o) be the first derivative of 0*o + 2 - 1/3*o**u - 1/2*o**2. Factor g(s).
-s*(s + 1)
Let h be ((-2)/(-4))/((-4)/(-16)). Suppose 0 = o - h. Let -2*w**2 + w**o - 6 + 3*w + 4*w**2 = 0. What is w?
-2, 1
Let w(i) be the first derivative of -i**6/120 + i**4/8 - i**3/3 - 2*i**2 - 6. Let d(h) be the second derivative of w(h). Solve d(k) = 0 for k.
-2, 1
Let t(k) = k - 2. Let x(y) = y - 1. Let p be x(5). Let a be t(p). Determine o, given that -2/3*o**a + 0 - 2/3*o**3 + 2/3*o**4 + 2/3*o = 0.
-1, 0, 1
Find o such that 2/5*o + 2/5*o**2 - 4/5 = 0.
-2, 1
Let h(b) be the first derivative of -3*b**4/4 + 2*b**3 + 3*b**2/2 - 6*b - 7. Determine n so that h(n) = 0.
-1, 1, 2
Let x(t) be the second derivative of t**6/1800 + t**5/300 + t**3/6 + 4*t. Let o(s) be the second derivative of x(s). Factor o(p).
p*(p + 2)/5
Suppose -10 + 5*j**2 + j**3 + 9 - 4*j**2 + 0*j**3 - j = 0. Calculate j.
-1, 1
Let b be 0/(-1) - (5 + -7). Find a such that 8*a**b + 0*a**2 + a**2 + 12*a**3 - 3*a = 0.
-1, 0, 1/4
Factor 2*y**5 + 138*y - 4*y**2 + 3*y**4 - 140*y + y**4.
2*y*(y - 1)*(y + 1)**3
Let o be 6/2 + (-7 - (-10 - -1)). Let d(r) be the third derivative of 1/18*r**4 + 0 - 4*r**2 + 0*r**3 + 0*r + 1/90*r**o. Factor d(v).
2*v*(v + 2)/3
Factor 3/5*s**2 - 1/5*s**3 + 1/5*s - 3/5.
-(s - 3)*(s - 1)*(s + 1)/5
Suppose -3*g**5 + 0*g**4 + 27 - 27 + 6*g**3 - 3*g**4 = 0. What is g?
-2, 0, 1
Let a(y) be the third derivative of 0*y**4 - 1/70*y**7 + 1/40*y**6 + 0 + 1/20*y**5 + 0*y - 2*y**2 + 0*y**3 - 1/112*y**8. Factor a(g).
-3*g**2*(g - 1)*(g + 1)**2
Let u(b) be the third derivative of -b**7/280 - b**6/480 + b**5/20 + b**4/24 + 23*b**2. Suppose u(a) = 0. What is a?
-2, -1/3, 0, 2
Let g(x) be the first derivative of -x**4/12 + 5*x**3/9 - 7*x**2/6 + x + 6. Solve g(d) = 0.
1, 3
Let t(r) be the first derivative of -3*r**4/10 - 7*r**3/15 + r/5 - 5. Determine j, given that t(j) = 0.
-1, -1/2, 1/3
Let g(c) = -c**3 - 3*c**2 + c - 12. Let o be g(-4). Suppose 4/9*i**3 + 0*i + 2/9*i**2 + o + 2/9*i**4 = 0. Calculate i.
-1, 0
Let j(x) = -2*x**3 - 25*x**2 + 13*x + 3. Let w be j(-13). Find h such that 0 + 2/5*h**w + 4/5*h**2 + 2/5*h = 0.
-1, 0
Let j(z) be the second derivative of z**6/1440 + z**5/240 + z**4/96 + z**3/3 - 3*z. Let m(n) be the second derivative of j(n). Factor m(