/3*j - 1/3*j**5 - 4/3*j**2 + 0.
-j*(j + 1)**4/3
Let o(t) be the second derivative of -1/10*t**4 - 2*t + 0*t**3 + 0 + 9/100*t**5 - 1/50*t**6 + 0*t**2. Factor o(w).
-3*w**2*(w - 2)*(w - 1)/5
Let p(k) be the first derivative of k**6/9 - k**5/3 - k**4/12 + 7*k**3/9 - k**2/6 - 2*k/3 - 8. Suppose p(j) = 0. Calculate j.
-1, -1/2, 1, 2
Let c(y) = 20*y**2 + 28*y + 8. Let l(d) = 8*d**2 + 11*d + 3. Let p(a) = -5*c(a) + 12*l(a). Factor p(h).
-4*(h + 1)**2
Suppose -1 + 1 = 4*j. What is n in 0 + 0*n**2 + 0*n**3 + 3/5*n**5 + 3/5*n**4 + j*n = 0?
-1, 0
Suppose -2/7*y**2 + 16/7*y - 32/7 = 0. What is y?
4
Let g(h) be the second derivative of -3/80*h**5 - 5/48*h**4 + 0*h**2 + 0 + 1/12*h**3 - 5*h. Determine c, given that g(c) = 0.
-2, 0, 1/3
Let 4/5 - 4/5*u**2 + 0*u = 0. Calculate u.
-1, 1
Let w be (-3)/3 + (-258)/(-140). Let l = w + 5/14. Factor 2/5*g**4 + 0 + l*g**2 - 6/5*g**3 - 2/5*g.
2*g*(g - 1)**3/5
Let o be (-1 - 0)/(2/4). Let m(l) = 2*l**3 + 2*l. Suppose 3 + 12 = 3*a. Let w(v) = 4*v**3 - v**2 + 5*v. Let p(b) = a*m(b) + o*w(b). Factor p(f).
2*f**2*(f + 1)
Let c(q) be the second derivative of 0*q**2 + 0*q**3 + 0*q**4 - 3*q + 0 + 0*q**5 + 1/60*q**6 - 1/84*q**7. Factor c(l).
-l**4*(l - 1)/2
Let l be -2 - ((-21)/5 - -2). Let q be (-3)/7 - (-5)/(350/240). Suppose l*k**q - 1/5*k**4 + 0 - 1/5*k**5 + 0*k + 1/5*k**2 = 0. What is k?
-1, 0, 1
Let i(k) be the first derivative of 0*k + 1/15*k**3 + 1 - 1/25*k**5 - 1/10*k**4 + 1/5*k**2. Factor i(v).
-v*(v - 1)*(v + 1)*(v + 2)/5
Solve 4*o**2 + o**2 - o**2 - 4 = 0 for o.
-1, 1
Suppose -3*f + 2*f = 0. Suppose -3*b + 5*c + 16 = f, -3 = 2*b + 5*c + 3. Factor 2/3*k**3 + 0*k**b + 0 + 2/3*k**5 + 0*k + 4/3*k**4.
2*k**3*(k + 1)**2/3
Suppose -5*y + 5 = 0, y = d - 4*y + 2. Factor -12*c**2 - 15*c**4 - c**d + 4*c**5 + 25*c**3 + 4*c**5 - 5*c**5.
3*c**2*(c - 2)**2*(c - 1)
Let o(l) be the first derivative of 5*l**3/3 + 15*l**2/2 + 10*l - 5. Let o(s) = 0. Calculate s.
-2, -1
Let i(s) = -s**2 - s + 3. Let r(c) = 8*c**2 + 4*c - 9. Let h(y) = 17*y**2 + 8*y - 17. Let o(m) = 4*h(m) - 9*r(m). Let a(b) = 26*i(b) - 6*o(b). Solve a(v) = 0.
-1, 0
Suppose 2*i - 6*i - 4*q - 12 = 0, -q = 3*i - 1. Solve 30*x**5 + 9*x**3 + 8*x - 35*x**3 + 23*x**4 - 16*x**i + 5*x**4 = 0 for x.
-1, 0, 2/5, 2/3
Factor -1/4 - 1/4*s**2 + 1/2*s.
-(s - 1)**2/4
Let j(u) = u**2 - u. Let x(s) = 4*s**2 - s - 4. Let d(i) = -15*j(i) + 3*x(i). Suppose d(r) = 0. What is r?
2
Let x(j) = -j**3 - 9*j + 1. Let u = -13 + 10. Let r(t) = -2*t**3 - 10*t. Let a(z) = u*r(z) + 4*x(z). Factor a(b).
2*(b - 1)**2*(b + 2)
Let k be (0 + (-10)/4)*20. Let a be k/8*(-4)/10. Solve 1/2*n**3 - 1/2*n - 6*n**5 + 0 + a*n**2 - 17/2*n**4 = 0.
-1, 0, 1/4, 1/3
Let u(m) be the second derivative of 2/3*m**3 + 5*m - 5/6*m**4 + 0 + 0*m**2. Factor u(k).
-2*k*(5*k - 2)
Suppose -4*k + 2*k = -4. Solve -54*r**3 - r**5 - 8*r**4 - 2*r**5 + 60*r**3 + 24*r**k + 21*r + 6 + 2*r**4 = 0.
-1, 2
Let h(b) = -7*b**2 - 18*b + 12. Let p(z) = 3*z**2 + 9*z - 6. Let k(g) = -6*h(g) - 13*p(g). Determine a so that k(a) = 0.
1, 2
Let g(n) = -n**3 - 6*n**2 + 6*n - 7. Let q be g(-7). Factor 2/3*x**3 + x**2 + q + 1/3*x.
x*(x + 1)*(2*x + 1)/3
Let v(a) be the first derivative of -2*a**3/27 + 2*a**2/9 - 6. Determine q, given that v(q) = 0.
0, 2
Suppose -4 = 3*r + 5*q, 0*r + 4*r - 16 = 4*q. Factor 2*y + 3*y**r - y**2 - 1 - 3*y**2.
-(y - 1)**2
Suppose 26 = -2*q + 34. Solve -3/4*f**2 + 0 - 3/4*f**3 - 1/4*f**q - 1/4*f = 0.
-1, 0
Let b = 279 - 1947/7. Suppose 0 - b*a - 2/7*a**2 = 0. Calculate a.
-3, 0
Let r be 2/10 - 3/(-15)*-1. Suppose 4*t - h = h + 8, -3*t = -4*h - 6. Factor -2/9*s**5 + r*s**3 + 2/9*s + 0 - 4/9*s**t + 4/9*s**4.
-2*s*(s - 1)**3*(s + 1)/9
Let w(d) be the first derivative of -d**5/30 + d**4/12 - 2*d**2 - 3. Let t(n) be the second derivative of w(n). What is h in t(h) = 0?
0, 1
Let f(v) = -v + 2. Let c be f(0). Factor 5 + c*q**3 + 6*q - 5*q**2 + 11*q**2 - 3.
2*(q + 1)**3
Let d = 23 - 68/3. Factor 1/6 + d*x + 1/6*x**2.
(x + 1)**2/6
Let m(p) be the second derivative of p**4/72 - p**3/18 + p**2/12 + 8*p. Factor m(j).
(j - 1)**2/6
Let f(t) be the third derivative of t**5/450 + t**4/45 + 24*t**2. Determine l so that f(l) = 0.
-4, 0
Let p(z) be the third derivative of -z**7/490 - z**6/140 + z**4/28 + z**3/14 - 2*z**2. Factor p(h).
-3*(h - 1)*(h + 1)**3/7
Factor -1/2*d**3 + 0 + 0*d - d**2.
-d**2*(d + 2)/2
Find k such that -3/2*k**3 - 1/4*k**4 + 1/4*k**5 - 1/2*k**2 + 5/4*k + 3/4 = 0.
-1, 1, 3
Let z(u) = 3*u**2 - 5*u - 6. Let c(a) = 1. Let m(v) = 21*v**2 - 36*v - 51. Let l(p) = 9*c(p) + m(p). Let q(i) = -2*l(i) + 15*z(i). Find s, given that q(s) = 0.
-1, 2
Let l(j) = 3*j**2 + 3*j - 3. Let k(w) = -3*w**2 - 4*w + 3. Let f(s) = 3*k(s) + 4*l(s). Determine u so that f(u) = 0.
-1, 1
Let h = 144 + -569/4. Let z(v) be the first derivative of 0*v + 1 + 0*v**2 - 9/5*v**5 + 2/3*v**3 - h*v**4. Factor z(k).
-k**2*(k + 1)*(9*k - 2)
Let o be 1 + 7 + -85 + 79. Factor -6*y - 3/2*y**o - 9/2.
-3*(y + 1)*(y + 3)/2
Let x(j) be the first derivative of j**7/1050 - j**6/300 + j**5/300 - j**2/2 + 1. Let h(q) be the second derivative of x(q). Suppose h(s) = 0. Calculate s.
0, 1
Let t(l) be the third derivative of l**7/35 - 4*l**6/15 + 17*l**5/30 - l**4/3 - 14*l**2 - 2*l. Factor t(h).
2*h*(h - 4)*(h - 1)*(3*h - 1)
Let f(q) be the second derivative of q**6/30 - q**5/20 - q**4/12 + q**3/6 - 6*q. Suppose f(u) = 0. What is u?
-1, 0, 1
Let g(q) be the third derivative of q**7/1155 - q**6/660 - q**5/330 + q**4/132 - 4*q**2. Factor g(r).
2*r*(r - 1)**2*(r + 1)/11
Let v(s) = s**5 + s**4 - s**3 - s**2. Let p(i) = -5*i**5 - 4*i**4 + 4*i**3 + 2*i**2 + i + 2. Let w(n) = p(n) + 6*v(n). Solve w(a) = 0 for a.
-2, -1, 1
Factor 0 - 1/6*t**4 + 0*t + 1/6*t**2 + 0*t**3.
-t**2*(t - 1)*(t + 1)/6
Let x(b) be the first derivative of -b**4/12 + 2*b - 2. Let f(j) be the first derivative of x(j). What is a in f(a) = 0?
0
Let p(w) be the first derivative of 2*w**3/21 - 8*w**2/7 - 18*w/7 - 53. Suppose p(n) = 0. What is n?
-1, 9
Suppose 5*v + 2*s - 8 = -0*v, 0 = -v - 2*s + 8. Find i such that -3/5*i**3 - 12/5*i**2 - 12/5*i + v = 0.
-2, 0
Suppose 0 = 9*n - 4*n + 4*n. Let v(f) be the second derivative of -1/12*f**4 + n + f**2 + 1/6*f**3 - 3*f. Factor v(g).
-(g - 2)*(g + 1)
Let i = 1 + 2. What is c in -c**3 - 3*c**4 + 3*c**2 + 2*c**5 - c**i + c**5 - c**3 = 0?
-1, 0, 1
Let l be 6/161*(0 - 10). Let x = -2/23 - l. Factor x*z + 6/7*z**3 + 2/7 - 10/7*z**2.
2*(z - 1)**2*(3*z + 1)/7
Let l(s) be the first derivative of 0*s**2 + 0*s**3 - 2*s + 1 - 1/10*s**5 - 4/75*s**6 - 1/30*s**4. Let c(k) be the first derivative of l(k). Factor c(u).
-2*u**2*(u + 1)*(4*u + 1)/5
Let a be 4*((-36)/56)/(-9). Let t be 3/7*6 + -2. What is y in a*y**2 + 2/7 - t*y = 0?
1
Let x(i) be the first derivative of 2 - 1/18*i**4 + 2/27*i**3 + 0*i**2 - 2/45*i**5 + 0*i + 1/27*i**6. Suppose x(l) = 0. Calculate l.
-1, 0, 1
Let b(x) = -x + 7. Suppose -5*r = -2*r + 15. Let l be b(r). Factor -k - 2*k**2 + 7*k**5 + k + l*k**4 + 3*k**3.
k**2*(k + 1)**2*(7*k - 2)
Let z(t) = 3*t**3 - 9*t**2 + 17*t + 17. Let v(u) = -u**3 + 3*u**2 - 6*u - 6. Let i(c) = -17*v(c) - 6*z(c). Suppose i(m) = 0. Calculate m.
0, 3
Let n(r) be the third derivative of r**5/240 - r**4/48 + 2*r**2. Solve n(u) = 0.
0, 2
Suppose -2*n - 4*f = -7*n + 19, -2*n + 4*f = -10. Let q(o) be the first derivative of -1/14*o**4 + 0*o**2 + 2/35*o**5 - 2 + 0*o + 0*o**n. Factor q(z).
2*z**3*(z - 1)/7
Let k(d) = -d**5 - 5*d**4 + 6*d**3 - 6*d + 6. Let l(h) = h**5 + 10*h**4 - 11*h**3 + 11*h - 11. Let w(s) = 11*k(s) + 6*l(s). Find v, given that w(v) = 0.
0, 1
Let j(d) be the second derivative of -9*d**5/80 - d**4 - 15*d**3/8 + 27*d**2/4 - 7*d. Factor j(o).
-3*(o + 3)**2*(3*o - 2)/4
Let x(k) be the first derivative of k**4/12 + 4*k**3/9 + 2*k**2/3 + 3. Determine z, given that x(z) = 0.
-2, 0
Let a = 17 - 33/2. Suppose 0 + 20 = 5*j. Suppose -1/2*p**5 + 0 + 1/2*p**3 - 1/2*p**2 + 0*p + a*p**j = 0. What is p?
-1, 0, 1
Let z(y) be the first derivative of y**6/10 + 9*y**5/20 + y**4/4 - 3*y**3/2 - 3*y**2 + 4*y - 3. Let n(j) be the first derivative of z(j). Factor n(c).
3*(c - 1)*(c + 1)**2*(c + 2)
Let v(h) be the third derivative of -h**8/336 - h**7/35 - h**6/10 - h**5/6 - h**4/8 - 24*h**2. Factor v(s).
-s*(s + 1)**3*(s + 3)
Let p(c) be the first derivative of 0*c + 0*c**2 - 2 + 2/9*c**3. Let p(l) = 0. What is l