*r = 0. Calculate r.
-1, 1
Let m = 1/9 - -1/9. Factor 0*l + 2/9*l**4 - 2/9*l**2 + 0 - m*l**3 + 2/9*l**5.
2*l**2*(l - 1)*(l + 1)**2/9
Let z(f) be the first derivative of f**3/3 + 4*f**2 + 16*f - 11. Factor z(w).
(w + 4)**2
Let y(z) = -2*z**2 + 20*z + 2. Let o be y(10). Let h be ((-18)/(-24))/((-42)/(-16)). Factor -12/7*c - 18/7 - h*c**o.
-2*(c + 3)**2/7
Let j(p) = 6*p**2 - p. Let h be j(1). Let g be 0 + 5 - (2 + -1). Let -4*q**2 + 2*q**h - g*q**5 - 3*q**4 + 5*q**2 = 0. What is q?
-1, 0, 1/2
Suppose -15 = -7*p - 1. Factor 1/2*w**4 + 1/2*w**p + w**3 + 0 + 0*w.
w**2*(w + 1)**2/2
Let s(c) be the first derivative of 2*c**5/65 + 4*c**4/13 + 32*c**3/39 + 5. Let s(q) = 0. What is q?
-4, 0
Factor 25/4*f**4 + 23/2*f**2 + 15*f**3 + 1/4 + 3*f.
(f + 1)**2*(5*f + 1)**2/4
Suppose -2*t + 3*f + 5 = -2, 3 = t - f. Let j be 0 + (t - (-8)/(-4)). Let 1/2*h**3 + 0*h**2 - 1/4*h + j + 0*h**4 - 1/4*h**5 = 0. What is h?
-1, 0, 1
Let j(l) be the second derivative of -9*l**7/14 - 29*l**6/10 - 99*l**5/20 - 15*l**4/4 - l**3 - 8*l. Find c, given that j(c) = 0.
-1, -2/9, 0
Suppose -16 = -t - 3*v - 1, 5*t - 3*v = 57. Let g be ((-16)/t)/(5/(-3)). Find q, given that 8/5*q**2 - 6/5*q**3 - g + 2/5*q = 0.
-2/3, 1
Let a(v) = -4*v**3 + 14*v**2 + 4*v - 14. Let q(z) = 12*z**3 - 41*z**2 - 12*z + 41. Let g(t) = 17*a(t) + 6*q(t). Factor g(p).
4*(p - 2)*(p - 1)*(p + 1)
Let n(s) be the second derivative of 2*s**6/135 + 2*s**5/45 - s**4/9 + 9*s. What is t in n(t) = 0?
-3, 0, 1
Factor 4/7*x**3 - 2/7*x**4 + 0*x - 2/7*x**5 + 0*x**2 + 0.
-2*x**3*(x - 1)*(x + 2)/7
Let q(l) be the first derivative of l**5/210 - l**4/84 + l**2/2 + 7. Let c(a) be the second derivative of q(a). Determine i, given that c(i) = 0.
0, 1
Suppose 14*k + 3*k**2 - 17*k - 3*k**4 + 3*k**3 + 0*k = 0. What is k?
-1, 0, 1
Suppose 3*p - 2*p - 5 = -2*j, 3*j - 2*p - 18 = 0. Let z = -4 - -7. Factor 2*l - 4*l**2 - 3*l**3 + j*l**z - 2 - 2*l**3 - 7*l.
-(l + 1)**2*(l + 2)
Let b(j) be the first derivative of -j**6/1080 + j**5/60 - j**4/8 - 4*j**3/3 + 3. Let a(s) be the third derivative of b(s). Solve a(t) = 0 for t.
3
Let n(l) be the third derivative of -7*l**6/540 - l**5/135 + 7*l**4/108 + 2*l**3/27 + 26*l**2. Let n(s) = 0. Calculate s.
-1, -2/7, 1
Let r(w) be the first derivative of -w**8/560 + w**7/140 + w**6/120 - w**5/20 + 4*w**3/3 + 2. Let y(n) be the third derivative of r(n). Factor y(f).
-3*f*(f - 2)*(f - 1)*(f + 1)
Let b be 102/44 - (-4 + (-42)/(-11)). Let 0*a - b*a**3 + 0 - a**2 = 0. What is a?
-2/5, 0
Suppose -3*q = -k - 7, -2*q + 4*q + 5*k - 33 = 0. Factor 2/13*t**q + 0*t**2 - 2/13*t**3 + 0*t + 0.
2*t**3*(t - 1)/13
Suppose -5*w - 2*b + 4 = -b, -2*w - 2*b = 0. Let j(h) = h**4 - 2*h**3 - 3*h**2 - 2. Let d(g) = -g**3 + g - 1. Let y(u) = w*j(u) - 2*d(u). Factor y(r).
r*(r - 2)*(r + 1)**2
Let x(c) be the second derivative of -c**6/180 - c**5/45 + c**4/12 - 5*c**2/2 - c. Let g(u) be the first derivative of x(u). Factor g(v).
-2*v*(v - 1)*(v + 3)/3
Let u(h) be the third derivative of -2*h**2 + 0 + 0*h**3 + 1/30*h**5 + 0*h + 1/6*h**4. What is v in u(v) = 0?
-2, 0
Let v be 3 - 3 - 2 - (-1 - 1). Solve 2/7*x**2 - 2/7*x**4 + v*x + 2/7*x**5 - 2/7*x**3 + 0 = 0.
-1, 0, 1
Let d be (-9)/9*(-1 + 1). Let f(o) be the second derivative of 1/135*o**6 + 0*o**2 + 1/27*o**3 - 1/90*o**5 + o + d - 1/54*o**4. Let f(k) = 0. What is k?
-1, 0, 1
Let y be ((-8)/(-30))/((-12)/(-20)). Factor y - 10/9*s - 2/9*s**3 + 8/9*s**2.
-2*(s - 2)*(s - 1)**2/9
Let i be ((-10)/6)/((-7)/21). Let f(m) be the first derivative of -1/24*m**6 - 5/16*m**4 + 1/5*m**i + 2 + 0*m + 0*m**2 + 1/6*m**3. Let f(d) = 0. Calculate d.
0, 1, 2
Suppose 5*h + 0*h = 4*x + 42, 5*x - 40 = -3*h. Let r = -6 + h. Let 1/6 - 2/3*g**3 + 1/6*g**r - 2/3*g + g**2 = 0. Calculate g.
1
Factor 144 + 4*w**2 - 839*w - 3*w**2 + 815*w.
(w - 12)**2
Let x(r) = 1. Let o(c) = 2. Let i(b) = -o(b) + 3*x(b). Let f(s) = 5 + 2*s**2 + 4 - s**2 - 5. Let w(p) = f(p) - 4*i(p). Factor w(z).
z**2
Let k(r) be the second derivative of r**4/36 - r**3/3 - 7*r**2/6 - 2*r. Factor k(x).
(x - 7)*(x + 1)/3
Let u(s) be the third derivative of -7*s**6/360 - s**5/10 + s**4/6 - s**3/2 - s**2. Let l(o) be the first derivative of u(o). Let l(d) = 0. What is d?
-2, 2/7
Let j = -2/909 + 19097/3636. Solve j*i**2 - 15/4*i - 3/2 = 0 for i.
-2/7, 1
Let i(f) be the second derivative of f**4/4 - 2*f**3 + 6*f**2 - 24*f. Factor i(g).
3*(g - 2)**2
Let p(h) = 18*h**3 + 69*h**2 + 87*h + 24. Let b(q) = -19*q**3 - 70*q**2 - 88*q - 24. Let i(f) = 3*b(f) + 4*p(f). Factor i(l).
3*(l + 2)**2*(5*l + 2)
Let x(l) be the third derivative of l**6/30 + l**5/15 - 2*l**4/3 - 8*l**3/3 - 35*l**2. Let x(k) = 0. Calculate k.
-2, -1, 2
Let f(d) be the first derivative of d**7/84 - d**6/60 - d**5/8 + d**4/24 + 2*d**3/3 + d**2 - 3*d - 1. Let h(v) be the first derivative of f(v). Solve h(r) = 0.
-1, 2
Let d(a) = -9*a - 52. Let c be d(-6). Let -2/3*r + 2/3*r**3 - 2/3 + 2/3*r**c = 0. What is r?
-1, 1
Let z = 136 - 948/7. Factor -4/7 - 6/7*v + z*v**2.
2*(v - 2)*(2*v + 1)/7
Let u = -28 + 30. Factor -8/5*r**u + 9/5*r**4 - 6/5*r**3 - 1/5 + 6/5*r.
(r - 1)*(r + 1)*(3*r - 1)**2/5
Let u(q) be the second derivative of q**6/6 + q**5/2 - 5*q**4/3 - 5*q**3/3 + 15*q**2/2 - 2*q. Factor u(g).
5*(g - 1)**2*(g + 1)*(g + 3)
Let s(m) = 10*m**4 - 7*m**3 - 4*m**2 + 4*m - 4. Let w(f) = -21*f**4 + 9 - 9*f + 15*f**3 + 0*f + 5*f**2 + 4*f**2. Let k(g) = -9*s(g) - 4*w(g). Factor k(u).
-3*u**3*(2*u - 1)
Let l(x) = -x**3 - 10*x**2 - 7*x + 9. Let v be l(-9). Let u be (-12)/54 - 2/v. Factor 0 - 2/5*b**5 + 0*b**2 + 2/5*b**3 + 0*b + u*b**4.
-2*b**3*(b - 1)*(b + 1)/5
Suppose -4/9*f**3 + 4/9*f + 2/9*f**4 + 0*f**2 - 2/9 = 0. Calculate f.
-1, 1
Let v(f) = f**4 + f**3 - 1. Let y(c) = -24*c**4 + 70*c**3 + 2*c**2 - 76*c + 22. Let j(q) = 6*v(q) + y(q). Find o, given that j(o) = 0.
-1, 2/9, 1, 4
Let j(f) = 0*f - 4*f**2 - 7*f**2 - 5*f. Let b(u) = -4*u**2 - 2*u. Let o be (-1)/6 + (-170)/60. Let i(q) = o*j(q) + 8*b(q). Suppose i(t) = 0. Calculate t.
0, 1
Let u(v) be the first derivative of -4*v**5/5 + 2*v**4 - 4*v**3/3 + 18. What is c in u(c) = 0?
0, 1
Let i be (-2128)/(-24) - 2/(-6). Let o = 447/5 - i. Factor -4/5 + 6/5*d**2 + o*d.
2*(d + 1)*(3*d - 2)/5
Let k(s) = s**2 - 2*s - s**3 + 2*s**3 - 2*s**4 + 0*s**2. Let f(l) = -l**3 - l**2. Let o(z) = -f(z) + k(z). Determine p so that o(p) = 0.
-1, 0, 1
Let y(a) be the third derivative of -2*a**5/165 + 3*a**4/44 - 2*a**3/33 + 8*a**2. What is z in y(z) = 0?
1/4, 2
What is t in 1/6*t**3 + 0*t + 1/6*t**4 + 0 - 1/6*t**5 - 1/6*t**2 = 0?
-1, 0, 1
Let t(j) be the first derivative of j**4/48 - j**3/4 + 9*j**2/8 - 4*j + 5. Let z(m) be the first derivative of t(m). Determine q, given that z(q) = 0.
3
Determine l so that 16/9 + 28*l**2 - 98/9*l**3 - 40/3*l = 0.
2/7, 2
Let d(y) be the second derivative of 4*y**6/165 + 17*y**5/110 + 10*y**4/33 + 4*y**3/33 + 2*y. Suppose d(x) = 0. Calculate x.
-2, -1/4, 0
Let j = -215/2 + 109. Let x(v) be the first derivative of -9/2*v + j*v**2 + 2 - 1/6*v**3. Determine s so that x(s) = 0.
3
Let o(w) be the second derivative of -1/3*w**3 + 0 - w - 1/10*w**5 + 0*w**2 - 1/3*w**4. Find a, given that o(a) = 0.
-1, 0
Let x(m) be the second derivative of 2/35*m**5 - 13/42*m**4 - 6*m + 11/21*m**3 - 2/7*m**2 + 0. Determine p so that x(p) = 0.
1/4, 1, 2
Suppose -5*c**5 + 11*c**4 - 10*c - 54*c**3 - 35*c**2 - 19*c**4 + 9*c**3 - 17*c**4 = 0. Calculate c.
-2, -1, 0
Find h such that 9*h**2 - 15*h**3 - 18*h**3 + 529*h**4 - 541*h**4 = 0.
-3, 0, 1/4
Let c(n) be the first derivative of 2*n**5 + 6*n**4 + 6*n**3 + 2*n**2 - 4. Factor c(u).
2*u*(u + 1)**2*(5*u + 2)
Let c(p) = -p**3 + 5*p**2 + 5*p + 8. Let o be c(6). Let z be (-20)/(-12) + o/(-3). What is q in -q - 4*q**3 - z + 2*q - q**4 - 6*q**2 - 5*q = 0?
-1
Let s = -3 - -3. Let i(z) = -z. Let t be i(s). Solve -x**2 + 2*x + 4 + 0*x**2 + t*x**2 - x**2 = 0.
-1, 2
Determine v so that 28/9 + 46/9*v + 2/3*v**2 = 0.
-7, -2/3
Let y(u) be the second derivative of -u**4/3 + 8*u**3 - 72*u**2 + 23*u. Factor y(k).
-4*(k - 6)**2
Let l = 193/4 - 547/12. Determine p, given that 0 + 8/3*p - 2/3*p**5 + l*p**2 - 2*p**3 - 8/3*p**4 = 0.
-2, -1, 0, 1
Factor 10/11*y**2 + 8/11 + 2/11*y**3 + 16/11*y.
2*(y + 1)*(y + 2)**2/11
Let w(b) be the first derivative of 1/10*b**2 + 3 + 1/15*b**3 - 1/5*b - 1/20*b**4. Solve w(g) = 0.
-1, 1
Let y(o) be the secon