 = 0.
-2, 0
Let l(p) be the third derivative of 0*p + 0 - 1/36*p**4 + 0*p**5 - 2*p**2 + 1/540*p**6 - 2/27*p**3. Factor l(o).
2*(o - 2)*(o + 1)**2/9
Let z = -54 - -58. Let x(s) be the second derivative of 1/4*s**z - 1/10*s**6 - 1/3*s**3 + 0 - 3*s + 1/10*s**5 + 0*s**2. Let x(d) = 0. What is d?
-1, 0, 2/3, 1
What is g in -g**2 - 19*g + 1 - 17 - 3*g**2 - g = 0?
-4, -1
Let f = -24 - -27. Suppose -2*x - 2*n + 10 = 0, -f*x + 5*n - 19 = -6*x. Solve -x*l**3 + 0 + 0*l**2 + 3/2*l**5 + 3/2*l + 0*l**4 = 0.
-1, 0, 1
Let x(u) be the third derivative of u**6/600 - u**5/150 + u**4/120 + 6*u**2. Factor x(b).
b*(b - 1)**2/5
Let g = 12 - 10. Determine v so that 32 - 9*v + v + 2*v**g + 4*v - 12*v = 0.
4
Let o(b) be the third derivative of -b**7/210 + b**5/20 + b**4/12 + 19*b**2. Let o(t) = 0. Calculate t.
-1, 0, 2
Let p(q) be the third derivative of 3*q**6/160 + q**5/80 - q**4/12 - q**3/6 - 6*q**2. Factor p(w).
(w - 1)*(3*w + 2)**2/4
Let m(z) be the third derivative of -z**7/385 - z**6/132 - z**5/165 - z**2. What is i in m(i) = 0?
-1, -2/3, 0
Let p be -1*5/((-20)/8). Let f be -8*p/(-8)*1. Let 2/7*j**3 + 0 + 2/7*j + 4/7*j**f = 0. What is j?
-1, 0
Let w(d) = 5*d**2 + 33*d + 48. Let n(l) = 5*l**2 + 32*l + 47. Let r(m) = 3*n(m) - 2*w(m). Determine g so that r(g) = 0.
-3
Let v(p) be the second derivative of p**5/60 + p**4/8 + p**3/3 + p**2/2 + 2*p. Let q(b) be the first derivative of v(b). Suppose q(a) = 0. What is a?
-2, -1
Let f(u) be the second derivative of u**4/16 - 3*u**2/2 - 2*u. Find y such that f(y) = 0.
-2, 2
Let q(l) be the third derivative of 6*l**2 + 13/20*l**5 - 3/2*l**6 + 0*l**3 - 1/8*l**4 + 0*l - 4/7*l**8 + 8/5*l**7 + 0. Let q(m) = 0. Calculate m.
0, 1/4, 1
Let s be (-10)/(-12) - (-36)/54. Factor 3/4*z**5 + 0*z**3 + 0 - 3/4*z + s*z**2 - 3/2*z**4.
3*z*(z - 1)**3*(z + 1)/4
Let g(f) = 4*f**4 + 13*f**3 - 44*f**2 + 21*f - 3. Let z(v) = -v**3 - v - 1. Let b(a) = g(a) - 3*z(a). Determine o so that b(o) = 0.
-6, 0, 1
Let r(c) = -4*c + 6. Let t be r(1). Factor -2/7 - 2/7*h**3 + 2/7*h**t + 2/7*h.
-2*(h - 1)**2*(h + 1)/7
Let i(l) be the first derivative of 49/9*l**6 + 235/6*l**4 + 40/3*l**2 + 290/9*l**3 + 8/3*l + 6 + 70/3*l**5. Factor i(p).
2*(p + 1)**3*(7*p + 2)**2/3
Let g = 270 + -270. Solve g*h**2 - 2/3*h**4 - 4/3*h**3 + 0*h + 0 = 0 for h.
-2, 0
Let p = 71/205 - 6/41. Find f, given that p*f**2 - 3/5*f + 3/5*f**3 + 1/5*f**4 - 2/5 = 0.
-2, -1, 1
Suppose -3*t - 2*d + 81 = -5*d, -4*d = 0. Let -v + t*v**2 + 38*v**4 + 10*v**4 + 4*v + 72*v**3 = 0. Calculate v.
-1, -1/4, 0
Let t be 2/8 - 10/4 - -3. Factor -d**2 + t*d + 0 + 1/4*d**3.
d*(d - 3)*(d - 1)/4
Let w = 2/1209 + 16916/6045. Let v = -328/15 + 68/3. Factor w*k**2 - 8/5*k**3 - 2/5 - v*k.
-2*(k - 1)**2*(4*k + 1)/5
Let x(h) be the third derivative of 1/60*h**5 + 0 + 3*h**2 + 1/6*h**3 + 1/12*h**4 + 0*h. Factor x(s).
(s + 1)**2
Let y(r) be the second derivative of -r - 1/20*r**4 + 2/5*r**2 + 1/50*r**5 + 1/150*r**6 - 2/15*r**3 + 0. Factor y(n).
(n - 1)**2*(n + 2)**2/5
Let v(d) be the first derivative of 7*d**6/6 - 19*d**5/5 + 15*d**4/4 - d**3/3 - d**2 - 4. Factor v(x).
x*(x - 1)**3*(7*x + 2)
Factor 0*y**3 - 63*y**2 + 68*y**2 + 5*y**3.
5*y**2*(y + 1)
Let y(k) be the first derivative of -2*k**3/3 + 2*k**2 - 17. Let y(l) = 0. Calculate l.
0, 2
Let q(y) be the first derivative of -4/5*y**5 + 8*y**2 - y**4 + 0*y + 16/3*y**3 + 6. Determine o, given that q(o) = 0.
-2, -1, 0, 2
Let -18/5*c**2 + 96/5*c - 96/5*c**3 + 42/5*c**4 - 24/5 = 0. What is c?
-1, 2/7, 1, 2
Let p(u) = 7*u**2 + 13*u + 13. Suppose -5*y - 1 = 4*k + 18, -17 = 4*y + 5*k. Let z(w) = 8*w**2 + 12*w + 12. Let m(i) = y*z(i) + 4*p(i). Factor m(d).
4*(d + 2)**2
Let c(k) be the first derivative of -k**7/360 + 2*k**6/135 - 11*k**5/360 + k**4/36 + k**3/3 - 1. Let i(y) be the third derivative of c(y). Factor i(v).
-(v - 1)**2*(7*v - 2)/3
Let q = -61 - -185/3. Solve 2/3*p**3 + 0 - 4/3*p**2 + q*p = 0 for p.
0, 1
Let f(a) = -3*a - 6. Let p be f(-4). Suppose -5*i**2 - p + 2 + 8*i**2 + 0 - 4*i = 0. What is i?
-2/3, 2
Let v(k) be the second derivative of -k**4/6 + 2*k**3/3 + 35*k. Find t such that v(t) = 0.
0, 2
Let k(p) be the second derivative of -p**5/20 - p**4/3 - p**3/2 - 5*p + 7. Suppose k(m) = 0. Calculate m.
-3, -1, 0
Let m(b) = 8*b**5 - 2*b**4 - 10*b**3 - 2*b**2 - 4*b - 8. Let f(t) = -17*t**5 + 4*t**4 + 21*t**3 + 5*t**2 + 9*t + 17. Let i(r) = 6*f(r) + 13*m(r). Factor i(j).
2*(j - 1)**3*(j + 1)**2
Let i(x) be the second derivative of x**7/14 + x**6/2 + 27*x**5/20 + 7*x**4/4 + x**3 - 5*x. Factor i(n).
3*n*(n + 1)**3*(n + 2)
Suppose 0 = 3*i + y - 4, -4*y - 6 - 6 = -2*i. Suppose 0 + 2/5*j + 1/5*j**i = 0. What is j?
-2, 0
Let d(b) be the first derivative of -b**5/30 + b**4/6 - 5*b**3/18 + b**2/6 - 60. Solve d(u) = 0.
0, 1, 2
Let t(h) be the third derivative of h**8/2016 + h**7/1260 - h**6/720 - h**5/360 + 6*h**2. Factor t(w).
w**2*(w - 1)*(w + 1)**2/6
Suppose 12 = 3*c - 3. Suppose k = -4*p + 26, -4*k + 71 = c*p - 11. Let -10 + 14*i**3 + 4*i + 10 - k*i**2 = 0. Calculate i.
0, 2/7, 1
Let a be 1/(-5) - (-46)/5. Suppose 3 = -3*q + a. Factor -2/7*n**q - 2/7 + 4/7*n.
-2*(n - 1)**2/7
Suppose -2*l + 59 = -2*j + 15, 0 = 5*l + j - 92. Factor -14*f**3 - 12*f**2 + 18*f + 35*f**3 - l*f**3.
2*f*(f - 3)**2
Let k be 1*(5 - (5 + -4)). Let z(q) be the third derivative of 0*q**3 + 0 - 1/30*q**5 - 1/60*q**6 + 0*q**k - q**2 + 0*q. Factor z(m).
-2*m**2*(m + 1)
Factor 2/7*w**2 + 4/21*w + 0*w**3 - 2/21*w**4 + 0.
-2*w*(w - 2)*(w + 1)**2/21
Let n(o) = 10*o**2 - 4*o - 6. Suppose -2 - 26 = 4*d. Let c(j) = 3*j**2 - j - 2. Let w(h) = d*c(h) + 2*n(h). Suppose w(v) = 0. Calculate v.
-2, 1
Find c such that 6/5*c**2 + 3/5*c - 6/5*c**3 - 3/5 + 3/5*c**5 - 3/5*c**4 = 0.
-1, 1
Suppose 2*k - 4 = -0. Let l be (15/35)/(3/k). Let -6/7*c - 6/7*c**4 + 4/7*c**3 + 4/7*c**2 + l + 2/7*c**5 = 0. Calculate c.
-1, 1
Let m(a) = a**2 - 7*a + 6. Let f be m(6). Factor -4*c**4 - c**5 + c - 2*c**4 + 2*c**2 + 4*c**4 + f*c**4.
-c*(c - 1)*(c + 1)**3
Suppose 0 = u + 1, -12*k + 13 = -8*k - 5*u. Factor 1/3*d**k - 1/3*d**4 + 0 - 2/3*d + 2/3*d**3.
-d*(d - 2)*(d - 1)*(d + 1)/3
Let g be (-4)/5*(-60)/24. Factor 0*b + 2 + 2*b**2 + 8*b**3 - 10*b + 2*b**5 - 8*b**4 + 2 + g*b**2.
2*(b - 2)*(b - 1)**3*(b + 1)
Let j be 4/6*(20 - 2). Determine q so that 2 - 2*q**2 - j*q + 8*q**2 + 4*q = 0.
1/3, 1
Let d = -18 - -3. Let i be ((-24)/d)/(9/5). Factor -i - 2/9*w**2 - 8/9*w.
-2*(w + 2)**2/9
Let g be -6 - -23 - (-9)/6. Let x = g + -18. Determine p, given that 1/2*p**2 - p + x = 0.
1
Let f(d) be the first derivative of 1/6*d**3 + 0*d - 1/12*d**4 + 1 - d**2 + 1/60*d**5. Let s(i) be the second derivative of f(i). Factor s(q).
(q - 1)**2
Let n(v) be the third derivative of -v**6/10 - 2*v**5/3 - 3*v**4/2 - 4*v**3/3 - 16*v**2. Solve n(t) = 0 for t.
-2, -1, -1/3
Let h(b) = b + 4. Let c be h(0). Factor 3 - 2*j + c*j**2 - 4*j**2 - j - 6*j**2.
-3*(j + 1)*(2*j - 1)
Let 3*f**3 - 5*f**2 - 11*f**3 + 2*f**3 - 14*f**3 = 0. Calculate f.
-1/4, 0
Let x be (-4)/(-15)*15/6. Let t be (-24)/(-18) + 4/(-6). Factor -t*o + x*o**2 + 0.
2*o*(o - 1)/3
Let q(v) be the first derivative of -4*v**5/5 - 9*v**4/2 - 20*v**3/3 - 3*v**2 + 18. Factor q(o).
-2*o*(o + 1)*(o + 3)*(2*o + 1)
Determine l so that -24*l**3 + 28*l - 22*l**2 + 18*l**2 - 8 + 12*l**4 - 4*l**3 = 0.
-1, 1/3, 1, 2
Factor 494*y**2 + 4 + 11 + 335*y**2 + 625*y**4 - 1350*y**3 - 11 - 108*y.
(y - 1)**2*(25*y - 2)**2
Factor -2/3*d**2 - 2 - 8/3*d.
-2*(d + 1)*(d + 3)/3
Let x be (-2)/10*-5 + -1. Let w(b) be the second derivative of 0 - 1/6*b**4 + x*b**2 - 2*b + 0*b**5 + 0*b**3 + 1/15*b**6. Find j, given that w(j) = 0.
-1, 0, 1
Factor 3/4*r + 1/2*r**2 - r**3 - 1/2 + 1/4*r**5 + 0*r**4.
(r - 1)**3*(r + 1)*(r + 2)/4
Let g(w) be the second derivative of -3*w - 9/5*w**5 + 1/4*w**4 + 6*w**2 + 0 + 6*w**3 - 1/2*w**6. Let g(m) = 0. Calculate m.
-2, -1, -2/5, 1
Determine r, given that -2/7*r**4 - 4/7*r**2 - 6/7*r**3 + 0 + 0*r = 0.
-2, -1, 0
Let o(f) be the first derivative of f**7/840 - f**5/40 - f**4/12 - 2*f**3/3 - 1. Let m(v) be the third derivative of o(v). Solve m(s) = 0 for s.
-1, 2
Let x be -1*(-3 - -2) + 18. Let q = x + -15. Factor 4/5*s**2 - 2/5 + 0*s**3 - 2/5*s**q + 0*s.
-2*(s - 1)**2*(s + 1)**2/5
Factor -1/6*t + 0 - t**3 - 1/6*t**5 + 2/3*t**4 + 2/3*t**2.
-t*(t - 1)**4/6
Let n(w) = -4*w + w - 2 + 5*w. Let t be n(4). Factor -2*r**3 