 of -5*g - 1/20*g**5 + 0*g**2 + 1/36*g**4 + 1/6*g**3 + 1 - 1/90*g**6. Let a(d) be the first derivative of x(d). Factor a(f).
-f*(f - 1)*(f + 1)*(f + 3)/3
Suppose 2*z - 21*u = -25*u, 3*u = 3*z - 9. Factor 75/4 + 3/4*l**z - 15/2*l.
3*(l - 5)**2/4
Let t(m) be the second derivative of -2*m**7/21 + 4*m**6/5 - 12*m**5/5 + 10*m**4/3 - 2*m**3 - 2*m - 19. Determine u, given that t(u) = 0.
0, 1, 3
Determine k, given that -5/4*k + 1/2*k**3 - 3/2*k**2 + 7/4*k**4 + 3/4*k**5 - 1/4 = 0.
-1, -1/3, 1
Let r = -5822657/314 + 18545. Let u = r - 1/157. Factor 0 + 3/4*c**2 + u*c.
3*c*(c + 2)/4
Let z(l) be the first derivative of 128/9*l + 2/45*l**5 + 13/18*l**4 + 40/9*l**3 - 10 + 112/9*l**2. Find v such that z(v) = 0.
-4, -1
Suppose 8*a - 33*a = 0. Let y(s) be the third derivative of 8/15*s**3 - 1/75*s**5 + 0 - 1/300*s**6 + 1/15*s**4 + 2*s**2 + a*s. Factor y(b).
-2*(b - 2)*(b + 2)**2/5
Solve 9*f**3 - 13*f**3 + 264 + 193*f - 71*f**2 - 57*f**2 - 53*f = 0 for f.
-33, -1, 2
Let u = -22860/7 - -3266. Factor 0*d - 2/7*d**2 - u*d**3 + 2/7*d**4 + 2/7*d**5 + 0.
2*d**2*(d - 1)*(d + 1)**2/7
Let g(y) = y**2 - y - 1. Let c be g(-2). Suppose -c*d + 8 = -2. Suppose f**d - f**2 + 3 + 3*f**2 - 7*f + f = 0. Calculate f.
1
Let i(f) = 3*f**3 - 7*f**2 - f + 7. Let b be 11 + (4 - 0/5). Let t(d) = 2*d**2 - d**2 - b*d + 16*d + 3 - 4. Let l(s) = i(s) - 2*t(s). Factor l(w).
3*(w - 3)*(w - 1)*(w + 1)
What is s in 2/9*s**2 - 2/9*s**4 + 0 + 2/9*s**3 - 2/9*s = 0?
-1, 0, 1
Let m = -6667/930 + 1/465. Let y = -7 - m. Factor 0 + 1/2*a**2 - y*a.
a*(3*a - 1)/6
Let q(s) be the first derivative of s**6/30 - 2*s**5/25 + 2*s**3/15 - s**2/10 + 1. Factor q(m).
m*(m - 1)**3*(m + 1)/5
Let l(d) be the first derivative of 98*d**5/15 + 21*d**4 + 40*d**3/3 + 8*d**2/3 - 202. Determine c so that l(c) = 0.
-2, -2/7, 0
Let b = -45 - -50. Suppose b*j - 54 = -39. Find w such that 0*w**2 + 0 + 0*w - 2/3*w**j = 0.
0
Suppose 4*w = 84 - 0. Let m(y) = -9*y**4 + 21*y**3 + 30*y**2 + 21*y + 21. Let g(i) = -i**4 + 2*i**3 + 3*i**2 + 2*i + 2. Let n(j) = w*g(j) - 2*m(j). Factor n(h).
-3*h**2*(h - 1)*(h + 1)
Suppose 4*r - 8*r + 64 = 0. Suppose -r*a**2 - 19*a + 0*a**3 + 3*a - a**3 - 3*a**3 = 0. What is a?
-2, 0
Let n(m) = 2*m**2 + 11*m. Let w(i) = -6*i - i**2 - 216 + 216. Let f(g) = -6*n(g) - 11*w(g). Factor f(h).
-h**2
Let v(c) = c**2 - 2*c + 1. Let w(p) = p**2 + p - 2. Let b(i) = 4*v(i) - w(i). Find n such that b(n) = 0.
1, 2
Let c(t) be the first derivative of -1/5*t**4 - 6/25*t**5 + 2/5*t**2 - 12 - 2/5*t + 8/15*t**3. Solve c(u) = 0.
-1, 1/3, 1
Let z(q) be the third derivative of q**8/168 + 4*q**7/105 + q**6/30 - 2*q**5/15 - q**4/4 - 24*q**2 + 5. Factor z(v).
2*v*(v - 1)*(v + 1)**2*(v + 3)
Let m(k) be the first derivative of 4*k**3/15 - 126*k**2/5 - 256*k/5 + 227. Factor m(h).
4*(h - 64)*(h + 1)/5
Let t(w) = 2*w - 14. Let h be t(8). Factor 117*u**2 + 0*u**3 - u - 116*u**h + u**3 - 1.
(u - 1)*(u + 1)**2
Let q(d) be the third derivative of -1/360*d**6 + 1/18*d**3 + 0*d + 0 - 6*d**2 + 1/72*d**4 - 1/180*d**5. Factor q(k).
-(k - 1)*(k + 1)**2/3
Let g(x) = -x**3 - 2*x**2 + 1. Let k(z) = -7*z**3 + 46*z**2 + 56*z + 3. Let o(r) = -3*g(r) + k(r). Determine l so that o(l) = 0.
-1, 0, 14
Let k(t) = 2*t - 2. Let u(a) = -1. Let g(h) = -k(h) + u(h). Let r be g(-2). Factor -2*s**4 + s**r + s**3 + 0*s**3 + 0*s**5.
s**3*(s - 1)**2
What is o in 17/4*o**3 - 45/4*o**2 + 43/4*o - 1/4*o**4 - 7/2 = 0?
1, 14
Factor -596/5 + 2/5*h**2 + 294/5*h.
2*(h - 2)*(h + 149)/5
Factor 3/7*b**3 - 30/7 - 3*b + 12/7*b**2.
3*(b - 2)*(b + 1)*(b + 5)/7
Let s(t) be the third derivative of -t**7/525 - t**6/300 + t**5/150 + t**4/60 - 374*t**2. Factor s(f).
-2*f*(f - 1)*(f + 1)**2/5
Let d be (27/(-4))/((-2)/(-8)). Let z be 3/(-2)*18/d - -1. Factor -6/5*p**z + 6/5*p**3 + 9/5*p**4 - 9/5*p + 3/5*p**5 - 3/5.
3*(p - 1)*(p + 1)**4/5
Suppose -5*o = -16*o + 13640. Suppose -1228*l**2 + 0*l + 8*l + 4*l**3 + o*l**2 = 0. Calculate l.
-2, -1, 0
Let o(f) be the first derivative of -3 - 1/20*f**4 + 3*f - 1/5*f**2 + 1/100*f**5 + 1/150*f**6 - 1/6*f**3. Let s(a) be the first derivative of o(a). Factor s(z).
(z - 2)*(z + 1)**3/5
Let b be 25/(-10)*60/(-50). Let d(s) be the second derivative of 1/6*s**4 + 5*s - s**b + 0 + 2*s**2. Factor d(n).
2*(n - 2)*(n - 1)
Suppose 0 = -3*r + 4*r + 26. Let w be (-1)/(r/6 + (-2)/(-1)). Factor 6/7 + 12/7*b**2 - 15/7*b - w*b**3.
-3*(b - 2)*(b - 1)**2/7
Let q(i) = i**3 + 8*i**2 + 13*i - 8. Let m be q(-5). Suppose 21 = 5*a - 3*z, -2*z = -1 + 5. Factor n**m - n**3 - n + a*n - 1 - n.
-(n - 1)**2*(n + 1)
Let u(b) be the third derivative of 1/3*b**4 - 2/5*b**6 + 0*b - 1/5*b**5 - 2/15*b**7 + 0*b**3 - 10*b**2 + 0. Factor u(l).
-4*l*(l + 1)**2*(7*l - 2)
Let j(k) = -k**3. Suppose 3*w - 4*t - 26 = -2*t, 0 = 2*t - 4. Let q(f) = -5*f**4 - 25*f**3 - 10*f**2. Let y(h) = w*j(h) - q(h). Solve y(l) = 0.
-2, -1, 0
Let x(j) be the second derivative of j**7/1155 + j**6/660 - j**5/330 - j**4/132 + 15*j**2/2 + 21*j. Let m(h) be the first derivative of x(h). Factor m(c).
2*c*(c - 1)*(c + 1)**2/11
Let w(n) be the third derivative of 2/1155*n**7 + 0 + 0*n + 1/132*n**4 + 10*n**2 - 1/220*n**6 + 0*n**5 + 0*n**3. Factor w(m).
2*m*(m - 1)**2*(2*m + 1)/11
Let m(r) = 2*r**2 + r + 1. Let p(w) = -4*w**3 - 180*w**2 - 1770*w - 6. Let z(g) = 6*m(g) + p(g). Factor z(f).
-4*f*(f + 21)**2
Let z = -25 - -27. Factor -4*y**z + 0 + 3*y - 7*y + 0.
-4*y*(y + 1)
Let n be (-249)/(-168) - 24/28. Let -n*f**5 + 4*f**2 + 1/4 + 11/4*f**4 - 13/8*f - 19/4*f**3 = 0. What is f?
2/5, 1
Let k(o) = o**3 - 8*o**2 + 6*o + 12. Let i be k(7). Determine l, given that -55*l**i - 52*l**5 + 12*l**3 + 103*l**5 - 8*l**2 = 0.
-2, 0, 1
Let q(l) be the second derivative of -l**6/90 + l**5/10 - l**3/2 - 6*l. Let i(w) be the second derivative of q(w). Factor i(p).
-4*p*(p - 3)
Let k(p) be the first derivative of -p**6/180 + p**5/24 - p**4/8 + 7*p**3/36 - p**2/6 - 11*p + 4. Let v(d) be the first derivative of k(d). Factor v(f).
-(f - 2)*(f - 1)**3/6
Suppose 0 = 2*y - 4*r + 12, 0 = -5*y + 41*r - 43*r + 6. Factor y*q + 3/4*q**2 - 3/4.
3*(q - 1)*(q + 1)/4
Let t(v) be the second derivative of v**6/75 + 8*v**5/25 + 44*v**4/15 + 64*v**3/5 + 144*v**2/5 - 3*v - 4. Factor t(q).
2*(q + 2)**2*(q + 6)**2/5
Suppose 12*w**2 - 4474*w**3 - w + 2244*w**3 + 3*w + 2240*w**3 = 0. What is w?
-1, -1/5, 0
Let t(c) be the first derivative of -3*c**4/32 - 9*c**3/8 - 21*c**2/8 + 211. Factor t(h).
-3*h*(h + 2)*(h + 7)/8
Suppose -3*q + 8 = -7, -l = 2*q - 610. Let w be ((-2825)/l - (-1)/3) + 5. Factor 1/4 - w*z + 3/8*z**2.
(z - 1)*(3*z - 2)/8
Let k be 9/3 + 6*(-15)/5. Let g be (-16)/k*25/10. Factor -54*i**2 - 24*i - g.
-2*(9*i + 2)**2/3
Let k(q) be the second derivative of q**4/36 - 26*q**3/9 - 53*q**2/6 - 148*q. What is y in k(y) = 0?
-1, 53
Let g(i) be the first derivative of -2 - 1/10*i**5 + 0*i**3 - i**2 + 1/40*i**6 + 1/8*i**4 + 0*i. Let u(o) be the second derivative of g(o). Factor u(b).
3*b*(b - 1)**2
Suppose -1203 = -5*v - 4*h, 0*v + h = 3*v - 715. Let z = 3109/13 - v. Factor 2/13*r**2 - z*r**3 + 0 + 0*r.
-2*r**2*(r - 1)/13
Let q = -24509/8 + 3073. Suppose -q + 15/4*y - 3/8*y**2 = 0. What is y?
5
Let y = 14/5 - 13/5. Let z(x) be the second derivative of y*x**5 + 0*x**2 - 2/3*x**4 + 13*x + 0 + 2/3*x**3. Suppose z(j) = 0. Calculate j.
0, 1
Let n(a) be the second derivative of a**5/5 + 4*a**4/3 + 2*a**3 + 26*a - 1. Factor n(l).
4*l*(l + 1)*(l + 3)
Suppose -4*a + 4*n = 0, 2*a - n = -4*n - 5. Let s be 2*a*3/(-51). Factor -s + 4/17*k - 2/17*k**2.
-2*(k - 1)**2/17
Let b(m) be the first derivative of m**4/30 - m**3/15 - 45*m - 40. Let q(r) be the first derivative of b(r). Let q(y) = 0. What is y?
0, 1
Let l(t) = t**3 - t**2 + 2. Let s(g) = 26*g**3 - 96*g**2 + 119*g - 47. Let w(q) = -l(q) + s(q). What is h in w(h) = 0?
1, 7/5
Let c(q) = -4*q**3 - q**2 - 2*q - 2. Let z(i) = -2*i**2 + i + 3. Let u be z(2). Let v(h) = -5*h**3 - h**2 - 3*h - 3. Let y(f) = u*c(f) + 2*v(f). Factor y(b).
b**2*(2*b + 1)
Let t(z) be the first derivative of -7*z**5 + 55*z**4 - 235*z**3/3 + 25*z**2 - 557. Let t(s) = 0. Calculate s.
0, 2/7, 1, 5
Let g(y) = y + 11. Let c be g(-9). Factor -12*t**2 - 12 - 32*t + 13*t**3 + 8*t**c - 11*t**2 - 4*t**3.
(t - 3)*(3*t + 2)**2
Suppose -5*h - 99 = -104. Let z(k) = -k**3 + k**2. Let b be z(h). Factor 2/5*n**4 - 6/5*n**3 + b + 0*n**2 + 0*n.
2*n**3*(n - 3)/