*t**3 - 3*t**2 - 20*t + 3. Let p(m) = -125*m**4 - 245*m**3 + 20*m**2 + 140*m - 20. Let y(b) = -20*j(b) - 3*p(b). Factor y(v).
5*v*(v + 1)*(v + 2)*(3*v - 2)
Suppose 0 = 3*p - 12 - 39. Factor -2*r**3 - p + 17 - 2*r**4.
-2*r**3*(r + 1)
Let v(d) be the third derivative of 2*d**2 + 27/40*d**5 + 3/40*d**6 + 81/8*d**3 + 0 + 1/280*d**7 + 27/8*d**4 + 0*d. Factor v(f).
3*(f + 3)**4/4
Let x(d) be the first derivative of 2*d**6/3 - d**4 + 24. Factor x(p).
4*p**3*(p - 1)*(p + 1)
Let p = -1 - -8. Factor 2 + 2*v**2 - 19*v**3 + 21*v**3 + 3*v**2 + 2*v**2 + p*v.
(v + 1)*(v + 2)*(2*v + 1)
Let u(f) = -3*f**4 + 2*f**3 + 3*f**2 + 2*f. Let q(g) = 4*g**4 - 3*g**3 - 4*g**2 - 2*g. Let i(o) = -4*q(o) - 5*u(o). Let i(h) = 0. Calculate h.
-1, 0, 1, 2
Let r(s) be the first derivative of 4*s**3/3 - 4*s - 6. Let r(h) = 0. What is h?
-1, 1
Let u = -503/12 + 42. Let n(o) be the second derivative of 0 + 0*o**2 - u*o**4 - 4*o + 0*o**3. Suppose n(j) = 0. Calculate j.
0
Let x = -86 - -260/3. Factor -2/3*f**2 + 1/3*f**3 - 1/3*f + x.
(f - 2)*(f - 1)*(f + 1)/3
Let d(n) be the second derivative of -n**8/840 + n**6/90 - n**4/12 - n**3/6 + 9*n. Let x(w) be the second derivative of d(w). Factor x(c).
-2*(c - 1)**2*(c + 1)**2
Let h(y) be the first derivative of -13*y**4 - 44*y**3/3 + 56*y**2 - 16*y - 17. Let h(s) = 0. Calculate s.
-2, 2/13, 1
Let g(q) be the third derivative of -q**7/210 - q**6/30 - 11*q**2. Factor g(c).
-c**3*(c + 4)
Factor -183*q + 3*q**5 + 24*q**3 + 183*q - 15*q**4 - 12*q**2.
3*q**2*(q - 2)**2*(q - 1)
Let x(s) be the second derivative of s**5/50 - s**4/6 + 7*s**3/15 - 3*s**2/5 + 17*s. Find n, given that x(n) = 0.
1, 3
Let s(k) be the third derivative of k**7/2940 + k**6/1260 - k**5/420 - k**4/84 - k**3/3 + 2*k**2. Let f(b) be the first derivative of s(b). Factor f(g).
2*(g - 1)*(g + 1)**2/7
Let b(y) be the second derivative of -2*y + 1/60*y**6 - 1/36*y**4 - 1/252*y**7 + 0 + 1/12*y**3 - 1/12*y**2 - 1/60*y**5. Solve b(t) = 0 for t.
-1, 1
Let n(q) = -3*q - 15. Let b(c) = -7*c - 30. Let r(p) = 2*b(p) - 5*n(p). Let l be r(-13). Factor -6 + 4*o - 2/3*o**l.
-2*(o - 3)**2/3
Let d(z) be the second derivative of -z**7/14 + z**6/5 + 3*z**5/20 - z**4/2 + 22*z. Find j, given that d(j) = 0.
-1, 0, 1, 2
Let n(h) be the second derivative of 0 + h**2 + 1/10*h**5 - 1/3*h**3 - 1/6*h**4 - 2*h. Determine p so that n(p) = 0.
-1, 1
Let i = 92/9 - 10. Solve -2/9*a + 0 - i*a**2 = 0 for a.
-1, 0
Suppose 5*n + 3 - 2 + 3 + n**2 = 0. Calculate n.
-4, -1
Let x(z) be the third derivative of z**5/54 - z**4/36 - 2*z**3/27 + 3*z**2. Factor x(g).
2*(g - 1)*(5*g + 2)/9
Let d(t) = t**3 + t**2 + t + 2. Let n be d(0). Suppose -2*c + 7 = 5*z, 3*c = -n*z + 2*c + 2. Factor -2/5*x**z + 2/5*x + 4/5*x**2 - 4/5.
-2*(x - 2)*(x - 1)*(x + 1)/5
Let r(w) be the first derivative of -w**4/3 + 4*w**3/3 + 2*w**2/3 - 4*w - 24. Let r(z) = 0. Calculate z.
-1, 1, 3
Suppose 0 = 2*r + 1 - 9. Let l(x) be the first derivative of 0*x - 2 - 1/16*x**r + 1/10*x**5 + 0*x**3 + 0*x**2 - 1/24*x**6. Find g such that l(g) = 0.
0, 1
Let h(s) = -s**3 + 4*s**2 - 2*s - 2. Let p be h(2). Suppose 0 = -p*m - m + 12. Factor -4 + 14*i**3 - 6*i**4 + 8*i**m + 4*i**4 + 6*i**2 - 6*i.
2*(i + 1)**3*(3*i - 2)
Let l(t) be the second derivative of -t**5/30 + t**4/18 + t**3/9 - t**2/3 + 2*t. Suppose l(o) = 0. Calculate o.
-1, 1
Let q be (8/2 + 1)*1. Suppose -g + i - q = -3*g, -4*g - i = -9. Factor -2/3*n**g + 1/3 + 1/3*n.
-(n - 1)*(2*n + 1)/3
Let c(n) = -2*n**2 + 0 + n**2 + 0*n**2 + 14 - 9*n. Let h be c(-10). Factor 0 + 1/5*d**h + 1/5*d - 1/5*d**3 - 1/5*d**2.
d*(d - 1)**2*(d + 1)/5
Let f(l) be the first derivative of l + 1/36*l**4 - 1/18*l**3 + 1/60*l**5 - 1/6*l**2 + 2. Let c(g) be the first derivative of f(g). Solve c(q) = 0.
-1, 1
Let p(c) be the second derivative of c**7/63 - c**5/40 + c**4/72 + 11*c. Factor p(n).
n**2*(n + 1)*(2*n - 1)**2/6
Let h(o) be the first derivative of o**6/3 - 2*o**5/5 - 3*o**4/2 + 2*o**3/3 + 2*o**2 - 6. Factor h(r).
2*r*(r - 2)*(r - 1)*(r + 1)**2
Let h(g) be the third derivative of -g**8/840 + g**7/525 + g**6/60 + g**5/50 + 8*g**2. Suppose h(z) = 0. Calculate z.
-1, 0, 3
Let y(v) be the third derivative of 1/60*v**4 + 3*v**2 - 1/300*v**5 + 0*v + 0 + 0*v**3. Factor y(w).
-w*(w - 2)/5
Let w = 3 - 1. Factor -l**4 + 0*l**2 - 2*l**w - l**3 + 3*l**2 + l + 0*l**3.
-l*(l - 1)*(l + 1)**2
Suppose 3*i - 16 = 2*f, -f - f - 2 = 4*i. Let o be 6/(-9)*(-4 + 87/24). Factor 0*k + o*k**i + 0 + 1/4*k**3.
k**2*(k + 1)/4
Let z(r) be the second derivative of r**7/2100 - r**5/100 - r**4/30 + r**3/6 + r. Let x(a) be the second derivative of z(a). Suppose x(b) = 0. What is b?
-1, 2
Let x(m) = -19*m**3 + 77*m**2 - 230*m + 139. Let u(f) = -5*f**3 + 19*f**2 - 58*f + 35. Let d(o) = 22*u(o) - 6*x(o). Factor d(b).
4*(b - 8)*(b - 2)*(b - 1)
Let g be (48/9)/((-2)/(-3)). Factor 5*s - 5*s + 2*s**2 - 6*s**2 + g*s**3 - 4*s**4.
-4*s**2*(s - 1)**2
Let g(z) be the second derivative of 0*z**3 - 1/3*z**4 + z**2 + 0 + 0*z**5 + 8*z + 1/15*z**6. Suppose g(m) = 0. Calculate m.
-1, 1
Find v such that -4*v**5 - 2*v**3 - 10*v**5 + 15*v**5 + v = 0.
-1, 0, 1
Let l(p) = -p**3 + 2*p**2 + 4*p - 3. Suppose 0*n - 3*n = -9. Let j be l(n). Determine f, given that -8/3*f + j + 16/3*f**2 + 10/3*f**3 = 0.
-2, 0, 2/5
Suppose -4*r + r + 51 = 0. Suppose -2*p + 2 = n - 0, 0 = 4*n - p - r. Factor 0*w + 1/2*w**3 + 0*w**2 + 0 - 1/2*w**n.
-w**3*(w - 1)/2
Let i = 4931/27927 - 4/963. Let x = i + 207/145. Let -x*n**2 + 0 + 2/5*n = 0. Calculate n.
0, 1/4
Let f = -1900 - -2845. Let s be 330/f - (-2)/9. Factor 0 + s*o**2 + 2/7*o.
2*o*(2*o + 1)/7
Let a(o) be the third derivative of -o**8/560 + o**7/50 - 19*o**6/200 + o**5/4 - 2*o**4/5 + 2*o**3/5 - 3*o**2. Factor a(b).
-3*(b - 2)**2*(b - 1)**3/5
Let i(z) be the third derivative of z**8/1008 + z**7/210 + z**6/180 + 31*z**2. Determine g, given that i(g) = 0.
-2, -1, 0
Suppose -2 - 6 = -q. Factor -12*d**2 + q + 3*d - 11*d**3 - 2*d**3 - 2 + 4*d**3.
-3*(d + 1)**2*(3*d - 2)
Suppose 2*p - 6 = 6. Let z be ((-5)/15)/((-1)/p). Factor 0 + 2/9*m + 2/9*m**z.
2*m*(m + 1)/9
Solve -5*l**2 + 0*l**2 + 4 + 3*l**2 - 2*l = 0.
-2, 1
Suppose 18 = w - 12. Let b be (-10)/4*(-48)/w. Solve 6*v + b*v**3 + 2 - 4*v - 2*v**2 - 6*v = 0.
-1, 1/2, 1
Suppose 0*m + 4*m = 12. Factor 4*g**3 + g - 1 + g**2 - 2*g - 3*g**m.
(g - 1)*(g + 1)**2
Suppose 5 = -5*w, -4 = -2*g - 5*w - 9. Factor g - 15/4*n**4 - 6*n**3 - 3/4*n**2 + 3/2*n.
-3*n*(n + 1)**2*(5*n - 2)/4
Determine y so that 5/3*y**3 - 5/3*y**4 + 0*y**2 + 0 + 0*y = 0.
0, 1
Suppose -n = -1 - 1. Let -5*c**2 - 4*c**3 + 3*c**2 + 3*c**2 + n*c**3 + c**4 = 0. Calculate c.
0, 1
Let x be (-13)/(-3) - 3/9. Factor -4 + 6*a**x - 8*a**3 + 8*a + 0 - 2*a**4.
4*(a - 1)**3*(a + 1)
Let y be 116/30 + -4 - 6/(-20). Determine i so that -y*i**5 - 1/3*i**3 + 1/2*i**4 + 1/2*i - 1/3*i**2 - 1/6 = 0.
-1, 1
Let h(a) = -5*a**3 + 3*a**2 + 8*a - 2. Let m(s) = -s**2 - s - 1. Let n(p) = h(p) - 2*m(p). Determine t, given that n(t) = 0.
-1, 0, 2
Factor 1/5*v**3 + 0 + 2/5*v**2 - 3/5*v.
v*(v - 1)*(v + 3)/5
Let m(o) be the third derivative of o**10/60480 - o**9/30240 - o**8/13440 + o**7/5040 - o**4/6 + 4*o**2. Let c(a) be the second derivative of m(a). Factor c(v).
v**2*(v - 1)**2*(v + 1)/2
Suppose d = 3*n - 8, -5*n = d + 2*d - 18. Let g be 14/45 - d/9. Determine x so that -g + 1/5*x**2 + 1/5*x - 1/5*x**3 = 0.
-1, 1
Suppose 87*o - 170*o + 95*o + 12*o**2 + 3*o**3 = 0. What is o?
-2, 0
Let b(l) = 2*l - 9. Let q be b(6). Let g(w) be the second derivative of -7/9*w**q + 2/3*w**2 + 5/18*w**4 + 0 - 2*w. Factor g(j).
2*(j - 1)*(5*j - 2)/3
Suppose 3*p = 2*p. Suppose 2*r - 10 = -p. Let 0*u**4 + 4*u**2 + 0*u**4 - 5*u**5 - 5*u**r + 10*u**3 - 4*u**4 = 0. Calculate u.
-1, -2/5, 0, 1
Let g(x) be the third derivative of x**8/16800 - x**7/700 + 3*x**6/200 - 9*x**5/100 - x**4/6 + 3*x**2. Let h(u) be the second derivative of g(u). Factor h(t).
2*(t - 3)**3/5
Let j(k) = 7*k**4 + 7*k**3 - 12*k**2. Let h(o) = 120*o**4 + 120*o**3 - 205*o**2. Let g(f) = 2*h(f) - 35*j(f). Factor g(m).
-5*m**2*(m - 1)*(m + 2)
Let d(n) be the second derivative of n**6/15 - n**5/10 - n**4/6 + n**3/3 - 8*n. Factor d(o).
2*o*(o - 1)**2*(o + 1)
Suppose -14 = -5*p + 1. Let s(k) be the first derivative of -3 - 12/35*k**5 + 1/14*k**6 - 15/14*k**2 + 6/7*k + 2/7*k**p + 3/7*k**4. Factor s(i).
3*(i - 2)*(i - 1)**3*(i + 1)/7
Let j