 = 0.
0, 1
Let h(z) be the first derivative of -z**6/600 - z**5/60 - z**4/40 + 3*z**3/10 - z**2/2 - 4. Let g(r) be the second derivative of h(r). Solve g(d) = 0.
-3, 1
Let w(y) be the first derivative of 1/4*y**4 - 5 + 0*y - 1/2*y**2 - y**3 + 3/5*y**5. Factor w(d).
d*(d - 1)*(d + 1)*(3*d + 1)
Factor -2*f**2 - 2*f + 18*f - 14 + 5 - 23.
-2*(f - 4)**2
Solve -140*x**2 - 2 + 136*x**2 + 15*x - 6*x = 0 for x.
1/4, 2
Factor 0 - 40/19*f**3 + 4/19*f + 14/19*f**2 + 22/19*f**4.
2*f*(f - 1)**2*(11*f + 2)/19
Let j(d) be the third derivative of -d**5/20 + d**4/8 + d**3 + 10*d**2. Solve j(u) = 0 for u.
-1, 2
Suppose -3*s - 5 - 1 = 0. Let t be (-2)/(s/1) - -1. Factor 0 - 1/2*k**t + 1/2*k.
-k*(k - 1)/2
Let r(t) = 17*t**2 - 75*t**3 + t + 40*t - 58*t**2 + 34*t + 41. Let p(s) = 15*s**3 + 8*s**2 - 15*s - 8. Let d(w) = -11*p(w) - 2*r(w). Solve d(c) = 0.
-1, -2/5, 1
Let z(l) = 7*l**2 - 5*l - 6. Let h(u) be the second derivative of 2*u**4/3 - u**3 - 7*u**2/2 - 3*u. Let w(v) = 6*h(v) - 7*z(v). Factor w(b).
-b*(b + 1)
Let r(u) be the first derivative of 10 - 2/15*u**5 + 0*u**3 + 0*u + 0*u**2 + 1/6*u**4. Factor r(w).
-2*w**3*(w - 1)/3
Let c(i) = -6*i**4 + 11*i**3 - 16*i**2 + 11*i. Let t(y) = 2*y - 7*y**2 + 0*y**2 - y**4 + y**2 + 2*y**3 + 3*y**2. Let p(j) = -2*c(j) + 11*t(j). Factor p(k).
k**2*(k - 1)*(k + 1)
Let z(k) be the first derivative of k**6/240 - k**5/60 + k**4/48 + 9*k**2/2 + 7. Let w(l) be the second derivative of z(l). Factor w(q).
q*(q - 1)**2/2
Let w(i) be the first derivative of -i**8/1120 + i**6/80 + i**5/40 + i**3/3 + 10. Let r(s) be the third derivative of w(s). Solve r(t) = 0.
-1, 0, 2
Let v(b) be the third derivative of -b**6/24 + b**5/6 + 5*b**4/24 - 5*b**3/3 - 18*b**2. Solve v(u) = 0 for u.
-1, 1, 2
Let t(y) be the third derivative of -y**9/60480 + y**8/3360 - y**7/420 + y**6/90 - y**5/20 + 5*y**2. Let l(u) be the third derivative of t(u). Factor l(m).
-(m - 2)**3
Let h be -2 - (-4)/(-48)*-26. Let c(d) be the second derivative of 0*d**3 + 2*d + 0 + h*d**2 - 1/36*d**4. Factor c(l).
-(l - 1)*(l + 1)/3
Let t(m) be the third derivative of -m**8/1512 - 4*m**7/945 - m**6/108 - m**5/135 + 23*m**2. Suppose t(d) = 0. What is d?
-2, -1, 0
Let l(d) = 2*d**2 - 2*d. Let i be l(-1). Factor 0 + 6/7*f**i + 0*f - 2/7*f**3 + 0*f**2.
2*f**3*(3*f - 1)/7
Let v(i) = -i**3 + 25*i**2 + 3*i - 72. Let l be v(25). Let r be -1 + 4 + -1 + 0. Factor 9/5*t**l + 0*t - 6/5*t**r + 0.
3*t**2*(3*t - 2)/5
Let 48*a**3 - 50*a**3 - 2*a**2 - 2 + 2 = 0. What is a?
-1, 0
Let v(x) be the third derivative of -x**7/42 - x**6/12 + 5*x**4/12 + 5*x**3/6 + x**2. Factor v(c).
-5*(c - 1)*(c + 1)**3
Let z be (-6)/(-4) - 4/(-8). Solve 0*u + 0 - 1/5*u**z - 1/5*u**3 = 0.
-1, 0
Factor -7*l**2 + 0*l**2 + 3*l**2 - 9 - 12*l + l**2.
-3*(l + 1)*(l + 3)
Suppose -2*p + p = 0. Let r(g) be the second derivative of g + 0*g**3 + p - 1/6*g**4 + g**2. Suppose r(z) = 0. Calculate z.
-1, 1
Let a(u) = u**2 - 1. Let s(b) = 4*b**3 + 20*b**2 + 12*b - 4. Let p(w) = -4*a(w) + s(w). Factor p(f).
4*f*(f + 1)*(f + 3)
Let l(n) = -1 + n**3 + 2*n + 5*n**3 - 2*n**3. Let y be l(1). Suppose -4*i**2 + 2*i**4 + 9*i - y*i - 4*i - 2*i**3 = 0. What is i?
-1, 0, 2
Let w = -805 - -808. Factor 2*h**4 + 0*h**2 + 0 - 2/3*h**5 - 4/3*h**w + 0*h.
-2*h**3*(h - 2)*(h - 1)/3
Factor -1/6*g**4 - 11/3*g**2 + 4*g - 3/2 + 4/3*g**3.
-(g - 3)**2*(g - 1)**2/6
Let c = -12 + 37/3. Let f(j) be the second derivative of 1/2*j**2 + 0 - j + c*j**3 + 1/12*j**4. Factor f(d).
(d + 1)**2
Let r(x) = x - 10. Let k be r(10). Let b(t) be the second derivative of 0 + k*t**2 - 1/3*t**3 + 1/12*t**4 - t. Determine d so that b(d) = 0.
0, 2
Suppose -l + 4*q - 2 = 0, 2*l = -0*q + 4*q. Solve l - 25*b + 4*b**2 - b**3 - 25*b + 45*b = 0.
1, 2
Let h = 11 - 10. Let k be (-6)/3 - (-7)/h. Suppose w**4 + w - 1/3*w**k - 1/3 - 2/3*w**3 - 2/3*w**2 = 0. What is w?
-1, 1
Suppose 1/9*l**4 + 7/9*l**2 + 5/9*l**3 + 1/3*l + 0 = 0. Calculate l.
-3, -1, 0
Suppose -r + 36 - 33 = 0. Let d(j) be the first derivative of 40/3*j**r + 4*j**2 + 8/5*j**5 + 0*j - 1 + 17/2*j**4. Let d(g) = 0. What is g?
-2, -1/4, 0
Let i(n) = 1. Let w(c) = -4*c**2 - 24*c - 48. Let r(j) = -12*i(j) - w(j). Find s, given that r(s) = 0.
-3
Suppose -3*q + 5*j = -4*q - 21, 5*q - 2*j - 30 = 0. Let a(v) be the first derivative of -q*v - 4 - 10*v**4 + 34/3*v**3 + 5*v**2. Find o, given that a(o) = 0.
-2/5, 1/4, 1
Let -2*t - t - 2*t**2 - 2*t**2 + 12 - 5*t = 0. What is t?
-3, 1
Let h(l) be the third derivative of 2*l**7/105 + l**6/15 - l**5/15 - l**4/3 - l**2. Factor h(u).
4*u*(u - 1)*(u + 1)*(u + 2)
Let c(n) = -2*n + 1. Let o be c(-2). Factor m**2 - m**5 + 7*m**3 - 2*m**2 + 0*m**o + 2*m**5 - 4 + 5*m**4 - 8*m.
(m - 1)*(m + 1)**2*(m + 2)**2
Let z(w) = -w**2 + 5*w - 2. Let g be z(3). Let r = g + -1. Factor -4*l + l**3 + 2*l - r*l**2 + 4*l**3.
l*(l - 1)*(5*l + 2)
Suppose 2*t + 5 = t. Let n be (-2)/(-24) - t/30. Factor -3/4*w - 3/4*w**2 - 1/4*w**3 - n.
-(w + 1)**3/4
Let c(k) be the second derivative of -2*k + 0 + 1/2*k**2 - 1/27*k**3 + 0*k**4 + 1/270*k**5. Let p(y) be the first derivative of c(y). Find n such that p(n) = 0.
-1, 1
Solve -2/5*u**2 + 0 - 2/5*u**3 + 0*u = 0.
-1, 0
Let m be (-6)/3 + 1 + 3. Suppose -3*p = 3*b + b + 3, 6 = -m*p - 4*b. Factor 4 - g**2 - 4 + 3*g**p - 2*g.
g*(g - 1)*(3*g + 2)
Let r be (4/36)/(70/194). Let j = -3/35 + r. What is w in 0 + 0*w - j*w**4 + 0*w**2 - 2/9*w**3 = 0?
-1, 0
Let d(o) be the first derivative of -3*o**5/40 - 3*o**4/16 + 5*o**3/2 - 9*o**2/2 + 17. Let d(j) = 0. What is j?
-6, 0, 2
Let -21*c - 3 - 9*c**5 - 30*c**3 - 33*c**3 - 3*c**3 - 54*c**2 - 39*c**4 = 0. Calculate c.
-1, -1/3
Let c(i) = 3*i**3 - 4*i. Let x(h) = -h**3 + h. Let t(o) = -o**2 + 4*o + 4. Let y be t(4). Let q(d) = y*x(d) + c(d). Solve q(v) = 0.
0
Let g(i) be the second derivative of -i**7/5040 + i**4/6 - 2*i. Let d(z) be the third derivative of g(z). Factor d(r).
-r**2/2
Suppose -61 = -12*a - 13. Factor 0*h + 4/5*h**3 + 2/5*h**a + 0 + 2/5*h**2.
2*h**2*(h + 1)**2/5
Let m = 6 + -2. Suppose 2*i - 24 = -z - 3*z, m*z - 10 = 5*i. Determine f so that -3*f**2 + 2*f + 3*f**5 + i*f**4 + 6*f**5 + 2 - 7*f**5 - f**2 - 4*f**3 = 0.
-1, 1
Let j(f) be the first derivative of -1/2*f**2 + 4/5*f + 1/15*f**3 + 7. Find v, given that j(v) = 0.
1, 4
Suppose 2*o + 38 = -2*h, 0 = 4*h - 4*o + 87 + 5. Let w be (-1 - -1)/(h + 20). Find l, given that 0*l + w - 6/5*l**3 + 2/5*l**2 + 6/5*l**4 - 2/5*l**5 = 0.
0, 1
Suppose 3*b = -3, 5 = 3*w + 4*b - 3*b. Factor 0*c**w - 3*c - 2 + c**2 - 2*c**2.
-(c + 1)*(c + 2)
Let o = 77/57 + -1/57. Factor -2/3*s + 2/3*s**2 - o.
2*(s - 2)*(s + 1)/3
Determine n so that -32 + 119*n**3 - 123*n**3 - 47*n - 24*n**2 - n = 0.
-2
Let f = 81/194 - -8/97. Factor f*w**2 + 1/2 + w.
(w + 1)**2/2
Factor -3/2*f**2 + 0*f - 3/4*f**3 + 0 + 3/4*f**4.
3*f**2*(f - 2)*(f + 1)/4
Let t(d) = 3 - 4 + 16*d**2 - 30. Let f(n) = 3*n**2 - 6. Let o(w) = 22*f(w) - 4*t(w). Factor o(u).
2*(u - 2)*(u + 2)
Let y = -4 + -5. Let z be ((-12)/y)/((-4)/(-6)). Let 2 - z*d + 1/2*d**2 = 0. Calculate d.
2
Suppose -22*z = -13*z. Determine w, given that 0*w + 0*w**2 + z + 2/7*w**3 - 2/7*w**4 = 0.
0, 1
Let -y + y + 121*y**3 - 120*y**3 = 0. What is y?
0
Let v(p) = -p**3 - 4*p**2 - 2*p. Let w be v(-4). Suppose -h + w - 5 = 0. Factor 12*g - 18*g**2 - 8/3 + 9*g**h.
(3*g - 2)**3/3
Find m, given that 0*m**2 + 6*m**2 - m**3 - 4*m**2 - m = 0.
0, 1
Let f(k) be the first derivative of -k**3/12 - 3*k**2/8 + 5. Factor f(l).
-l*(l + 3)/4
Factor -75*n**2 - 57*n**3 - 12*n - 6*n**5 - 12 + 0*n**5 - 21*n**4 - 36*n + 3*n**5.
-3*(n + 1)**3*(n + 2)**2
Let v(d) be the third derivative of 0*d + 1/20*d**4 - 1/10*d**3 + 0 + d**2 - 1/100*d**5. Let v(u) = 0. What is u?
1
Factor -9 - 4*s**3 - 2*s + 36*s**2 - 34*s**2 + 14*s - s**4.
-(s - 1)**2*(s + 3)**2
Suppose -4/11*y**2 - 10/11*y**4 + 0*y - 14/11*y**3 + 0 = 0. Calculate y.
-1, -2/5, 0
Let v be 9/6 + (-3)/(-2). Factor -10*o**3 + 3*o**v - o**2 + 0*o**4 - 8*o**4 + 0*o**2 + 16*o**5.
o**2*(o - 1)*(4*o + 1)**2
Solve 0 - 4/9*c - 2/9*c**2 = 0 for c.
-2, 0
Let s(j) = 55*j**2 + 100*j - 65. Let r(a) = 5*a**2 + 9*a - 6. Let z(n) = 65*r(n) - 6*s(n). Let z(p) = 0. Calculate p.
-3, 0
Let x(n) be the third derivative of 2*n**7/63 + 13*n**6/135 - 4*n**5/45 - 4*n**4/27 - 8*n**2. Solve x(c) = 0 for c.
-2, -2/5, 0, 2/3
Let l(y) be the second derivative of 4/273*y**7 + 9/130*y**5