5335 + 8/829. Let h = r + 21/23. Factor -2/5*a - h*a**2 + 0.
-2*a*(2*a + 1)/5
Factor 55*f**2 - 28*f**2 - 24*f**2 + 24 + 27*f.
3*(f + 1)*(f + 8)
Let c(q) be the first derivative of -q**6/21 + 2*q**4/7 + 4*q**3/21 - 3*q**2/7 - 4*q/7 + 14. Suppose c(y) = 0. What is y?
-1, 1, 2
Let p(w) = w**3 - 16*w**2 + 15*w + 4. Let z be p(15). Factor 0 + 1/3*y**z + 1/3*y**3 - 1/3*y**5 + 0*y - 1/3*y**2.
-y**2*(y - 1)**2*(y + 1)/3
Let y(z) be the second derivative of z**10/30240 - z**9/1680 + 9*z**8/2240 - 3*z**7/280 + z**4/12 + 3*z. Let n(r) be the third derivative of y(r). Factor n(d).
d**2*(d - 3)**3
Let x(c) be the second derivative of -c**4/28 - c**3/14 + 13*c. Solve x(d) = 0.
-1, 0
Suppose 0 = w - 2*f + 6, 3*f = -5*w + f + 6. Let z(d) be the second derivative of -d + 0 + w*d**2 - 1/6*d**4 + 1/3*d**3. Factor z(r).
-2*r*(r - 1)
Let z(r) be the third derivative of -r**7/1050 - r**6/200 - r**5/100 - r**4/120 + 11*r**2. Factor z(i).
-i*(i + 1)**3/5
Let i(t) = t**4 + t**3 + t**2 + 1. Let z(o) = o**4 + o**3 + 9*o**2 + o - 4. Let h(w) = -2*i(w) + z(w). Find q, given that h(q) = 0.
-3, -1, 1, 2
Let h be 8/3*(19/6 + -3). Solve -14/9*x - 4/9 - h*x**2 + 2/3*x**3 = 0.
-1, -1/3, 2
Let j(o) be the first derivative of -o**3 + 3*o + 27. Factor j(l).
-3*(l - 1)*(l + 1)
Let f be 10/(-15)*(4 + (-100)/16). Factor -3/2*b**4 - 1/2*b**2 + f*b**3 + 1/2*b**5 + 0 + 0*b.
b**2*(b - 1)**3/2
Let v(p) be the first derivative of 2/25*p**5 + 3 + 0*p**2 - 4/15*p**3 - 1/10*p**4 + 0*p. What is n in v(n) = 0?
-1, 0, 2
Let j = 53 - 53. Factor 2*v - 9/4*v**4 + j - 7*v**2 + 15/2*v**3.
-v*(v - 2)*(3*v - 2)**2/4
Let m(s) be the third derivative of s**6/60 + s**5/6 + s**4/3 - 34*s**2. Factor m(y).
2*y*(y + 1)*(y + 4)
Let n(p) be the first derivative of -2 + 6/5*p**5 - p**4 - 2/3*p**3 + 0*p + 0*p**2. Factor n(a).
2*a**2*(a - 1)*(3*a + 1)
Let m = 119 + -113. Let k(u) be the third derivative of 0*u - 1/132*u**4 - 2/165*u**5 + 0*u**3 + 0 - 2*u**2 - 1/220*u**m. Find h such that k(h) = 0.
-1, -1/3, 0
Let a(z) be the first derivative of 2*z**3/51 + z**2/17 - 4*z/17 + 11. Factor a(w).
2*(w - 1)*(w + 2)/17
Let y = -10 + 12. Let n(s) be the third derivative of -1/96*s**6 + y*s**2 - 1/12*s**3 - 1/96*s**4 + 1/30*s**5 + 0*s + 0. Factor n(g).
-(g - 1)**2*(5*g + 2)/4
Let m(t) be the third derivative of 0*t**3 + 0*t - 1/210*t**5 - 4*t**2 + 0 - 1/84*t**4. Factor m(n).
-2*n*(n + 1)/7
Factor -2/5 - 1/5*c + 1/5*c**2.
(c - 2)*(c + 1)/5
Let b(c) be the second derivative of -c**5/4 + 5*c**4/4 - 10*c**2 + 6*c. Factor b(z).
-5*(z - 2)**2*(z + 1)
Factor -336*y - 784/3 - 108*y**2.
-4*(9*y + 14)**2/3
Let c be (-132)/(-28) - 10/(-35). Determine t so that 5*t**2 + 10*t**2 - 4*t - 8*t**3 + 2*t**4 - c*t**2 = 0.
0, 1, 2
Let c(k) be the third derivative of k**5/140 - k**4/56 + 11*k**2. Factor c(v).
3*v*(v - 1)/7
Solve -4/9*t**4 - 2/3 + 10/9*t**2 - 10/9*t**3 + 10/9*t = 0.
-3, -1, 1/2, 1
Let o(t) be the third derivative of -t**7/1680 + t**6/80 - 9*t**5/80 + 9*t**4/16 - 5*t**3/6 - 3*t**2. Let b(m) be the first derivative of o(m). Factor b(p).
-(p - 3)**3/2
Factor -2*v**2 + 11*v**5 - 9*v**5 + 7*v**3 - 7*v**4 - 1 + 1.
v**2*(v - 2)*(v - 1)*(2*v - 1)
Let u = -16 + 7. Let n be (-4)/u*6/4. Determine m so that 4/9*m**2 - 8/3*m**4 + n*m**3 + 14/9*m**5 + 0*m + 0 = 0.
-2/7, 0, 1
Factor -1/6*q + 0 + 0*q**2 + 0*q**4 + 1/3*q**3 - 1/6*q**5.
-q*(q - 1)**2*(q + 1)**2/6
Let r(s) be the second derivative of -2/5*s**5 + 0 - 8/3*s**3 - 3*s - 5/3*s**4 - 2*s**2. Suppose r(g) = 0. What is g?
-1, -1/2
Let s = -5 + 7. Let 1 - 3*t**s - 2 + 3 + t**2 = 0. What is t?
-1, 1
Let h(o) be the third derivative of -o**8/28 - 4*o**7/105 + 3*o**6/10 + 4*o**5/5 + 2*o**4/3 + 6*o**2. Suppose h(v) = 0. Calculate v.
-1, -2/3, 0, 2
Suppose 0 = -3*t - 3*n + 15, -2*t + 5 = -n - 8. Let y = 10 - t. Find s such that 6*s**3 - 3*s - 8*s**2 + 2*s**2 + 5*s - 2*s**y = 0.
0, 1
Let n(v) = 3*v - 9. Let u be n(3). Factor u*z + 2/7*z**2 + 2/7*z**4 + 0 - 4/7*z**3.
2*z**2*(z - 1)**2/7
Let d = 617/408 - 25/17. Let g(b) be the first derivative of 1/12*b**3 + b**2 + 1 + b + d*b**6 - 5/16*b**4 - 1/20*b**5. What is x in g(x) = 0?
-1, 2
Let a(x) be the first derivative of -1/9*x**3 + x + 3 - 1/36*x**4 - 1/6*x**2. Let h(g) be the first derivative of a(g). Determine j, given that h(j) = 0.
-1
Suppose -j + 1 = -1. Solve -4*w**4 + 0*w**2 - 4*w**3 + 5*w**2 + 5*w**4 - j*w = 0 for w.
0, 1, 2
Let o(y) be the second derivative of -y**5/5 + 5*y**4/3 - 16*y**3/3 + 8*y**2 + 24*y. Factor o(i).
-4*(i - 2)**2*(i - 1)
Let p(b) be the second derivative of b**7/420 - 7*b**6/300 + 11*b**5/200 - b**4/24 - 17*b. Factor p(c).
c**2*(c - 5)*(c - 1)**2/10
Let d = -421 + 424. Factor 8/3*v + 14*v**d + 16*v**2 + 0 - 98/3*v**4.
-2*v*(v - 1)*(7*v + 2)**2/3
Suppose 3*v = 14 - 2. Suppose -2*m**4 - 2*m**4 + 2*m**4 - 2*m**2 + 4*m**v = 0. What is m?
-1, 0, 1
Let -4*b**2 + b**2 + 5*b**2 + 8 + 8*b = 0. Calculate b.
-2
Let b(q) be the second derivative of q**6/120 - q**4/48 + 11*q. Factor b(t).
t**2*(t - 1)*(t + 1)/4
Let -8*s - 10 - 16*s - 4 - 7 - 3*s**2 = 0. Calculate s.
-7, -1
Suppose 3*t - 10 = 8. Determine j so that 32*j**2 + 8*j**4 + j**5 + 24*j**3 + 5*j - t*j + 17*j = 0.
-2, 0
Suppose -3*n = -40 - 14. Let h be 2/(-8) - n/(-8). Factor -3*d + 2 - h*d + 4*d**2 - 4*d**3 + 3*d**3.
-(d - 2)*(d - 1)**2
Suppose 5*j + 224 = j + r, -2*j - 94 = 4*r. Let y be (-26)/(-10) + 33/j. Factor 1/6*x + 0 - 1/6*x**y.
-x*(x - 1)/6
Let p = 22/17 + -37/68. Factor 0*q - p + 3/4*q**2.
3*(q - 1)*(q + 1)/4
Factor -14*n - 4*n**2 - 900 - 79*n - 27*n.
-4*(n + 15)**2
Let d(x) = x**3 - 8*x**2 - 8*x - 10. Let f be d(9). Let u = 5 + f. Factor -1 + 7/2*o + 5/2*o**3 - 1/2*o**u - 9/2*o**2.
-(o - 2)*(o - 1)**3/2
Let c be (3/(-8))/((-23)/(-10074)). Let r = c - -165. Determine w so that -5/4*w**2 + 1/2 - r*w = 0.
-1, 2/5
Suppose -a = -4*a + 12. Let p be (2/(-6)*a)/(-2). Factor 0 + p*o**2 - 2/3*o**3 + 0*o.
-2*o**2*(o - 1)/3
Suppose 5*l = -4*g + 9 + 3, 4*l + g - 3 = 0. Let y(r) be the first derivative of 0*r + 1/6*r**4 + l*r**2 - 1/9*r**3 + 1/5*r**5 + 1. What is k in y(k) = 0?
-1, 0, 1/3
Let z(j) be the first derivative of -2*j**3/21 + 3*j**2/7 - 4*j/7 + 8. What is f in z(f) = 0?
1, 2
Let l(w) be the second derivative of 25*w**7/84 + 79*w**6/12 + 2179*w**5/40 + 4685*w**4/24 + 700*w**3/3 + 125*w**2 - 15*w. Factor l(x).
(x + 5)**3*(5*x + 2)**2/2
Factor -5/4*a**2 - 5/2 + 25/4*a - 5/2*a**3.
-5*(a - 1)*(a + 2)*(2*a - 1)/4
Suppose 0*a + 2*a + 24 = 0. Let c be a/(-54) + 8/18. Factor -2*n**2 - c + 2/3*n**3 + 2*n.
2*(n - 1)**3/3
Suppose -2*a + 3 + 7 = 0. Let k(v) be the second derivative of -1/126*v**7 + 7/36*v**4 - 1/9*v**3 + 1/18*v**6 - 3/20*v**a + 0*v**2 + 0 - 2*v. Factor k(n).
-n*(n - 2)*(n - 1)**3/3
Let d(j) = 3*j**2 - j + 1. Let f be d(1). Determine c, given that 0 + 4*c**2 + 5*c - f + c**3 + 5 = 0.
-2, -1
Let n(a) = 2*a**4 - 2*a**3 + 5*a + 4. Let u(j) = j**4 - 2*j**3 + 4*j + 3. Let g = -8 - -10. Suppose 0 = c - 0 - g. Let w(b) = c*n(b) - 3*u(b). Factor w(v).
(v - 1)*(v + 1)**3
Let x(q) be the third derivative of -q**7/700 - q**6/180 - q**5/300 + q**4/60 + q**3/6 + 2*q**2. Let o(v) be the first derivative of x(v). Factor o(g).
-2*(g + 1)**2*(3*g - 1)/5
Let y(x) be the first derivative of -x**4/4 - 10*x**3/3 - 5*x**2 - 8*x + 3. Let r be y(-9). Solve -r + 5/2*t**2 + 3/2*t = 0.
-1, 2/5
Let g(u) be the third derivative of -u**8/840 + u**6/50 + 4*u**5/75 + u**4/20 + 14*u**2. Find m, given that g(m) = 0.
-1, 0, 3
Determine q so that 3/2*q - 3/4*q**3 + 0 - 3/4*q**2 = 0.
-2, 0, 1
Let l(c) = -5*c + 62. Let u be l(12). Let d(m) be the first derivative of m + m**u + 2 + 1/3*m**3. Suppose d(t) = 0. Calculate t.
-1
Factor 2/7*s**3 + 0 + 0*s + 4/7*s**2.
2*s**2*(s + 2)/7
Let x(c) be the first derivative of 27/4*c**4 + 0*c**2 - 7 + 0*c + 36/5*c**5 + 5/2*c**6 + 2*c**3. Solve x(m) = 0 for m.
-1, -2/5, 0
Factor 10*n**2 - 3*n**3 + 3 - 27*n + 8*n**2 + 9.
-3*(n - 4)*(n - 1)**2
Let h(p) be the first derivative of -p**4 + 4*p**2 + 3 + 0*p - 4/3*p**3. Determine m so that h(m) = 0.
-2, 0, 1
What is r in -26*r**4 + 24*r**3 + 9*r**3 - 12*r**5 + 6 + 69*r**2 + 39*r + 11*r**4 = 0?
-1, -1/4, 2
Let l(p) = -13*p**4 - 8*p**3 + 13*p**2 + 13*p. Let n(u) = -20*u**4 - 12*u**3 + 20*u**2 + 20*u. Let d(i) = 8*l(i) - 5*n(i). Factor d(r).
-4*r*(r - 1)*(r + 1)**2
Suppose -4*z + 74 = 8*c - 3*c, 0 = 4*c - z - 55. Let m