d = -6*d - 15. Determine b so that 0*b + 1/2*b**x + 0 - 1/2*b**3 = 0.
0, 1
Let r(v) be the third derivative of 1/210*v**6 + 0*v - 1/21*v**3 + 0 + 5*v**2 + 1/210*v**5 - 1/42*v**4. Factor r(s).
2*(s - 1)*(s + 1)*(2*s + 1)/7
Let k(q) be the first derivative of -3*q**5/25 - 3*q**4/20 + q**3/5 + 3*q**2/10 + 7. Suppose k(f) = 0. Calculate f.
-1, 0, 1
Let v be (-1)/24*10 + (-2)/(-3). Factor 1/2*n**4 + 0 + 5/4*n**3 + v*n + n**2.
n*(n + 1)**2*(2*n + 1)/4
Suppose 8 = 4*m + 3*g, 5*m = -2*g + 5*g + 10. Let o = -3 + 3. Suppose -q + o*q + 3*q - 2*q**m = 0. Calculate q.
0, 1
Let i(p) be the third derivative of -p**5/510 - 5*p**4/204 - 4*p**3/51 + 8*p**2. Factor i(z).
-2*(z + 1)*(z + 4)/17
Let r(b) = -b**2 + b - 1. Let x(s) = 7*s**2 - 5*s + 6. Let h = 13 + -12. Let y(u) = h*x(u) + 6*r(u). Factor y(w).
w*(w + 1)
Let z(q) be the second derivative of -q**5/110 - q**4/22 - q**3/11 - q**2/11 - q. Determine n, given that z(n) = 0.
-1
Suppose -2*p + 39 = -3*p. Let v be p/65 - (-19)/15. Determine o so that -2/3*o**2 + 2/3*o**3 - 2/3*o + v = 0.
-1, 1
Let a(q) be the first derivative of 3 + 0*q + 9/5*q**5 + 4*q**3 - 6*q**4 + 0*q**2. Factor a(f).
3*f**2*(f - 2)*(3*f - 2)
Factor 18/7*x - 3/7*x**2 + 0.
-3*x*(x - 6)/7
Let s(k) = -k**3 + 4*k**2 + 2*k - 3. Let u be s(4). Suppose 0 = 2*h + 3*t - 9 - 2, 3*h = u*t + 7. Factor -4*y**2 - y**h + 4*y**2 + y**5.
y**4*(y - 1)
Let -2/7*j**5 + 0 + 0*j + 0*j**4 + 6/7*j**3 + 4/7*j**2 = 0. What is j?
-1, 0, 2
Let l(w) = 9*w + 336. Let f be l(-37). What is z in 2/3*z**f - 2/3*z + 0 - 2/3*z**2 + 2/3*z**4 = 0?
-1, 0, 1
Let i be (-4 - -1) + 6 + -1. Let g(w) be the first derivative of 5 - i*w - w**3 - 7*w + 3*w + 6*w**2 - 6*w. Let g(o) = 0. Calculate o.
2
Let m be (-1 - (4 - (-52)/(-12)))/(-4). Factor 1/2*b + 0 + m*b**2.
b*(b + 3)/6
Let j be (-26)/20 - (-51)/34. Let h(z) be the first derivative of -j*z**5 + 0*z**3 - 1 + 0*z + 0*z**2 + 0*z**4. Solve h(f) = 0 for f.
0
Suppose -3*g - 4 = -4*g. Suppose -2*f = 2*f + 20, g*f + 28 = 2*s. Factor 0 + 0*q - 8/7*q**2 - 54/7*q**s + 48/7*q**3.
-2*q**2*(3*q - 2)*(9*q - 2)/7
Let u = -849/10 + 85. Let t(x) be the second derivative of 0 + 0*x**3 - u*x**5 + 2*x + 1/6*x**4 + 0*x**2. Factor t(d).
-2*d**2*(d - 1)
Let g(r) be the first derivative of -9/2*r**4 - 11/5*r**3 + 18/5*r**2 + 12/5*r + 3*r**5 + 8. Find o, given that g(o) = 0.
-2/5, 1
Let i(u) be the first derivative of 0*u + 1/12*u**3 + 1/4*u**2 - 3. Let i(q) = 0. What is q?
-2, 0
Let i = 216 - 214. Determine z, given that 2/3 + 28/3*z**i + 16/9*z**4 - 38/9*z - 8*z**3 = 0.
1/2, 3
Let s(q) = 5*q**3 - 16*q**2 + 11*q. Let d(j) = -10*j**3 + 33*j**2 - 23*j. Let a(f) = -6*d(f) - 13*s(f). Factor a(i).
-5*i*(i - 1)**2
Let o(i) be the first derivative of 2*i**5/45 - 2*i**4/9 + 10*i**3/27 - 2*i**2/9 + 9. Suppose o(a) = 0. Calculate a.
0, 1, 2
Let p(l) be the third derivative of -4*l**2 + 0*l**3 + 0*l**4 + 0*l + 0 - 1/30*l**5 + 1/60*l**6. Factor p(n).
2*n**2*(n - 1)
Let o be -4*(-2 + 0 + 0). Suppose -g - 4*m + 3 = 0, -4*m - o = -3*g + 1. Determine z so that 6 + z**g + 3*z**4 - 5*z**3 + z**3 - 21*z - 12*z**3 + 27*z**2 = 0.
1, 2
Let n(r) be the first derivative of 0*r**2 + 0*r + 0*r**5 + 1/3*r**3 + 1/1800*r**6 - 2 - 1/120*r**4. Let c(x) be the third derivative of n(x). Factor c(t).
(t - 1)*(t + 1)/5
Let s(v) be the second derivative of v**6/225 - 2*v**5/75 + v**4/30 + 11*v. Factor s(j).
2*j**2*(j - 3)*(j - 1)/15
Let f(p) = -1222*p**2 - 440*p - 28. Let a(d) = -489*d**2 - 176*d - 11. Let h(z) = -12*a(z) + 5*f(z). Solve h(t) = 0 for t.
-2/11
Suppose 0 = -2*i - 0*i, 0 = 2*z - 5*i. Suppose j + 5*w = 8, 17 = -z*j + 4*j + 5*w. Factor 1/2*a**j - 1/2*a - 1/2*a**2 + 1/2.
(a - 1)**2*(a + 1)/2
Let k(u) = u**2. Let h(r) be the second derivative of 0 - 5/6*r**4 - r - 1/3*r**3 + 0*r**2. Let g(b) = h(b) + 8*k(b). Factor g(c).
-2*c*(c + 1)
Solve 0 - 2/3*x**3 + 0*x + 0*x**2 = 0 for x.
0
Let j(t) be the second derivative of t**5/10 + t**4/6 - 11*t. Find m such that j(m) = 0.
-1, 0
Suppose 2*q = 3*i - 62, 2*q = -i + q + 14. Let p be 18/30*20/i. Solve -2/3*h + 4/3 - p*h**2 = 0 for h.
-2, 1
Let f(m) = 44*m**3 + 28*m**2 - 44*m + 28. Let u(s) = -8*s**3 - 5*s**2 + 8*s - 5. Let i(a) = -5*f(a) - 28*u(a). Suppose i(y) = 0. What is y?
-1, 0, 1
Factor c**4 - 4*c**2 + 9*c**3 + c**2 - 9*c**4 + 3*c**5 - c**4.
3*c**2*(c - 1)**3
Let w(s) be the first derivative of s**5/40 + s**4/8 + s**3/6 + 3*s - 1. Let t(g) be the first derivative of w(g). Factor t(m).
m*(m + 1)*(m + 2)/2
Let x be (-3 + 1)*1/(-2). Let v be 1*(1 - 1)*x. Factor 2*l + 2*l**2 + v*l + 5*l**2 - 5*l**2 - 4.
2*(l - 1)*(l + 2)
Let g = 615 + -7375/12. Let x(f) be the third derivative of 1/60*f**6 - 1/10*f**5 + 2*f**2 + 0 + 0*f + 1/105*f**7 - g*f**4 - 2/3*f**3. Let x(p) = 0. What is p?
-1, 2
Let t(a) = a**2 - a. Let z(w) = -8*w**2 + 6*w + 2. Let n(m) = -23*m**2 + 18*m + 5. Let q(v) = 6*n(v) - 17*z(v). Let g(f) = q(f) + 4*t(f). Factor g(y).
2*(y - 1)*(y + 2)
Let h(l) be the first derivative of 2*l**3/9 - l**2 + 4*l/3 + 5. Find y, given that h(y) = 0.
1, 2
Let p be (-15)/6*(-8)/10. Suppose -p*r + 9 = -t, -3*r + 30 = -5*t + 6. Suppose -k**4 + 3/5*k - 3/5*k**r + 7/5*k**2 - 2/5 = 0. What is k?
-1, 2/5, 1
Let s(i) = 2*i**3 - 6*i**2 + 8*i - 4. Let y(n) = -3*n**3 + 11*n**2 - 15*n + 7. Let b be 4 + -2 + 0 + -1. Let c = b - 5. Let j(h) = c*y(h) - 7*s(h). Factor j(a).
-2*a*(a - 1)*(a + 2)
Let u(b) be the third derivative of b**5/150 + b**4/20 + 2*b**3/15 + 2*b**2. What is w in u(w) = 0?
-2, -1
Factor 5 - 12*y - 2*y**2 - 18 - 9 + 6.
-2*(y + 2)*(y + 4)
Let r(c) = -2*c**3 - 18*c**2 - 42*c - 8. Let m be r(-5). Find x such that 1/2*x**m + 0 + x = 0.
-2, 0
Let b(u) = -10*u**4 + 15*u**3 + 35*u**2 - 75*u + 45. Let n(c) = 5*c**4 - 8*c**3 - 17*c**2 + 38*c - 22. Let m(x) = -2*b(x) - 5*n(x). Factor m(w).
-5*(w - 2)*(w - 1)**2*(w + 2)
Let k = -63 + 757/12. Let l = k + 17/12. Factor 1/2*a**5 + 0*a + l*a**3 + 0 + 1/2*a**2 + 3/2*a**4.
a**2*(a + 1)**3/2
Let o(p) = -p**2 + 12*p + 9. Let y be o(12). Solve -10 - y + 3*n**2 + 16 = 0 for n.
-1, 1
Find l, given that 0*l**2 + 0*l**2 + l**2 + l**2 - 6*l + 4 = 0.
1, 2
Factor 10 - 1 + 3 - 163*j**2 - 2*j + 155*j**2 - 2*j**3.
-2*(j - 1)*(j + 2)*(j + 3)
Determine x so that -3 + 5*x - 4/3*x**2 = 0.
3/4, 3
Let y(r) be the third derivative of -r**6/2160 + r**5/720 + r**3/3 - 4*r**2. Let v(q) be the first derivative of y(q). Factor v(o).
-o*(o - 1)/6
Let g(k) be the third derivative of -k**2 + 1/150*k**5 + 0*k + 0 + 1/5*k**3 + 1/15*k**4. What is j in g(j) = 0?
-3, -1
Let t(a) = -21*a**2 + 12*a - 1. Let r(i) = -2*i - 3*i - i + 10*i**2. Let h(u) = -5*r(u) - 2*t(u). Factor h(l).
-2*(l - 1)*(4*l + 1)
Suppose -g - g = 0. Let b = 5 + g. Suppose s**4 + 4*s**2 + 2*s - 5*s**4 + 3*s**b - 5*s**5 = 0. Calculate s.
-1, 0, 1
Let w(n) be the second derivative of -2*n**6/45 - 2*n**5/15 - 5*n**4/36 - n**3/18 - 7*n. Factor w(l).
-l*(l + 1)*(2*l + 1)**2/3
Let v(t) be the first derivative of -3*t**4/8 + 5*t**3 - 75*t**2/4 - 17. Factor v(k).
-3*k*(k - 5)**2/2
Let i be 16/3 + 4 + -6. Factor -i*t + 4/3 + 2*t**2.
2*(t - 1)*(3*t - 2)/3
Let o = -1/9 - -11/18. Let u(y) be the first derivative of 1 + 3/4*y**3 - o*y - 7/8*y**2. Let u(s) = 0. Calculate s.
-2/9, 1
Let g(f) be the second derivative of -f**4/4 + f**3/2 - 43*f. Factor g(h).
-3*h*(h - 1)
Let q = -386 - -388. Let 12/5 + 4/5*f**q + 16/5*f = 0. Calculate f.
-3, -1
Let z = 123 + -109. Solve -2 + z*y - 49/2*y**2 = 0 for y.
2/7
Let x = 19 + -22. Let m(f) = f**3 + 2*f**2 - 4*f - 3. Let n be m(x). Factor 0*q**3 + 1/2*q**2 + n - 1/2*q**4 + 0*q.
-q**2*(q - 1)*(q + 1)/2
Let g = 3 + 10. Let j = -11 + g. Factor 2/3*d**j + 5/3*d**4 + 0*d + 0 - 7/3*d**3.
d**2*(d - 1)*(5*d - 2)/3
Let v = -3 + 3. Let q = 2 + v. Find a such that a**3 - 5*a**2 + 3*a**q + a**2 - 2*a = 0.
-1, 0, 2
Let z(q) be the third derivative of 2/39*q**4 + 0 - 4/39*q**3 + 1/780*q**6 - 1/78*q**5 - 3*q**2 + 0*q. Find a, given that z(a) = 0.
1, 2
Let j be (-10 - -10) + 3850/18. Let g = -213 + j. Factor 2/9*c**4 - 8/9 + g*c - 8/9*c**3 + 2/3*c**2.
2*(c - 2)**2*(c - 1)*(c + 1)/9
Suppose 3*q + 3 - 27 = 0. Factor 11*x - 7*x**2 + 5*x + 17*x**2 - q.
2*(x + 2)*(5*x - 2)
Let a be (-3 - -5) + 4*1. Determine l so that 4 + 9*l - 2 - 3*l**4 + 11*l**3 + 15*l**2 + a*l**4 = 0.
-1, -2/3
Let p(c) = -3*c**5 + 5*c**4 - 8*c**3. Let a(t) = t**5 - t**4 + t**3 - t**2. Let h(j) =