 -53 + 55. Solve 1/6 + 1/3*h + 1/6*h**y = 0.
-1
Let j be (-3)/(-10*3/(-984)). Let l = -98 - j. Factor -2/5*c**4 + 2/5*c - 2/5 + 4/5*c**2 - 4/5*c**3 + l*c**5.
2*(c - 1)**3*(c + 1)**2/5
Let d = 416/9 - 46. Find k, given that -2/9*k**4 + d*k**3 - 2/9*k + 0 + 2/9*k**2 = 0.
-1, 0, 1
Factor 1/5*c**2 + 0*c - 4/5.
(c - 2)*(c + 2)/5
Let y(t) be the third derivative of t**6/1440 - t**4/96 + t**3/3 - t**2. Let m(f) be the first derivative of y(f). Let m(n) = 0. What is n?
-1, 1
Let k(t) = 2*t**2 + 2*t - 5. Let a(z) = z**2 - 3*z**2 - 2 - 2*z + 2 + 4. Let y(n) = -5*a(n) - 4*k(n). Solve y(h) = 0 for h.
-1, 0
Let o(r) = -r**5 + 5*r**4 + r**3 + 7*r**2. Let s(l) = l**3 - 5*l**2 - 8*l + 6. Let x be s(6). Let z(g) = -g**4 - g**2. Let q(d) = x*z(d) - o(d). Factor q(a).
a**2*(a - 1)*(a + 1)**2
Suppose -80 - 35*l**2 + 15*l**4 + 80 + 35*l**3 - 15*l = 0. What is l?
-3, -1/3, 0, 1
Factor -1/7*s**3 + 1/7 - 1/7*s**2 + 1/7*s.
-(s - 1)*(s + 1)**2/7
Let k = -4 + 13/3. Let j(y) be the second derivative of k*y**3 + 0 - y + 0*y**2 + 1/10*y**5 - 1/3*y**4. Factor j(o).
2*o*(o - 1)**2
Let p be 7/4 - 36/48. Let s be 0/(8/4 - p). Factor s - 3/2*j - 3/2*j**3 - 3*j**2.
-3*j*(j + 1)**2/2
Let i(o) = -o**3 - 3*o**2 - 2*o - 2. Let r be i(-3). Suppose r*q - q - 9 = 0. Solve -2*g**4 + 4*g**q + 3*g**2 - 3*g**5 + 0*g**2 - g - g**2 = 0 for g.
-1, 0, 1/3, 1
Let y(z) be the first derivative of -z**4/16 - 5. Factor y(b).
-b**3/4
Let x be (0/(-18))/((2*1)/2). Solve 2/7*t**3 + x*t + 0 + 4/7*t**2 = 0 for t.
-2, 0
Suppose -12 = -3*k + 3. Suppose 0 = -a + t, -k*t = -2*t - 9. Solve 0 + 0*g**a + 0*g + 2/5*g**5 - 2/5*g**4 + 0*g**2 = 0 for g.
0, 1
Let l be (3/16)/((-36)/(-8)). Let m(t) be the second derivative of 1/48*t**4 + 0 - 2*t - l*t**3 + 1/80*t**5 + 0*t**2 - 1/120*t**6. Find p such that m(p) = 0.
-1, 0, 1
Let f = 15 + -3. Factor 12*v**4 - 8*v**3 - 4 + 2*v**5 + 10*v - 4*v + 4*v**2 - f*v**4.
2*(v - 1)**3*(v + 1)*(v + 2)
Factor 143/3*l**2 - 15*l**3 - 20/3*l - 4.
-(l - 3)*(5*l - 2)*(9*l + 2)/3
Suppose 2*z - 9 = -z. Solve -3*b**4 + b**4 + 0*b - 5*b + 2*b**3 + z*b + 2*b**2 = 0 for b.
-1, 0, 1
Let l(y) be the second derivative of 1/9*y**3 + 1/18*y**4 + 0 - 2*y + 1/9*y**2 + 1/90*y**5. Factor l(g).
2*(g + 1)**3/9
Let w(h) be the second derivative of h**7/14 + 7*h**6/50 - 9*h**5/100 - 7*h**4/20 - h**3/5 + 8*h. Find k, given that w(k) = 0.
-1, -2/5, 0, 1
Let a(f) = -f**2 + 16*f - 11. Let r be a(15). Let b be r + 4/(-1) - 0. Factor 0*y + 2/11*y**2 + b.
2*y**2/11
Let h be (1/(-1))/(1/(-5)). Let v(x) be the third derivative of 0 - 1/240*x**h + 1/160*x**6 + 0*x**3 + 0*x - 2*x**2 + 0*x**4. Suppose v(c) = 0. Calculate c.
0, 1/3
Factor 4*b + 8*b**2 - 3/2.
(4*b - 1)*(4*b + 3)/2
Let h(p) be the third derivative of p**7/350 + 3*p**6/200 + p**5/100 - 3*p**4/40 - p**3/5 + 7*p**2. Find a, given that h(a) = 0.
-2, -1, 1
Let b(n) be the third derivative of -n**5/12 + 5*n**4/24 + 5*n**3 + 2*n**2. Solve b(t) = 0 for t.
-2, 3
Let y(r) = 3*r**3 - r**2 - r + 1. Let q be y(1). Let c be (3 - (q - 0))*2. Determine f so that -24/5*f**2 + 18/5*f + c*f**3 - 4/5 = 0.
2/5, 1
Let u(p) = 5*p**2. Let q be u(1). Determine k, given that k**2 + 0*k**3 + 1/2*k - 1/2*k**q - k**4 + 0 = 0.
-1, 0, 1
Let t(k) be the first derivative of 0*k - 2/3*k**3 - 1 + 2/5*k**5 - 1/6*k**6 + 0*k**4 + 1/2*k**2. Find i, given that t(i) = 0.
-1, 0, 1
Suppose -11 + 31 = 2*f. Solve -3*h**2 + 2*h**2 + f + 4*h - 14 = 0.
2
Factor -2/7*r**4 + 8/7*r**2 - 6/7*r**3 + 0 + 0*r.
-2*r**2*(r - 1)*(r + 4)/7
Suppose 11*l = 21*l - 30. Factor 0 + 0*x**2 + 2/7*x**l + 0*x.
2*x**3/7
Let y(f) = -f**2 - 1. Let i(r) be the second derivative of r**4/2 + 5*r**2/2 - 2*r. Let x(b) = 2*i(b) + 11*y(b). Factor x(l).
(l - 1)*(l + 1)
Let a(m) be the first derivative of -7*m**6/3 - 32*m**5/5 + 3*m**4/2 + 32*m**3/3 + 4*m**2 + 17. What is u in a(u) = 0?
-2, -1, -2/7, 0, 1
Let c(g) = g + 3. Let o be c(-3). Suppose 0 = 3*x + b - 4*b, -x - 2*b + 9 = o. Factor 1/4*f + 1/4*f**x + 1/2*f**2 + 0.
f*(f + 1)**2/4
Suppose -3*q + i = -i - 31, 3*i - 6 = -3*q. Suppose -4 = t - 2*a, -4*t + q + 7 = 2*a. Determine r, given that 2/7 - 2/7*r**t + 2/7*r - 2/7*r**3 = 0.
-1, 1
Let q(r) be the third derivative of r**5/20 - r**4/4 + r**3/2 - 5*r**2. Find n such that q(n) = 0.
1
Let v(x) = -10*x**5 + 20*x**4 - 14*x. Let h(k) = -2*k**5 + 4*k**4 - 3*k. Let f(w) = -28*h(w) + 6*v(w). Factor f(b).
-4*b**4*(b - 2)
Let o(v) be the third derivative of v**5/90 - v**4/9 + 4*v**3/9 + 14*v**2. Let o(b) = 0. Calculate b.
2
Suppose -16*h + 14 = -9*h. Let m(t) be the second derivative of 4*t**5 + 10/3*t**4 - 3*t + 0 + 16/21*t**7 + 8/3*t**6 + 1/2*t**h + 5/3*t**3. Factor m(q).
(2*q + 1)**5
Let o be (3 - (0 + 3 + -1))/5. Factor 0*j - o*j**2 + 2/5*j**3 + 3/5*j**4 + 0.
j**2*(j + 1)*(3*j - 1)/5
Suppose -14*n**2 + 4*n**4 + 6*n**3 - 10*n**3 - 12*n**3 - 6*n**4 = 0. What is n?
-7, -1, 0
Let 2/7*o**3 + 0*o - 4/7*o**2 + 0 = 0. What is o?
0, 2
Let m(i) be the first derivative of i**6/15 + 6*i**5/25 - 9*i**4/10 + 2*i**3/3 + 41. Suppose m(r) = 0. What is r?
-5, 0, 1
Let n be ((-3)/3)/(114 + -1). Let i = n - -5540/339. Factor -4/3*q + 0 + 32/3*q**2 + i*q**4 - 77/3*q**3.
q*(q - 1)*(7*q - 2)**2/3
Let f = 136 - 133. Let 0*r + 4/3*r**2 + 0 + 2/3*r**f = 0. Calculate r.
-2, 0
Suppose j - 6 = -g + 1, -4*j + 10 = -2*g. Factor 2*a**5 + a**j - a**5 + 95 - 95 - a**3 - a**2.
a**2*(a - 1)*(a + 1)**2
Factor 3/2*f**3 + 0*f**2 - 3/2*f + 0.
3*f*(f - 1)*(f + 1)/2
Let v(q) be the first derivative of 0*q + 1/24*q**6 + 1/12*q**3 - 1/16*q**4 + 0*q**2 - 1/20*q**5 - 1. Factor v(c).
c**2*(c - 1)**2*(c + 1)/4
Let j(h) = h**3 - h + 1. Let n(u) = 10*u**3 - 10*u + 11. Let d = -129 - -85. Let q(p) = d*j(p) + 4*n(p). Factor q(w).
-4*w*(w - 1)*(w + 1)
Let a = -6 - -9. Suppose -m + a + 2 = 0. Factor 9*t**3 - 4*t**3 - 6*t - m*t - 7*t**2 + 4 + 3*t.
(t - 2)*(t + 1)*(5*t - 2)
Let c(m) be the second derivative of 5*m**4/12 - 5*m**3/6 + 5*m. Solve c(d) = 0 for d.
0, 1
Let q be 176/468 - 4/26. Find y, given that -q*y**2 + 2/9 + 0*y = 0.
-1, 1
Let f(d) = -d**2 - d + 2. Let b(l) = 4*l**2 + 4*l - 8. Let u(m) = -2*b(m) - 9*f(m). Factor u(c).
(c - 1)*(c + 2)
Let a = 20 - 20. Suppose a + 2/5*b + 2/5*b**2 = 0. What is b?
-1, 0
Let p(v) = 20*v**2 - 104*v + 76. Let t(w) = 13*w**2 - 69*w + 51. Let d(f) = 5*p(f) - 8*t(f). Find a such that d(a) = 0.
1, 7
Let w(b) be the third derivative of -1/270*b**5 - 2*b**2 + 1/1512*b**8 + 1/945*b**7 + 0*b**4 + 0 + 0*b**3 + 0*b - 1/540*b**6. Factor w(q).
2*q**2*(q - 1)*(q + 1)**2/9
Let o(j) be the first derivative of j**3 - 15*j**2/2 + 12*j + 24. Find z such that o(z) = 0.
1, 4
Solve -114*v**2 - v**3 + 16 + 12*v + 114*v**2 = 0.
-2, 4
Let a be 11/((-22)/(-12)) - 2. Determine i, given that -12*i**3 - 8*i**4 - 8*i + 20*i**2 + i**4 + 4*i**5 + 3*i**a = 0.
-2, 0, 1
Let n = -818/91 + 64/7. Factor -4/13*d**2 - n*d**3 + 0*d + 0.
-2*d**2*(d + 2)/13
Let b = -2 - 0. Let h be (-57)/(-12) + b/(-8). Determine s so that h*s - 4 + 4*s**3 + s + 4*s**5 - 2*s**5 + 4*s**2 - 12*s**3 = 0.
-2, -1, 1
Let w(s) = -s**3 + s**2 + s. Let t be w(2). Let q be 8/6 - t/(-3). What is v in 2/9*v**2 - q*v + 4/9 = 0?
1, 2
Suppose 3*t - 11 = 4. Let c**2 + c**4 - 2*c**t + c**2 + 0*c**5 - 3*c**4 + 2*c**3 = 0. Calculate c.
-1, 0, 1
Let k(j) = -8*j**4 - 12*j**3 - 2*j**2 + 18*j + 7. Let m(l) = -l**4 + l**3 + l**2 + l - 1. Let s(o) = k(o) - 3*m(o). Factor s(z).
-5*(z - 1)*(z + 1)**2*(z + 2)
Let s be (-18)/(-2)*4/12. Let q(f) = 3*f - 4. Let a be q(s). Factor 2*i**3 + 7*i**a + 0*i**3 - 9*i**5.
-2*i**3*(i - 1)*(i + 1)
Let m = -364 + 368. Let c be 3/12*2 + 0. Factor 0*p**3 - 3/2*p**2 + 0 + c*p**m - p.
p*(p - 2)*(p + 1)**2/2
Let g be (-2)/(-7) + 10/(-35). Find f, given that 8*f - 2*f**3 + g*f**3 - 5*f - f = 0.
-1, 0, 1
Let p(s) = -5*s**2 + 60*s - 180. Let l(t) = 5*t**2 - 60*t + 180. Let d(n) = -7*l(n) - 6*p(n). Let d(v) = 0. What is v?
6
Let q(o) be the first derivative of 0*o**5 - 5 + 0*o + 1/12*o**4 - 1/12*o**2 - 1/36*o**6 + 0*o**3. Determine l so that q(l) = 0.
-1, 0, 1
Let v(i) = 2*i - 6. Let y be v(5). Factor -3*r**4 + y + 6*r**3 - 2*r - 4*r + r**4 - 2*r**2.
-2*(r - 2)*(r - 1)**2*(r + 1)
Factor 2*l**3 - 3*l - 7*l - l**3 + l**2 + 8*l.
l*(l - 1)*(l + 2)
Solve -9/2 + 3*w - 1/2*w**2 = 0.
3
Determine k so that -5*k**2 + 13*k**3 + 13*k**3 - 21*k**3 = 0.
0, 1
Let f(i) = 5*i**3 + 5*i**2 + 5*i. Let m(c) = c**2. Let y