u be s/((-48)/(-9))*-4. What is v in -v**3 - 2*v + 3*v**4 + 2*v**u - v**2 - 2*v**4 + v = 0?
-1, 0, 1
Let g(y) be the second derivative of 0 - 3/20*y**5 + 3/2*y**2 - 1/4*y**4 + 1/2*y**3 - 2*y. Determine k, given that g(k) = 0.
-1, 1
Let z(m) be the third derivative of -m**8/2520 - m**7/630 - m**6/540 - m**3/6 + 2*m**2. Let l(r) be the first derivative of z(r). Determine o so that l(o) = 0.
-1, 0
Let v(d) be the first derivative of d**6/180 - d**5/90 - d**4/36 + d**3/9 + d**2 + 5. Let g(j) be the second derivative of v(j). Factor g(r).
2*(r - 1)**2*(r + 1)/3
Suppose 0 = 6*t - 5*t + 7. Let b = 37/5 + t. Solve -b*k**3 + 0*k + 0 - 2/5*k**4 + 0*k**2 = 0 for k.
-1, 0
Let n be (-19)/(-10*2/(-44)). Let u = 1483/35 + n. Let 2/7*q**2 - 6/7*q + u = 0. What is q?
1, 2
Let w = 29/26 + -8/13. Suppose w - 1/2*r**2 + 1/4*r**3 - 1/4*r = 0. Calculate r.
-1, 1, 2
Let v(w) be the first derivative of -5*w**4/12 - 20*w**3/3 - 40*w**2 - 320*w/3 + 15. Factor v(i).
-5*(i + 4)**3/3
Let l(k) be the first derivative of 4/15*k**2 + 8/15*k + 2/45*k**3 + 1. Factor l(s).
2*(s + 2)**2/15
Solve 3/4*i**2 + 1/4 + 3/4*i + 1/4*i**3 = 0.
-1
Find k, given that 9/2 - 21/2*k**2 + 6*k**4 - 9*k**3 + 21/4*k + 15/4*k**5 = 0.
-2, -1, -3/5, 1
Let s(i) be the second derivative of -i**3/3 - 2*i**2 - 2*i. Let m be s(-4). Determine u so that -4*u**2 + 2*u**2 - 4*u + 4 - m = 0.
-2, 0
Let 9/4*h**2 + 0 + 3/2*h + 3/4*h**3 = 0. What is h?
-2, -1, 0
Factor -3*l + l**2 + 3*l - 2*l.
l*(l - 2)
Factor 18/5*d**2 + 8/5 - 24/5*d.
2*(3*d - 2)**2/5
Let 2*z + 20/9*z**2 + 2/3*z**3 + 4/9 = 0. What is z?
-2, -1, -1/3
Let r(j) be the first derivative of -j**6/6 - j**5/5 + j**4/4 + j**3/3 - 9. Factor r(d).
-d**2*(d - 1)*(d + 1)**2
Let k(y) be the third derivative of -y**7/105 - y**6/30 - y**5/30 - 9*y**2. Solve k(q) = 0.
-1, 0
Let g(o) = 2*o**3 - 29*o**2 + 60*o + 2. Let u be g(12). Factor 0 + y**4 + 2/5*y - 8/5*y**3 + 1/5*y**u.
y*(y - 1)**2*(5*y + 2)/5
Suppose -43*a**2 + 21*a**2 - 10*a + 17*a**2 = 0. Calculate a.
-2, 0
Factor 3*c**2 - 10*c - c**2 + 34*c + c**2 + 48.
3*(c + 4)**2
Suppose -k - k = -36. Let u = 27 - k. Factor 4 - 4*h - u*h - 18*h**2 - h.
-2*(h + 1)*(9*h - 2)
Let u = 11 + -7. Let z(r) be the first derivative of -1 + 0*r + 4/3*r**3 - 1/3*r**6 + 0*r**u + r**2 - 4/5*r**5. Factor z(f).
-2*f*(f - 1)*(f + 1)**3
Let n(v) = -2*v**3 - 12*v**2 - 6*v + 1. Let k(z) = z**3 + z + 1. Let s(t) = -3*k(t) + n(t). Factor s(d).
-(d + 1)**2*(5*d + 2)
Let b(n) be the second derivative of -n**5/16 - 5*n**4/48 + 5*n**3/24 + 5*n**2/8 + 27*n. Factor b(o).
-5*(o - 1)*(o + 1)**2/4
Let x(s) be the first derivative of s**4/12 + s**3/3 + s**2/2 + s/3 + 2. Find i, given that x(i) = 0.
-1
Let x = 1943/7 + -277. Let p = 2/21 + x. Let 0 - 5/3*z**4 + 0*z**2 - z**5 - p*z**3 + 0*z = 0. Calculate z.
-1, -2/3, 0
Let w = -7 + 9. Let o(j) be the third derivative of -1/525*j**7 + 2*j**w - 1/150*j**6 + 0*j**5 + 0 + 1/30*j**4 + 0*j + 1/15*j**3. Factor o(t).
-2*(t - 1)*(t + 1)**3/5
Let i(g) = -1. Let l(b) = -4*b**2 - 3. Let p(w) = -3*w**2 - 2. Let a(s) = -5*l(s) + 7*p(s). Let h(q) = -a(q) - i(q). Factor h(r).
r**2
Let v = 233/10 - 114/5. Suppose 0*k = -3*k + 6. Let 2*q + 3/2*q**k + v = 0. What is q?
-1, -1/3
Let a = 8 + -6. Suppose -o**3 + 5*o**5 + o**5 + 16*o**4 + 11*o**3 - a*o + 2*o**3 = 0. Calculate o.
-1, 0, 1/3
Let a = 5 - 5. Find l such that -2*l + 0*l + a*l - l**2 = 0.
-2, 0
Let x(c) be the first derivative of -c**6/14 + 6*c**5/35 + 3*c**4/28 - 2*c**3/7 - 11. Find y such that x(y) = 0.
-1, 0, 1, 2
Let x be 2 - (-1 + (-3 - 0)). Let y(a) be the second derivative of 1/4*a**2 - 1/6*a**3 + a - 1/60*a**x + 0*a**4 + 1/20*a**5 + 0. Factor y(h).
-(h - 1)**3*(h + 1)/2
Find k, given that 1/4*k**4 + 1 - 3*k - 3/2*k**3 + 13/4*k**2 = 0.
1, 2
Let v(u) be the third derivative of 2*u**7/105 + u**6/10 + u**5/15 - u**4/2 - 4*u**3/3 + 2*u**2 - 3*u. Factor v(f).
4*(f - 1)*(f + 1)**2*(f + 2)
Let r be (1 + -31)/(-5)*1. Let q(l) be the second derivative of 0*l**2 - 2/105*l**r + 0*l**4 + 1/70*l**5 + 0 + 0*l**3 + 3*l + 1/147*l**7. Solve q(o) = 0.
0, 1
Let u(x) = -5*x**2 + 11*x + 11. Let y = -6 - -8. Let i = y - 0. Let z(o) = -o**2 + 2*o + 2. Let p(n) = i*u(n) - 11*z(n). Factor p(c).
c**2
Let i = 1443/4 - 357. Factor 0 + 3/2*s - i*s**4 + 9*s**3 - 27/4*s**2.
-3*s*(s - 1)**2*(5*s - 2)/4
Solve 6/7*x**4 + 8/7*x + 4*x**2 - 26/7*x**3 - 16/7 = 0.
-2/3, 1, 2
Let w(n) be the third derivative of 0*n**4 + 1/315*n**7 + 0 + 2*n**2 + 0*n + 0*n**3 + 0*n**5 + 1/360*n**6 + 1/1008*n**8. What is r in w(r) = 0?
-1, 0
Determine n so that 324/5 + 4/5*n**2 + 72/5*n = 0.
-9
Let o(u) be the first derivative of -2*u**3 + 7*u**2/2 + 6*u + 2. Let z(x) = -3*x**2 + 3*x + 3. Let q(c) = 3*o(c) - 7*z(c). Factor q(a).
3*(a - 1)*(a + 1)
Let q(n) be the first derivative of -3*n**4/4 + 15*n**3 - 72*n**2 - 192*n - 41. Factor q(x).
-3*(x - 8)**2*(x + 1)
Suppose 0 = -3*r + 2*n - 10, 2*r + 4*n = 5*r + 20. Factor 1/4 - 1/4*b**2 + r*b.
-(b - 1)*(b + 1)/4
Let w(d) = d - 2. Let o be w(6). Factor -2*n + 4*n**2 - o*n**4 + 2*n**5 - 4 + 4.
2*n*(n - 1)**3*(n + 1)
Determine s so that -6/7*s + 2/7*s**2 + 4/7 = 0.
1, 2
Let p(r) = -r**2 - 43*r + 243. Let a be p(5). Factor 2*u**a - u - 7/2*u**2 + 0.
u*(u - 2)*(4*u + 1)/2
Let d(w) be the first derivative of 0*w**4 - 1/2*w**2 + 1/10*w**5 - 1/2*w**3 + 0*w + 5. Factor d(j).
j*(j - 2)*(j + 1)**2/2
Let p(r) be the third derivative of 4*r**7/2835 - r**6/405 + r**5/540 + r**4/12 - 2*r**2. Let h(q) be the second derivative of p(q). Factor h(l).
2*(4*l - 1)**2/9
Suppose 6 = -2*m - 10. Let t be m/28 - 60/(-14). Factor i - i + 2*i**t - 4*i**2 + 2*i**4 - 2*i**5 + 2*i.
-2*i*(i - 1)**3*(i + 1)
Factor -2/3*c**4 - 20/3*c**3 - 74/3*c**2 - 24 - 40*c.
-2*(c + 2)**2*(c + 3)**2/3
Let o(m) = m**2 - 4*m - 2. Let y(s) = 2*s**2 - 4*s - 1. Let g(t) = -3*o(t) + 2*y(t). Factor g(j).
(j + 2)**2
Let p = 1873/24 + -78. Let c(v) be the second derivative of 0*v**3 + 0 + 0*v**2 + 4*v - p*v**4. Find y, given that c(y) = 0.
0
Suppose -7 = -2*h + 3*s, -4*s = -3 - 1. Factor 9*w**4 + 7*w**3 + 2*w**3 + 3*w**2 + 0*w**3 + 3*w**h.
3*w**2*(w + 1)**3
Let i = 2/5 + 0. Factor 1/5*v**2 - i*v + 0.
v*(v - 2)/5
Let 2/9*a + 0 + 16/9*a**2 + 32/9*a**3 = 0. Calculate a.
-1/4, 0
Let p be (-429)/(-55) + 8/(-2). Let o(l) be the second derivative of 22/15*l**6 + 16/3*l**4 + 2*l**2 - p*l**5 - 5/21*l**7 + 0 - 13/3*l**3 + 2*l. Factor o(f).
-2*(f - 1)**4*(5*f - 2)
Let j = -104 - -106. Let -1/3*x**3 + 0 + 0*x**j + 1/6*x + 1/6*x**5 + 0*x**4 = 0. What is x?
-1, 0, 1
Let g(l) = -7*l**2 + 10*l. Let j(p) = 13*p**2 - 19*p. Let w(o) = 7*g(o) + 4*j(o). Solve w(m) = 0 for m.
0, 2
Let y(r) = 2*r**5 + r**4 - 6*r**3 + r**2 + 2*r - 3. Let s(t) = -3*t**5 - 3*t**4 + 12*t**3 - 3*t**2 - 3*t + 5. Let x(l) = -3*s(l) - 5*y(l). Factor x(o).
-o*(o - 1)**4
Let g(j) be the second derivative of -j**4/28 - j**3/14 - 4*j. Factor g(q).
-3*q*(q + 1)/7
Let a be 0/((-35)/(-7) + -4). Factor 0*c**3 + 1/6*c**4 + a + 0*c**2 + 0*c + 1/6*c**5.
c**4*(c + 1)/6
Factor 1721*k**3 - 4 - 1725*k**3 - 3*k**2 - 12*k - 9*k**2.
-4*(k + 1)**3
Let b(g) be the first derivative of g**7/1680 - g**6/360 + g**5/240 - g**3 - 1. Let d(u) be the third derivative of b(u). Determine l, given that d(l) = 0.
0, 1
Let n(p) be the second derivative of -p**7/14 + 3*p**5/10 - p**3/2 + p. Factor n(g).
-3*g*(g - 1)**2*(g + 1)**2
Suppose -591 = -5*w + 374. Let s = 1353/7 - w. Factor -4/7*h - 2/7 - s*h**2.
-2*(h + 1)**2/7
Let f(u) be the first derivative of 4*u**5/25 - u**4/2 + 8*u**3/15 - u**2/5 - 4. Find x, given that f(x) = 0.
0, 1/2, 1
Solve 53*z**3 + 3*z**4 - 11*z**4 - 4*z**5 - 57*z**3 = 0 for z.
-1, 0
Let r(h) be the third derivative of h**8/42 + 2*h**7/35 - h**6/30 - h**5/5 - h**4/6 + 9*h**2. Let r(f) = 0. Calculate f.
-1, -1/2, 0, 1
Let s(l) = -l - 6. Let w be s(-9). Let g be 4*(w + 26/(-9)). Let 2/9 - g*r + 2/9*r**2 = 0. Calculate r.
1
Factor 38/5*r**2 - 68/5*r + 16/5 + 14/5*r**3.
2*(r - 1)*(r + 4)*(7*r - 2)/5
Let v be -8*(-3)/(-6)*-1. Suppose 22 = 3*a + 2*a + n, -20 = -v*a - 2*n. Solve i**2 + 1/2 + i**3 + 1/2*i**5 - 3/2*i - 3/2*i**a = 0 for i.
-1, 1
Factor -10 + 2*x**2 + 42 + 0*x**2 + 16*x.
2*(x + 4)**2
Let n(b) be the second derivative of 3*b + 5/18*b**3 - 1/90*b**6 + 0 - 1/60*b**5 + 1/3*b**2 + 1/12*b**4. Let n(o) = 0. Calculate o.
-1, 2
Suppose 4*i = 33 - 13. Factor -3 - 7*l**2 + 2*l + l 