*t**3 + 1/2*t.
t*(t + 1)**3/2
Let d(p) be the second derivative of p**5/190 - p**4/57 - 5*p**3/57 + 6*p**2/19 - 175*p. Suppose d(n) = 0. Calculate n.
-2, 1, 3
Let w(r) be the first derivative of 0*r + 2/55*r**5 - 2 + 0*r**2 - 2/33*r**3 + 0*r**4. Suppose w(a) = 0. Calculate a.
-1, 0, 1
Let a be 116/6 - (6 + (-174)/30). Let d = 58/3 - a. Factor -2/5*x**3 + 2/5*x + d - 1/5*x**2.
-(x - 1)*(x + 1)*(2*x + 1)/5
Let p = 435/5993 - -2/461. Let v = p - -21/65. Find t, given that v + 4/5*t + 7/10*t**3 - 19/10*t**2 = 0.
-2/7, 1, 2
Let s be ((-21)/((-147)/14))/1. Let i(r) be the second derivative of -3*r + 0*r**4 + 1/45*r**5 + 0 + 0*r**s + 1/27*r**7 - 1/15*r**6 + 0*r**3. Solve i(h) = 0.
0, 2/7, 1
Let l(v) be the second derivative of -121*v**6/75 + 11*v**5/50 + 16*v**4/5 - 12*v**3/5 + 110*v - 2. Suppose l(m) = 0. What is m?
-1, 0, 6/11
Suppose 0 = -7*p + 44 - 2. Suppose -z - z = -p*z. Find f such that -2/9*f**4 + 2/9 + 4/9*f**3 + z*f**2 - 4/9*f = 0.
-1, 1
Suppose 8707 + 4*v**5 - 12*v**4 - 48*v**2 - 8707 - 64*v**3 = 0. Calculate v.
-2, -1, 0, 6
Let v(c) be the second derivative of 1/48*c**4 + 4*c - 1/160*c**5 + 0 + 0*c**2 + 1/1440*c**6 + 2/3*c**3. Let h(z) be the second derivative of v(z). Factor h(j).
(j - 2)*(j - 1)/4
Let q = 7946 + -7944. Let 16/7*x - 2/7*x**q - 32/7 = 0. Calculate x.
4
Let w(v) = 167327*v**3 - 330653*v**2 - 7978*v - 48. Let d(f) = 55776*f**3 - 110218*f**2 - 2660*f - 16. Let b(q) = -7*d(q) + 2*w(q). Let b(r) = 0. What is r?
-2/167, 2
Let 9/8*a**4 - 9/2*a - 3/8*a**3 - 33/8*a**2 + 3/8*a**5 - 3/2 = 0. What is a?
-2, -1, 2
Suppose -30 = 37*w - 104. Let k(y) be the first derivative of -2*y**5 - 1/3*y**6 - 10 - 2*y**w - 9/2*y**4 - 14/3*y**3 + 0*y. Factor k(s).
-2*s*(s + 1)**3*(s + 2)
Let -103 + 249*r**2 - 726*r + 27*r**3 + 43 + 510*r = 0. What is r?
-10, -2/9, 1
Let n(m) be the second derivative of -m**4/60 - 13*m**3/30 - 14*m + 7. Determine r so that n(r) = 0.
-13, 0
Let c = 441141/13 + -33931. Determine n so that -c*n**2 - 10*n**4 + 114/13*n**3 + 4/13*n + 0 + 50/13*n**5 = 0.
0, 1/5, 2/5, 1
Let u(n) be the first derivative of 4*n**5/5 - 8*n**4/3 - 20*n**3/9 + 4*n**2 + 13. Let u(g) = 0. What is g?
-1, 0, 2/3, 3
Let m(n) = -n**3 - 2*n**2 + 5. Let c(g) = -g**4 - 3*g**3 + 9*g**2 + 7*g - 20. Let q(o) = c(o) + 4*m(o). Solve q(u) = 0 for u.
-7, -1, 0, 1
Let f = 114440/77 + -10396/7. Solve -2/11*n**2 + 2/11*n + f = 0.
-2, 3
Suppose 5*w - 4*l - 11 = 0, -3*w + 4*l + 1 = -4. Let 7*m**2 - 7*m**w + 2*m**2 + 4*m + 3*m**2 = 0. What is m?
-2/7, 0, 2
Let p(j) be the second derivative of -j**4/3 + 28*j**3/3 + 64*j**2 + 92*j. Factor p(x).
-4*(x - 16)*(x + 2)
Let b = -11/7 + 1/14. Let k = -1 - b. Factor 1/2*h - k*h**2 - 1/2*h**3 + 0 + 1/2*h**4.
h*(h - 1)**2*(h + 1)/2
Let c be (-5)/((-30)/(-18))*(-1 + -1). Let t(v) = 5*v**3 - 7*v**2 + v + 7. Let d(k) = -k**3 + k**2 - k - 1. Let b(i) = c*d(i) + 2*t(i). Let b(l) = 0. What is l?
-1, 1, 2
Factor -6*p**2 - 82 + 2*p**2 + 64 + 57 + 25.
-4*(p - 4)*(p + 4)
Let l(p) be the second derivative of 0*p**2 + 1/4*p**5 + 5/6*p**4 - 7*p + 0*p**3 + 0. Suppose l(v) = 0. Calculate v.
-2, 0
Suppose -5*m = -l + 358, 4*m + l + 242 = -39. Let i = -69 - m. Factor 6 + 2/3*v**i - 4*v.
2*(v - 3)**2/3
Let q(u) be the second derivative of 3/20*u**4 - 22*u - 2/5*u**3 - 6/5*u**2 + 1/50*u**6 + 3/25*u**5 + 0. Factor q(f).
3*(f - 1)*(f + 1)*(f + 2)**2/5
Let p = 146 + -80. Let j = p - 64. What is z in 0*z**3 - 1/2*z**j + 0*z + 1/2*z**4 + 0 = 0?
-1, 0, 1
Let s = 15 - 19. Let v = s - -6. Factor 2/7*m**v + 2/7*m + 0.
2*m*(m + 1)/7
Let i = 21683 + -21678. Suppose -25/2*c - 5/2*c**i + 25*c**2 + 5/2 - 25*c**3 + 25/2*c**4 = 0. Calculate c.
1
Find y, given that -18*y**5 - 381*y + 28*y**4 + 9*y**5 + 3500 + 152*y**3 - 1480*y**2 + 5*y**5 + 719*y + 1562*y = 0.
-7, -1, 5
Let y(w) be the first derivative of w**3/21 + w**2/14 - 35. Let y(m) = 0. Calculate m.
-1, 0
Suppose -w + 10 = w. Suppose -7*c - w*m = -3*c - 16, -5*c = -m - 20. Factor -3*j**3 - 4*j**2 + 2*j**2 + 4*j + 2*j**c - 2*j**2 + j**5.
j*(j - 1)**2*(j + 2)**2
Let x(j) be the third derivative of j**8/60480 - j**7/2520 - 7*j**6/2160 + 7*j**5/12 - 2*j**2. Let q(d) be the third derivative of x(d). What is f in q(f) = 0?
-1, 7
Let b(f) be the third derivative of f**6/24 + 7*f**5/12 + 35*f**4/12 + 20*f**3/3 + 17*f**2 - 1. Factor b(y).
5*(y + 1)*(y + 2)*(y + 4)
Solve 34*l + 18 + 40*l**2 + 32 - 14 - 42*l**2 = 0.
-1, 18
Let j = 2 + -11. Let z = j + 11. What is l in 0*l**2 - z*l**2 + 6*l**2 = 0?
0
Let m(d) be the second derivative of -d**5/20 + 5*d**4/6 + 23*d**3/6 + 6*d**2 - 2*d - 39. Factor m(s).
-(s - 12)*(s + 1)**2
Suppose -4*g = -5*c + g - 35, -3*c = 4*g - 7. Let k be c + (8 - (0 + 0)). Suppose 0 - 8/5*o**2 + 4/5*o + 0*o**3 - 4/5*o**k + 8/5*o**4 = 0. Calculate o.
-1, 0, 1
Factor -5*t**2 - 11*t**4 + 5*t**4 + 2542*t - 2617*t + 11*t**4 + 75*t**3.
5*t*(t - 1)*(t + 1)*(t + 15)
Determine k so that 4/5*k**2 - 76/5*k**3 + 0 - 16*k**4 + 0*k = 0.
-1, 0, 1/20
Let k(g) be the first derivative of -g**6/10 - 24*g**5/25 - 12*g**4/5 - 2*g**3/5 + 51*g**2/10 + 6*g + 56. What is n in k(n) = 0?
-5, -2, -1, 1
Let a(d) be the third derivative of -d**7/70 + d**6/10 + 3*d**5/10 - d**4/2 - 5*d**3/2 + 4*d**2 - 7*d. Factor a(t).
-3*(t - 5)*(t - 1)*(t + 1)**2
Let z(f) be the first derivative of 3*f**2 + 5/4*f**3 + 7 - 3*f. Suppose z(d) = 0. Calculate d.
-2, 2/5
Let m(v) = v**2 + 9*v - 3. Let z be m(-7). Let g = 21 + z. Let -12*o**5 + 167 - 16*o**2 - 167 + 28*o**g = 0. Calculate o.
-2/3, 0, 1, 2
Let k(j) be the first derivative of -2*j**3/3 - 127*j**2 + 256*j - 213. What is h in k(h) = 0?
-128, 1
Factor -36*v**2 + 5*v**3 + 27137*v**4 - 225*v + 141*v**2 - 27142*v**4.
-5*v*(v - 3)**2*(v + 5)
Let o be 9*(8/6 - (-2)/(-3)). Let m(a) be the first derivative of 0*a - 2/3*a**3 + 2/5*a**5 + a**2 + o - 1/2*a**4. Factor m(r).
2*r*(r - 1)**2*(r + 1)
Let q(y) be the third derivative of 1/30*y**5 + 4/3*y**3 + 0*y**4 + 0 + 0*y - 3*y**2. Let o(k) = 1. Let j(f) = 10*o(f) - q(f). Factor j(u).
-2*(u - 1)*(u + 1)
Let a = -6439/5 - -1291. What is i in -a*i**3 + 32/15*i + 6/5*i**4 - 28/15*i**2 - 2/5 = 0?
-1, 1/3, 3
Let f(j) = 101*j - 804. Let g be f(8). Factor -1/2*w**g + 0*w**2 + 0 + 1/2*w**3 + 0*w.
-w**3*(w - 1)/2
Let 40/3 - 13/3*c + 1/3*c**2 = 0. Calculate c.
5, 8
Let s(n) = n - 15. Let l be s(17). Factor 7*t**2 - 10*t**l - 3*t - 3*t.
-3*t*(t + 2)
Suppose t = -0*t + 18. Let b = 44 + -24. Factor -t - s + s + b - s**2 - s.
-(s - 1)*(s + 2)
What is m in -88*m + 162*m**4 + 238*m**3 - 2486*m**3 - 784*m**2 + 538*m**3 = 0?
-2/9, 0, 11
Let z(l) be the third derivative of l**8/1848 - 4*l**7/231 + 59*l**6/330 - 6*l**5/11 + 27*l**4/44 - 50*l**2. Factor z(h).
2*h*(h - 9)**2*(h - 1)**2/11
Let n(i) be the first derivative of 4/3*i**6 - 6*i**4 + 0*i + 2*i**2 + 2/5*i**5 + 39 + 10/3*i**3. Solve n(t) = 0 for t.
-2, -1/4, 0, 1
Suppose -20 = 6*z - 32. Let o(l) be the third derivative of 0*l**3 - l**z + 0*l + 0*l**4 + 0 + 1/100*l**5. Factor o(s).
3*s**2/5
Let s(n) be the first derivative of 0*n - 18/5*n**5 + 3*n**2 - 14 + 3/8*n**4 - 5/4*n**6 + 6*n**3. Determine j, given that s(j) = 0.
-2, -1, -2/5, 0, 1
Let z(m) be the first derivative of m**2 - 1/2*m**4 - 4*m - 15 + 4/3*m**3. Determine h, given that z(h) = 0.
-1, 1, 2
Let d = 4/69 + -329/4485. Let l = 53/65 + d. Factor 0*w**3 - 2/5*w**4 + 6/5*w**2 - l*w + 0.
-2*w*(w - 1)**2*(w + 2)/5
Let r(x) be the first derivative of -7 + 1/9*x**2 + 1/90*x**5 - x - 1/54*x**4 - 1/27*x**3. Let m(q) be the first derivative of r(q). Find l such that m(l) = 0.
-1, 1
Factor -24/5*o - 2/5*o**4 - 28/5*o**2 - 38/15*o**3 - 16/15.
-2*(o + 2)**3*(3*o + 1)/15
Find i, given that 23 - 945*i - 114*i**3 - 13*i**3 + 1800*i**2 - 373*i**3 + 112 = 0.
3/10, 3
Let k(q) be the first derivative of -2*q**5/55 - q**4/11 + 2*q**2/11 + 2*q/11 + 371. Suppose k(j) = 0. What is j?
-1, 1
Suppose -26*q + 5*q + 84 = 0. Suppose 3*g - 15 = q*k, 0 = -k - 2*k - 2*g + 10. Suppose -3/4*d**4 + k - 3/4*d + 3/4*d**2 + 3/4*d**3 = 0. What is d?
-1, 0, 1
Let k(s) be the first derivative of s**7/1365 - s**6/780 - s**5/195 + 4*s**2 + 3. Let x(z) be the second derivative of k(z). Factor x(d).
2*d**2*(d - 2)*(d + 1)/13
Let h(o) = -o + 1. Let r(q) = -8*q**2 - 32*q + 28. Let f be 1 - -2 - (-7 - -3). Let u = -8 + f. Let w(n) = u*r(n) + 20*h(n). Find m such that w(m) = 0.
-2, 1/2
Let s(d) be