1, 1
Let h = -60615/11 - -5515. Factor 12/11*d**2 + 16/11*d**3 + h - 80/11*d + 2/11*d**4.
2*(d - 1)**2*(d + 5)**2/11
Let k(c) be the second derivative of c**4/6 - c**3/3 + 65*c**2/2 - 9*c. Let t(f) = -f**2 + f - 22. Let x(v) = 4*k(v) + 11*t(v). What is w in x(w) = 0?
-2, 3
Let d(c) = c**2 + 4*c - 26. Let h be d(-8). Factor -12*l**3 - 3*l**5 + 12*l**4 + 4*l - h*l + 2*l.
-3*l**3*(l - 2)**2
Let w = -34 - -52. What is n in 3*n + 5*n - 27*n**3 + 39*n**3 - 2*n**2 - w*n**2 = 0?
0, 2/3, 1
Solve 0 + 72*i**2 - 50/7*i**5 - 56*i + 118/7*i**3 - 180/7*i**4 = 0 for i.
-14/5, 0, 1
Factor -1/8*z**2 + 1/4 + 1/8*z.
-(z - 2)*(z + 1)/8
Suppose -5*k + 0 = -2*y - 26, 2*y + 3*k + 42 = 0. Let u be 1 - (-14)/y - 18/(-648). Find g, given that -g - u*g**2 - 1 = 0.
-2
Let k(a) = a**3 + 2*a**2 - a - 3. Let h(v) = 5*v**3 + 10*v**2 - 7*v - 12. Let x(r) = 3*h(r) - 12*k(r). Determine m, given that x(m) = 0.
-3, 0, 1
Let l = -164 + 344. Determine x so that 128*x - l*x**2 - 122*x**3 - 15 - 202*x**3 - 1 = 0.
-1, 2/9
Let d(i) = i + 13. Let a be d(-10). Let o be a/(2/12*9). Factor -m**2 - 3*m**o + 96*m**3 + 12*m**2 - 129*m**5 + 330*m**4 + 371*m**5.
2*m**2*(m + 1)*(11*m + 2)**2
Let d(a) be the third derivative of 2*a**6/105 - a**5/3 + 26*a**4/21 - 2*a**3 - 3*a**2 - 9*a. Determine f so that d(f) = 0.
3/4, 1, 7
Let a(d) = d**2 + 3*d - 1. Let o be a(-4). Suppose -4*b = 8*b - 60. Let -6*m**4 + o*m**b + 4*m**3 - m**3 + 0*m**3 = 0. What is m?
0, 1
Let c(b) be the second derivative of -2/3*b**3 + 1/20*b**5 + 0 + 3*b - 1/3*b**4 + 0*b**2 + 1/30*b**6. Factor c(n).
n*(n - 2)*(n + 1)*(n + 2)
Let u = -10836/13 - -61824/65. Suppose -1/5*x**3 - 2744/5 - u*x - 42/5*x**2 = 0. Calculate x.
-14
Factor 3/7*r**2 + 5547/7 - 258/7*r.
3*(r - 43)**2/7
Suppose t + 4*l = -l + 25, -5*t + 10 = 2*l. Let p(v) be the third derivative of 0*v**4 - 4*v**2 + 0*v**3 + 0*v + t + 1/15*v**5. Determine c so that p(c) = 0.
0
Factor -83/2*n**2 + 0 - 41*n - 1/2*n**3.
-n*(n + 1)*(n + 82)/2
Suppose 0 = 5*r - 7 - 18. Determine b, given that 4*b**2 - 2 + r*b + 3 + 1 + 0 + b**3 = 0.
-2, -1
Let u(r) = -2*r**2 - 27*r + 144. Let x(l) = -l**2 - 3*l. Let b(m) = -m. Let f(j) = 2*b(j) - x(j). Let g(y) = -12*f(y) - 4*u(y). Factor g(p).
-4*(p - 12)**2
Suppose -v - 5 = -6*u + 11*u, 5*v + 2*u + 2 = 0. Let l = -73 + 367/5. Factor v - l*g**3 + 0*g + 4/5*g**2.
-2*g**2*(g - 2)/5
Let t = -1630/63 + 238/9. Let r be (-2 - -4) + 0 + (-6 - -6). Let -t + 2/7*v + 2/7*v**r = 0. Calculate v.
-2, 1
Let j(b) be the second derivative of b**5/5 + b**4 - 8*b**2 - 3*b + 3. Suppose j(o) = 0. What is o?
-2, 1
Let o be (-14160)/(-3600) - (-7)/5. Let -8*b + 1/3*b**4 + 2*b**3 + 1/3*b**2 + o = 0. Calculate b.
-4, 1
Let x be 108/1350*60/8. Factor -x - 3/5*t**3 + 3/5*t + 3/5*t**2.
-3*(t - 1)**2*(t + 1)/5
Let q(k) = 4*k**2 + k - 1. Let b be q(1). Let l(n) = -n - 1. Let d be l(-3). Let 3*t**d - b*t**2 - 3*t**2 - t + 3*t + 2*t**3 = 0. What is t?
0, 1
Solve 102*z + 6*z**3 - 14*z**2 - 4*z**3 - 4*z**3 - 62*z**2 - 24*z**2 = 0 for z.
-51, 0, 1
Let a(y) be the first derivative of y**6/40 - 3*y**5/10 + 9*y**4/8 - 2*y**3 + 3*y**2/2 + 26. Let g(d) be the second derivative of a(d). What is z in g(z) = 0?
1, 4
Let a be ((-6)/(-4))/(1/2). Let c be ((-6)/14)/(6 + (-375)/50). Determine q, given that 0 - 6/7*q**2 - c*q**4 + 6/7*q**a + 2/7*q = 0.
0, 1
Suppose 175*m = -4*p + 173*m, -4*m = 16. Factor -3/4 + 5/2*g - 1/4*g**4 + 3/2*g**3 - 3*g**p.
-(g - 3)*(g - 1)**3/4
Suppose -3/7*k**4 + 225/7*k + 0 + 15/7*k**2 - 3*k**3 = 0. What is k?
-5, 0, 3
Let j be (5/15)/(4/24). Factor -5*u**3 - 250*u**2 + 265*u**j - 11*u + u.
-5*u*(u - 2)*(u - 1)
Let h(u) be the third derivative of 0 + 0*u + 0*u**4 - 1/30*u**5 + 5*u**2 - 1/3*u**3 + 1/180*u**6. Let d(q) be the first derivative of h(q). Factor d(c).
2*c*(c - 2)
Let r(b) = -2*b + 1 + 3 + 1 - b. Let y be r(1). Factor -6/5*n**3 + 0 + 16/5*n**y - 8/5*n.
-2*n*(n - 2)*(3*n - 2)/5
Let h = 5643 - 5640. Determine x so that -26/3*x**h - 2*x - 26/3*x**2 + 0 - 2*x**4 = 0.
-3, -1, -1/3, 0
Let h = -151/5 - -35. Factor h*f**2 + 16/5 - 4/5*f**3 - 36/5*f.
-4*(f - 4)*(f - 1)**2/5
Let n = 341/426 - 19/142. Let u(b) be the first derivative of -5 - b**2 - n*b**3 + 0*b - 1/8*b**4. Suppose u(t) = 0. Calculate t.
-2, 0
Let k(j) = -2*j**2 + 29. Let d(p) = -8*p**2 + 2*p + 119. Let x(z) = -6*d(z) + 26*k(z). Let x(i) = 0. Calculate i.
-5, 2
Let h(r) be the third derivative of 10*r**2 + 1/21*r**7 - 1/6*r**6 - 5/12*r**4 - 1/168*r**8 + 1/3*r**5 + 0*r + 1/3*r**3 + 0. Suppose h(m) = 0. Calculate m.
1
Let p(z) be the first derivative of z**5/25 + 2*z**4/5 - 3*z**3/5 + 161. Factor p(n).
n**2*(n - 1)*(n + 9)/5
Let g(i) be the third derivative of -i**6/60 - 107*i**5/30 + 217*i**4/12 - 109*i**3/3 + 2*i**2 - 57*i. Let g(x) = 0. Calculate x.
-109, 1
Let l(k) = k**5 - k**4 + k**2 + 1. Let f(s) = 10*s**5 - 12*s**4 + 4*s**3 + 15*s**2 + 11. Let p(m) = -2*f(m) + 22*l(m). Factor p(c).
2*c**2*(c - 2)*(c + 1)*(c + 2)
Let m = -3 - -7. Suppose 0 = i - m*i + 6. Factor 1/2*f + 3/2*f**i + 0.
f*(3*f + 1)/2
Suppose q = -4*q. Suppose i + 0 - 2 = q. Factor 4 - 6 + 4*y + 6*y**i + 3 + 4*y**3 + y**4.
(y + 1)**4
Factor 0 + 3/7*l**5 + 0*l + 15/7*l**4 + 3*l**3 + 9/7*l**2.
3*l**2*(l + 1)**2*(l + 3)/7
Let w(z) be the second derivative of z**6/60 - z**5/10 + z**4/6 + 31*z**2/2 + 38*z. Let v(x) be the first derivative of w(x). Factor v(g).
2*g*(g - 2)*(g - 1)
Let f(b) be the third derivative of -b**7/1680 + b**6/360 + b**5/80 - b**3/2 + 18*b**2. Let t(q) be the first derivative of f(q). Determine d so that t(d) = 0.
-1, 0, 3
Find r such that -r**3 + r - 1/4*r**4 + 3/2*r**2 - 5/4 = 0.
-5, -1, 1
Factor c**3 - 42*c**2 - c**3 - 5*c**3 - 38 + 2*c - 80*c + 3*c**3.
-2*(c + 1)**2*(c + 19)
Suppose -320*t = -319*t. Suppose -4*a = -7*f + 3*f - 8, t = -2*f + a. Solve 1/4*q**f + 1 - q = 0 for q.
2
Let p be (-16)/(-64) + (-18)/8 + (-36)/(-14). Factor p*i**2 + 0 - 4/7*i.
4*i*(i - 1)/7
Factor -12/5 + 9/5*t**2 + 3/5*t**4 - 3*t**3 + 3*t.
3*(t - 4)*(t - 1)**2*(t + 1)/5
Let f = -56 - -66. Factor f*p**2 + 0*p**4 + 14*p**3 - 7*p**3 + 5*p**4 + 8*p**3.
5*p**2*(p + 1)*(p + 2)
Let y(p) be the second derivative of -5*p**9/1512 - p**8/336 + p**7/168 - 2*p**3/3 + 16*p. Let t(m) be the second derivative of y(m). Factor t(w).
-5*w**3*(w + 1)*(2*w - 1)
Let h(w) = -w**2 - 8*w - 2. Let s be h(-7). Factor -10*y**4 + 15*y**3 - 5*y**2 + 18*y**2 - 13*y**2 - 5*y**s.
-5*y**3*(y - 1)*(y + 3)
Solve 12*v - 39*v**3 + 2*v**4 - 26*v**2 + 55*v**3 + 2*v**4 - 6*v**4 = 0.
0, 1, 6
Let q(f) be the second derivative of 0*f**4 + 2/75*f**6 - 2/25*f**5 - 22*f - 2/5*f**2 + 4/15*f**3 + 0. Determine h, given that q(h) = 0.
-1, 1
Let g(h) be the third derivative of -13*h**6/10 - 157*h**5/15 - 80*h**4/3 - 8*h**3/3 - 521*h**2. Factor g(s).
-4*(s + 2)**2*(39*s + 1)
Let 1/2*a**4 + 2*a - 9/2*a**2 + 0 + 3/4*a**3 = 0. What is a?
-4, 0, 1/2, 2
Let z(u) be the second derivative of 1/39*u**6 + 8/39*u**3 - 7/130*u**5 + 25*u - 4/13*u**2 - 1/273*u**7 - 1/78*u**4 + 0. Find x such that z(x) = 0.
-1, 1, 2
Let u(w) be the second derivative of -w**8/336 + w**7/168 + w**6/36 + w**3/6 + 7*w. Let d(g) be the second derivative of u(g). Suppose d(r) = 0. What is r?
-1, 0, 2
Let i be ((-888)/518)/(-2 + (-878)/(-448)). Determine v, given that 52*v**3 - i + 16/3*v**4 + 128*v + 472/3*v**2 = 0.
-4, -2, 1/4
Let b(v) = v**2 + 73*v + 214. Let g be b(-3). Suppose c**2 - 1/4*c**g + c + 0 - 1/4*c**3 = 0. What is c?
-2, -1, 0, 2
Let q(m) be the second derivative of m**4/16 + 9*m**3/8 - 33*m**2/4 - 569*m. Let q(u) = 0. What is u?
-11, 2
Let o = -15 + 18. Let k(c) = -2 - 2*c**o - 3*c**3 - 3 - c - 3*c**4 + 4. Let g(u) = -u**4 - u**3 - u - 1. Let w(h) = -g(h) + k(h). Factor w(f).
-2*f**3*(f + 2)
Let l be 69/21 - 4/14. Factor 54*c**l + 3*c**4 - 90*c**3 - 11*c**4 - 12*c**2 + 16*c.
-4*c*(c + 1)*(c + 4)*(2*c - 1)
Let f(v) be the third derivative of v**7/504 - v**6/72 - 5*v**4/24 - 10*v**2. Let z(m) be the second derivative of f(m). Factor z(n).
5*n*(n - 2)
Let s(m) = -m**2 - 13*m + 9. Let y be s(-14). Let q(n) = -n**3 - 5*n**2 - 2*n - 7. Let c be q(y). Factor 9*o - o**c - 39 + 4*o**3 + 15*o**2 + 12.
3*(o - 1)*(o + 3)**2
Suppose 0 = 53*a - 55*a. Factor -1/2*g**5 + g**3 + 0*g**4 + 0*g**2 - 1/2*g + a.
-g*(g - 1)**2*(g + 1)**2/2
Suppose 23 = h + 5*q, -5*h - 61*q = -56*q - 35. Solve 3/5*r**h - 3/5*r + 0*r**2 + 0 = 0 fo