e second derivative of 3*r**5/160 - r**4/32 - 8*r. Factor y(c).
3*c**2*(c - 1)/8
Let i(z) = z**3 + z**2 - z + 1. Let x be i(1). Determine y, given that x*y**2 - 9*y**4 + 12 + y**2 + 24*y**2 - 6*y**3 + 36*y = 0.
-1, -2/3, 2
Let c(q) be the third derivative of q**5/60 + 5*q**4/24 + 2*q**3/3 + 2*q**2. Suppose c(n) = 0. Calculate n.
-4, -1
Let u = 7 + -2. Let s(d) be the third derivative of -5/24*d**4 + 1/6*d**3 + 7/120*d**7 + 0*d + 0 + 2*d**2 + 7/48*d**6 - 1/80*d**u. What is t in s(t) = 0?
-1, 2/7
Let f(i) be the third derivative of i**6/420 - 2*i**5/105 + i**4/21 - 28*i**2. Let f(p) = 0. Calculate p.
0, 2
Determine z, given that -4/3*z**2 + 14/3*z**4 + 10/3*z**3 + 0*z + 0 = 0.
-1, 0, 2/7
Let x(u) be the second derivative of -4/21*u**4 - 8/21*u**3 + 0 + 10*u - 2/7*u**2. Factor x(w).
-4*(2*w + 1)**2/7
Suppose -5*j + 19 + 16 = 0. Determine t so that 27 + 3*t + 3*t**2 + 8*t + j*t = 0.
-3
Factor -23*c - 3*c**3 + c**2 + 3*c**2 + 22*c.
-c*(c - 1)*(3*c - 1)
Let r(g) be the first derivative of g**6/45 - 2*g**5/75 - g**4/15 + 4*g**3/45 + g**2/15 - 2*g/15 - 2. Find x such that r(x) = 0.
-1, 1
Let f(o) = o**2 + 15*o + 49. Let s be f(-11). Let i(t) be the third derivative of -1/18*t**3 + 0*t + 0 - 2*t**2 - 1/180*t**s - 1/36*t**4. Solve i(k) = 0 for k.
-1
Let l(z) be the second derivative of 0*z**2 - 2/9*z**3 + 5/18*z**4 + z + 11/30*z**5 + 5/21*z**7 + 0 - 29/45*z**6. Let l(f) = 0. What is f?
-2/5, 0, 1/3, 1
Find s, given that 2*s**2 + 2*s + 29 - 29 = 0.
-1, 0
Let r(u) be the first derivative of -u**8/560 + u**7/70 - u**6/20 + u**5/10 - u**4/8 - 2*u**3/3 + 4. Let x(w) be the third derivative of r(w). Factor x(g).
-3*(g - 1)**4
Suppose -12/11*u + 18/11 + 2/11*u**2 = 0. What is u?
3
Let c = 2/449 + 1337/2245. Find w, given that 3/5*w**2 + 3/5*w - c*w**4 + 0 - 3/5*w**3 = 0.
-1, 0, 1
Let h = -15/2 - -47/6. Determine b, given that -1/3*b**2 + h*b + 0 = 0.
0, 1
Let u(s) be the first derivative of s**6/15 - s**4/5 + s**2/5 + 6. Factor u(n).
2*n*(n - 1)**2*(n + 1)**2/5
Let g(f) be the second derivative of -f**7/10080 + f**6/960 + f**4/12 + 4*f. Let t(q) be the third derivative of g(q). What is z in t(z) = 0?
0, 3
Let o(q) = q**3 + 18*q**2 + 29*q - 48. Let c be o(-16). Suppose -9/7*g**2 + 2/7*g + c + 4/7*g**3 = 0. Calculate g.
0, 1/4, 2
Factor -12*g - 4 + 5*g**2 - 13*g**2 - 73*g**4 + 8*g**3 + 85*g**4 + 4*g**5.
4*(g - 1)*(g + 1)**4
Let n(p) = p**3 + 9*p**2 + 8*p + 8. Let a be n(-8). Let b be (a/20)/(12/10). Factor -1/3*j - 1/3 + 1/3*j**3 + b*j**2.
(j - 1)*(j + 1)**2/3
Let -7*x**2 - 5*x**3 - 9*x**4 + 5*x**5 + 2*x**2 + 14*x**4 = 0. What is x?
-1, 0, 1
Let t(u) be the third derivative of u**9/3780 - u**8/840 + u**7/630 + u**4/12 + 8*u**2. Let j(y) be the second derivative of t(y). Factor j(f).
4*f**2*(f - 1)**2
Let a(x) be the third derivative of -4*x**2 - 1/3*x**3 + 0*x + 0 - 5/12*x**4 - 2/15*x**5. Factor a(r).
-2*(r + 1)*(4*r + 1)
Let n(k) = -k**2 - 5*k + 8. Let w be -1 + -1 + (1 - -3). Let v(p) = 6*p + 3 + 8*p**w - 7*p**2 - 12. Let f(y) = 7*n(y) + 6*v(y). Solve f(z) = 0.
-1, 2
Suppose -2/9*r**2 - 16/9 - 4/3*r = 0. Calculate r.
-4, -2
Let z(i) be the second derivative of 0 + 1/15*i**5 + 1/3*i**2 - 1/2*i**3 + 1/12*i**4 + 2*i. Factor z(d).
(d - 1)*(d + 2)*(4*d - 1)/3
Factor 0*k + 0 + 2/7*k**2.
2*k**2/7
Suppose 21 = -6*c + 51. Factor 4*r**2 + 8*r**2 - 4*r**3 - c*r - 7*r + 4.
-4*(r - 1)**3
Find l, given that -2*l - 16*l**2 - 6*l + 6*l**4 - 8*l**4 - 10*l**3 = 0.
-2, -1, 0
Let l be 0/1 + 42/21. Let s(b) be the third derivative of 1/150*b**5 + 0 + 0*b - 1/15*b**3 + 1/300*b**6 - 2*b**l - 1/60*b**4. Suppose s(x) = 0. What is x?
-1, 1
Let k be 16/(-56)*(3 + -17). Find a, given that 0*a + 0*a**3 + 1/3*a**2 - 1/3*a**k + 0 = 0.
-1, 0, 1
Let r = 439/4 - 108. Factor 3/4*m**5 - 1/4 + 1/2*m**3 - 5/4*m + r*m**4 - 3/2*m**2.
(m - 1)*(m + 1)**3*(3*m + 1)/4
Let u(r) = 5*r**3 - 10*r**2 + 20*r + 5. Let x(b) = 5*b**3 - 9*b**2 + 22*b + 6. Let q(l) = 6*u(l) - 5*x(l). Factor q(m).
5*m*(m - 2)*(m - 1)
Factor -2 + r**2 - 2*r**2 + 6*r**2 - 3.
5*(r - 1)*(r + 1)
Let w(y) be the second derivative of y**5/20 - y**4/2 + y**2 + 9*y. Let p be w(6). Factor -2/3*k**p + 2/3 + 8/3*k**3 - 8/3*k.
2*(k - 1)*(k + 1)*(4*k - 1)/3
Determine n, given that 4/3*n**3 - 4*n + 0*n**2 + 8/3 = 0.
-2, 1
Let m(w) be the third derivative of -1/21*w**5 - 2*w**2 + 5/84*w**4 + 1/1176*w**8 + 0 + 0*w - 1/21*w**3 - 1/147*w**7 + 1/42*w**6. Factor m(s).
2*(s - 1)**5/7
Suppose -24 = 3*b - 9*b. Let f(x) be the third derivative of 0*x**3 + 0*x + 0 - 1/6*x**4 + 1/30*x**5 - b*x**2. Let f(p) = 0. What is p?
0, 2
Let n(r) be the second derivative of 0*r**3 + r + 0*r**5 - 1/5*r**6 + 1/14*r**7 + 0*r**2 + 0*r**4 + 0. Let n(z) = 0. What is z?
0, 2
Let j(h) be the third derivative of 2*h**7/105 - 3*h**6/40 - h**5/6 + h**4/8 + 35*h**2. Let j(o) = 0. What is o?
-1, 0, 1/4, 3
Let n(p) be the second derivative of -p**7/210 - p**6/75 + p**4/30 + p**3/30 + 3*p. Suppose n(h) = 0. What is h?
-1, 0, 1
Let c(t) = t**2 + t - 1. Let k(d) = -2*d**2 - d - 12. Let b(x) = -6*c(x) - 2*k(x). Factor b(m).
-2*(m - 3)*(m + 5)
Suppose 43 - 3 = -5*w. Let c be ((-5)/(-30))/((-2)/w). Factor -x**3 - 2/3 + c*x**2 + x.
-(x - 1)*(x + 1)*(3*x - 2)/3
Suppose -100 = 8*t - 116. Suppose -2/3*b + 0 - 2*b**2 - 2/3*b**4 - t*b**3 = 0. Calculate b.
-1, 0
Let d(g) = 4*g**2 + g. Let o be d(-1). Let x = o - 2. Factor 2*i + x + 4*i**4 - 6*i**4 + i**4 - 2*i**3.
-(i - 1)*(i + 1)**3
Suppose -5 - 27 = -4*q. Suppose 11*n**3 - 8*n - 10*n**4 + 15*n**3 - q*n**2 + 0*n**4 = 0. Calculate n.
-2/5, 0, 1, 2
Let o be (-4)/12 + (-2)/3. Let u = 2 - o. Factor 3 - 3 + 2*w**4 + 4*w**u + 2*w**2.
2*w**2*(w + 1)**2
Let j(v) be the third derivative of v**5/240 + v**4/96 - v**3/4 - 2*v**2 + 2. Factor j(h).
(h - 2)*(h + 3)/4
Find b such that 0*b**4 - 3*b**2 + b**2 - b**5 + 0*b**4 + 2*b**4 + b = 0.
-1, 0, 1
Suppose 4*n = 2*a - 16, a + 0*a = -2*n. Let s be 20/9 + a/(-18). Solve -2*h - 7*h**2 + 10*h**2 - s + 1 = 0 for h.
-1/3, 1
What is p in -46*p + 44*p - 2*p**3 + 5*p**2 - p**2 = 0?
0, 1
Let o = 30 - 28. Let u(w) be the third derivative of 2*w**o + 0*w**3 + 0*w - 1/120*w**5 + 0 + 1/24*w**4. What is d in u(d) = 0?
0, 2
Let b(k) = -k + 13. Let s be b(13). Suppose 0*c**2 - 1/2*c + 1/2*c**3 + s = 0. What is c?
-1, 0, 1
Let y(v) = -4*v**2 + 3*v**2 + 11 + 8*v - v**2 + v**2. Let j be y(9). Factor 2 - 2*p + 1/2*p**j.
(p - 2)**2/2
Factor 2*u**5 - 3*u + 0*u**5 - 6*u**2 + u**5 + 3*u**4 + 3*u**4.
3*u*(u - 1)*(u + 1)**3
Suppose 123*i - 143*i + 60 = 0. Factor 0*w**2 - 1/2 + w**i - w + 1/2*w**4.
(w - 1)*(w + 1)**3/2
Suppose 0 = 4*n - 17 + 9. Let w(j) be the first derivative of 1/30*j**5 + 1 + 1/18*j**3 + 0*j**n - 1/12*j**4 + 0*j. Factor w(g).
g**2*(g - 1)**2/6
Let p be -1*(-1 - 0) + 55. Let l be (-2)/7 + 16/p. What is t in 2*t + l*t**3 - 4*t - 3*t**2 - t**3 = 0?
-2, -1, 0
Factor 2/11*d**2 + 4/11*d - 6/11.
2*(d - 1)*(d + 3)/11
Factor 0 + 0*d + 0*d**2 + 2/5*d**3.
2*d**3/5
Let n = 1053 + -1051. Determine p so that -1/2 + 11/4*p**3 + 3/2*p**4 - 5/4*p + 1/2*p**n = 0.
-1, -1/2, 2/3
Let z(m) = 12*m**5 + 53*m**4 + 60*m**3 + 27*m**2 + 5*m. Let n(i) = -13*i**5 - 52*i**4 - 60*i**3 - 28*i**2 - 5*i. Let x(w) = -3*n(w) - 2*z(w). Factor x(g).
5*g*(g + 1)**3*(3*g + 1)
Let u(l) be the first derivative of 2/21*l**3 + 1/14*l**4 + 3 + 0*l**2 + 0*l. Suppose u(g) = 0. What is g?
-1, 0
Let r(z) be the third derivative of -z**7/1365 - z**6/780 + z**5/390 + z**4/156 - 6*z**2. Factor r(i).
-2*i*(i - 1)*(i + 1)**2/13
Let d(o) = -o + 5. Let h be d(0). Let j = -5 + h. Let 0*x + j + 1/3*x**2 - 1/3*x**3 = 0. Calculate x.
0, 1
Let a(k) be the second derivative of -2*k**6/75 + k**5/25 + k**4/3 + 2*k**3/5 + 6*k. Solve a(f) = 0.
-1, 0, 3
Let l(p) = -2*p. Let r be l(-3). Let h be (-40)/64*r/(-5). Solve -5/4*o + 5/4*o**3 + h*o**2 + 1/4 - o**4 = 0.
-1, 1/4, 1
Suppose 2*g + 4*a + 4 = 2*a, -4*g + 4 = -2*a. Factor -1/2*n**2 + g*n**3 + 1/2*n**4 + 0*n + 0.
n**2*(n - 1)*(n + 1)/2
Let f(x) be the first derivative of -x**4/8 - 7*x**3/6 - 7*x**2/2 - 4*x - 9. Suppose f(t) = 0. What is t?
-4, -2, -1
Suppose -3*k - 2*w = -0*k - 7, 5*k = -3*w + 13. Factor -2*c**2 + 6*c - 2*c**4 - c**3 + c + k*c**2 - 1 - 6*c.
-(c - 1)*(c + 1)**2*(2*c - 1)
Let l(f) be the first derivative of -2*f**2 + 0*f + 3 + 14/3*f**3. Factor l(d).
2*d*(7*d - 2)
Let i(c) be the third derivative of -c**6/80 - 7*