). Let c = 27/2 - n. Factor -c*j**3 + 0*j + 1/4*j**2 + 1/4*j**4 + 0.
j**2*(j - 1)**2/4
Factor -8/9*n + 4/9 + 4/9*n**2.
4*(n - 1)**2/9
Let 0 + 0*d**3 + 2/9*d**5 + 0*d - 2/9*d**4 + 0*d**2 = 0. Calculate d.
0, 1
Factor 1/2*b**3 - 1/6*b**4 - 1/2*b + 0 + 1/6*b**2.
-b*(b - 3)*(b - 1)*(b + 1)/6
Solve -3/5 - 9*u**2 + 15*u**3 - 27/5*u = 0 for u.
-1/5, 1
Suppose 4*v - 5 = -3*w, 4*v + 0 = -2*w + 6. Let a be w/10*(-15)/6. Suppose -a - 1/4*n**5 - 1/2*n**3 + 3/4*n**4 - 1/2*n**2 + 3/4*n = 0. Calculate n.
-1, 1
Let d(z) be the first derivative of z**6/12 - 3*z**4/8 - z**3/3 - 24. Find k such that d(k) = 0.
-1, 0, 2
Let o(h) be the first derivative of -1/2*h**3 - 3 + 3/4*h**2 + 1/8*h**4 - 1/2*h. Find b such that o(b) = 0.
1
Suppose -16 = f + 26. Let p be (-2)/4*21/f. Factor 0 - p*b + 1/2*b**2.
b*(2*b - 1)/4
Let a(c) be the third derivative of -3/280*c**7 + 0 - 3*c**2 - 1/40*c**6 + 1/40*c**5 + 0*c + 1/8*c**3 + 1/8*c**4. What is n in a(n) = 0?
-1, -1/3, 1
Let n(m) be the second derivative of 1/6*m**4 + 0 - 1/20*m**5 + 0*m**2 + 0*m**3 - 4*m. Factor n(b).
-b**2*(b - 2)
Let i(f) be the second derivative of 0*f**4 - f**2 + 0 + 1/15*f**6 - 7*f + 1/5*f**5 - 2/3*f**3. Factor i(u).
2*(u - 1)*(u + 1)**3
Suppose 5*v + l - 24 = 0, 2*v - v = 5*l - 16. Determine w, given that 14*w**2 - 14*w**3 - 2*w**3 + 3*w + 2*w**3 - 7*w + 4*w**v = 0.
0, 1/2, 1, 2
Let t(f) be the third derivative of 3*f**7/70 + f**6/40 - f**5/10 + 4*f**2. Find n, given that t(n) = 0.
-1, 0, 2/3
Let c(u) = -3 + u**2 - u - 2 + 5. Let n(v) = v. Let f(k) = c(k) + n(k). Find t, given that f(t) = 0.
0
Let a(v) be the third derivative of -5*v**8/48 - 5*v**7/42 + 3*v**6/8 + 5*v**5/12 - 5*v**4/12 - 6*v**2. Solve a(f) = 0 for f.
-1, 0, 2/7, 1
Let w be (-1 + 1 - 1)/(3/(-6)). Let s(k) be the second derivative of 1/3*k**3 + 1/12*k**4 + 1/2*k**w - 2*k + 0. Factor s(u).
(u + 1)**2
Let y(c) be the third derivative of 3*c**5/20 + 7*c**4/24 - c**3/3 + 2*c**2. Solve y(n) = 0 for n.
-1, 2/9
Suppose -25 = 5*j, 3*v - j = 4*v + 5. Suppose v = -2*q - 0*q + 4. Find h, given that 2/5*h**q - 4/5 + 2/5*h = 0.
-2, 1
Let r be (8/16)/((-2)/(-12)). Suppose -5*k = -5*s, -r + 7 = -2*s + 4*k. Factor 15*x + 5*x + 0*x + 21*x**s - 2*x**3 - 7*x**4 + 4.
-(x - 2)*(x + 1)**2*(7*x + 2)
Suppose 3*x - 2016 = -x. Factor -38*h - x*h**2 + 308*h - 132*h**3 + 548*h**3 - 128*h**4 - 54.
-2*(h - 1)*(4*h - 3)**3
Let i = -1/17 - -20/51. Suppose -3*k + 9 = -0. Determine a, given that 2/3*a**5 - 4/3*a + 2/3*a**k - 4/3*a**2 + 5/3*a**4 - i = 0.
-1, -1/2, 1
Let k(s) be the third derivative of -1/1008*s**8 - 4*s**2 + 0*s**3 + 0*s - 1/60*s**6 + 1/45*s**5 - 1/72*s**4 + 0 + 2/315*s**7. Suppose k(u) = 0. Calculate u.
0, 1
Let o(l) be the third derivative of 4*l**2 - 1/40*l**6 + 0*l + 2*l**3 + 0 + 1/2*l**4 - 1/20*l**5. What is q in o(q) = 0?
-2, -1, 2
Let p be -3*(0 + -3)/(-9). Let w(s) = -3*s**4 - 8*s**3 - 5*s**2 + 2*s. Let v(i) = -i**3 - i**2 + i. Let k(a) = p*w(a) + 2*v(a). Factor k(d).
3*d**2*(d + 1)**2
Let t be (20/(-8)*1)/(15/(-12)). Let 2/5*q**t + 8/5*q + 8/5 = 0. What is q?
-2
Let o be 60/(-8)*(-6)/(-9). Let m be 4/((650/(-5))/o). Find s such that 0 - m*s**4 - 6/13*s**2 + 2/13*s + 6/13*s**3 = 0.
0, 1
Let k = -28 + 47. Determine l so that 33*l**4 + k*l**4 + 15*l**3 + 28*l**2 + 45*l**3 + 16*l**5 + 4*l = 0.
-1, -1/4, 0
Let y be -3 + 2 + 5/5. Suppose -3*h + 11 + 1 = y. Find f, given that 4/5*f**3 + 2/5*f**h + 0*f + 0 - 2/5*f**2 - 4/5*f**5 = 0.
-1, 0, 1/2, 1
Find j such that -8*j**2 + 12*j**4 - 4*j**5 + 12*j - 8*j**3 + 0 - 1 - 3 = 0.
-1, 1
Let m = -40 - -57. Factor 16*k**5 + 3*k**3 - 2*k - 5*k**4 - 3*k**4 - 42*k**3 - m*k**2.
k*(k - 2)*(k + 1)*(4*k + 1)**2
Factor 4/11 - 2/11*f**2 + 2/11*f.
-2*(f - 2)*(f + 1)/11
Let u = 5 + -1. Let x = 7 - u. Factor 6 + 2*f - 6 - f**x - f.
-f*(f - 1)*(f + 1)
Let y(q) be the second derivative of q**8/6720 - q**7/2520 + q**4/12 + 3*q. Let l(r) be the third derivative of y(r). Determine v, given that l(v) = 0.
0, 1
Let c(g) be the first derivative of 2*g**5/5 - 2*g**3 + 2*g**2 - 5. Find x, given that c(x) = 0.
-2, 0, 1
Let t = -324 + 326. Factor -12/7 - 3/7*c**t + 12/7*c.
-3*(c - 2)**2/7
Let j(l) = l**2 + 9*l + 2. Let s be j(-9). Factor -g**2 + 3*g**3 + 8*g**2 - 3*g - 7*g**s.
3*g*(g - 1)*(g + 1)
Let r be (0 + (-453)/(-12))*-2. Let v = r - -77. Find m, given that v*m**3 + 3/2*m**2 + 0 + 1/2*m + 1/2*m**4 = 0.
-1, 0
Suppose 22*b + 3*n = 20*b - 3, 4*n = -3*b - 4. Suppose 0 - 1/6*m**3 - 1/3*m**2 + b*m = 0. Calculate m.
-2, 0
Let o(c) be the third derivative of c**8/110880 + c**7/9240 + c**6/1980 - 2*c**5/15 - 3*c**2. Let p(g) be the third derivative of o(g). Solve p(m) = 0 for m.
-2, -1
Suppose 3*x - x = 8. Suppose -x*n = -o - 33, 39 = 6*n - n + o. Factor -2*l**2 + 0 - 8 + 0 + n*l.
-2*(l - 2)**2
Let h(u) = -u**2 - 4*u + 2. Let x be h(-4). Let b be (-62)/93*9/(-12). Factor 1/2 + c + b*c**x.
(c + 1)**2/2
Let j = 5 - 2. Let i = -4 + 7. What is c in j*c**3 - 6*c**3 + c**i = 0?
0
Find u, given that -2/9*u**2 - 4/9*u + 2/3 = 0.
-3, 1
Let c be ((-22)/4 - -4)/(-75). Let d(j) be the second derivative of 1/5*j**2 + c*j**5 - 4*j + 0 + 1/5*j**3 + 1/10*j**4. Factor d(t).
2*(t + 1)**3/5
Let h(y) = -2*y**3 - 82*y**2 + 240*y - 192. Let a(v) = v**3 + 27*v**2 - 80*v + 64. Let o(m) = 14*a(m) + 5*h(m). Suppose o(q) = 0. Calculate q.
2, 4
Let w(o) be the second derivative of 3/100*o**5 + 0 - 1/20*o**4 + 0*o**3 - 3*o + 0*o**2. Factor w(l).
3*l**2*(l - 1)/5
Let y(g) be the first derivative of 1/6*g**6 + 1/5*g**5 - 1/4*g**4 - 1/3*g**3 + 0*g**2 - 3 + 0*g. Suppose y(w) = 0. What is w?
-1, 0, 1
Let m(c) be the first derivative of -3*c**5/25 + 3*c**4/10 + 2. Let m(l) = 0. Calculate l.
0, 2
Let v(h) be the first derivative of -2*h**5/75 + 7*h**4/30 - 22*h**3/45 + h**2/3 + 2. Factor v(r).
-2*r*(r - 5)*(r - 1)**2/15
Let o be (-24)/(-9)*(-6)/(-4). Factor -4*b**2 + 2*b**2 - 2*b**5 + o*b**4 - 10*b**4 - 6*b**3.
-2*b**2*(b + 1)**3
Let j(i) = 3*i**3 - 3*i**2 + 6*i - 3. Let c(t) = 3*t**3 - 2*t**2 + 7*t - 4. Suppose s + 4*s + 20 = 0. Let b(y) = s*j(y) + 3*c(y). Factor b(q).
-3*q*(q - 1)**2
Let g = 347/35970 - -3/545. Let p(d) be the second derivative of 0 + g*d**4 - 1/110*d**5 + 1/33*d**3 - 1/11*d**2 + 3*d. Solve p(c) = 0 for c.
-1, 1
Let q(u) = -17*u + 222. Let x be q(13). Suppose c**2 - x + 1/3*c - 1/3*c**3 = 0. Calculate c.
-1, 1, 3
Suppose 6*h - h = 15. Suppose n**h - 27*n - 3*n**2 + 27*n = 0. What is n?
0, 3
Let j(c) be the third derivative of -c**6/360 - c**5/15 - 5*c**4/8 - 25*c**3/9 - 2*c**2 - 8. Factor j(p).
-(p + 2)*(p + 5)**2/3
Let u(t) be the first derivative of 3*t**4/10 - 22*t**3/15 + 6*t**2/5 - 4. Suppose u(w) = 0. What is w?
0, 2/3, 3
Let h(b) be the third derivative of -b**8/2688 - b**7/1680 + b**6/480 + b**2. Determine t, given that h(t) = 0.
-2, 0, 1
Let y = 7/18 + -1/18. Suppose 3*h = -5*l - 15, -h + 12 = 3*h - 4*l. Factor h - 1/3*v**3 + 0*v + 0*v**2 + 0*v**4 + y*v**5.
v**3*(v - 1)*(v + 1)/3
Let s = 3 + -3. Let d be s/(5 - 3 - -1). Solve -14/3*j**4 - 10/3*j**3 + 4/3*j**2 + 0*j + d = 0 for j.
-1, 0, 2/7
Suppose r + 2 = -4*l - 8, 2*r + 26 = -2*l. Let i be 1/(-2) - r/12. Factor -i*o**2 + 0 - 4/3*o.
-2*o*(o + 2)/3
Let m = 5 - 0. Let r(i) = -9*i**3 + i**2 + 8*i. Let w(c) = -26*c**3 + 2*c**2 + 24*c. Let d(u) = m*w(u) - 14*r(u). Find p such that d(p) = 0.
-2, 0, 1
Factor -1/5*v**3 + 8/5*v - v**2 + 48/5.
-(v - 3)*(v + 4)**2/5
Factor 1/4*x**3 + 0*x**2 + 0 + 0*x.
x**3/4
Let w(t) be the first derivative of 0*t + 5/14*t**4 - 6/35*t**5 - 1/7*t**2 - 2/21*t**3 + 3. Let w(r) = 0. Calculate r.
-1/3, 0, 1
Factor -3*s**5 - 5*s - 7*s + 9*s**4 - 27*s**4 - 39*s**3 - 36*s**2.
-3*s*(s + 1)**2*(s + 2)**2
Let g(m) = 4*m**3 + 4 + 3*m**2 + m**2 - 3*m**3 + 3*m. Let i be g(-3). Factor 0*q - i*q + 7*q + 3*q**2.
3*q*(q + 1)
Let y(r) be the second derivative of -r**5/4 + r**4/4 + r**3/3 - r. What is u in y(u) = 0?
-2/5, 0, 1
Factor -2/5*b**3 - 12/5*b**2 + 0 - 2*b.
-2*b*(b + 1)*(b + 5)/5
Let f(i) be the second derivative of -11*i**5/10 - 91*i**4/24 - i**3/3 + i**2 - i. Let f(u) = 0. What is u?
-2, -1/4, 2/11
Let j(b) = 3*b**3 - 2*b**2 - 3*b + 7. Let x(s) = s**3 - s + 1. Let c(y) = -j(y) + 5*x(y). Factor c(z).
2*(z - 1)*(z + 1)**2
Let m(y) = 2*y + 23*y**2 + 46*y**2 - y. Let f be m(-1). Factor 5*g**3 - 13*g**2 - g - f*g**3 - 3 - 135*g**4 - 108*g**5 + 3.
-g*(3*g + 1)**3*(4*g + 1)
Let b(r) = 5*r