 0, 1
Let t(m) be the third derivative of -m**6/45 + m**5/60 + 5*m**4/72 + 54*m**2 - m. Factor t(g).
-g*(g - 1)*(8*g + 5)/3
Let j(p) = -2*p - 8. Let w be j(-4). Factor 8*k + 58*k**2 + w*k - 70*k**2.
-4*k*(3*k - 2)
Let k = -83 + 147. Let p be 1/7 + (k/42)/8. Find s such that -1/3 - p*s**4 + 1/6*s**5 + 2/3*s**2 + 1/6*s - 1/3*s**3 = 0.
-1, 1, 2
Let t be (-28 + 1)/((-2)/(-2)). Let k = -17 - t. Suppose -14*g**4 + 7 + 9*g**5 + 4*g**2 + 4*g**3 - 5 - k*g - 3*g**5 + 8*g**2 = 0. Calculate g.
-1, 1/3, 1
Factor 60*c**2 - 12*c**3 - 9*c - 13 - 20*c**2 - c**2 + 13.
-3*c*(c - 3)*(4*c - 1)
Let b(m) be the third derivative of -1/64*m**4 - 6*m**2 + 0*m - 1/480*m**5 + 0 + 0*m**3. Factor b(y).
-y*(y + 3)/8
Let i(n) = -2*n**3 - 10*n + 2. Let p(k) = -2*k**3 - k + 1. Let r(b) = -i(b) + 2*p(b). Factor r(y).
-2*y*(y - 2)*(y + 2)
Suppose 8*m + 7*m - 4*m = 0. Factor 0 + 1/6*v**2 + 1/2*v**3 + 1/2*v**4 + 1/6*v**5 + m*v.
v**2*(v + 1)**3/6
Find d such that -1/2*d**3 + 11*d - 3/2*d**2 + 12 = 0.
-6, -1, 4
Suppose 4*t + 1 = 9. Let u(x) = 2*x**3 - 2*x**2. Let k be u(t). Suppose -6 + 24*j**3 + 12*j**2 - k - 4*j**2 - 32*j - 2 - 9*j**4 = 0. What is j?
-2/3, 2
Let a be -5 - (5 - (4 - -9)). Let y(q) be the second derivative of 3/14*q**2 + 0 - a*q - 1/28*q**4 + 0*q**3. Determine p so that y(p) = 0.
-1, 1
Let o(z) = 21*z**2 - 22*z**2 + z - 2 + 2. Suppose -2 = -3*j - 5. Let k(d) = d**3 + 3*d**2 - 4*d. Let v(m) = j*k(m) - 3*o(m). Determine y so that v(y) = 0.
-1, 0, 1
Factor -92*v + 188*v - 3*v**2 + 180*v + 330*v - 71148 + 318*v.
-3*(v - 154)**2
Suppose -11*f - 180 = -7*f. Let t be (54/f)/(3/(-110)). Let 24*u**3 - 5*u**4 - 31*u**4 + 3*u + t*u**2 - 4*u - 16 - 15*u = 0. What is u?
-2/3, 1
Factor 0 - 88/7*n**2 + 2/7*n**3 + 0*n.
2*n**2*(n - 44)/7
Let w(n) be the second derivative of n**6/30 - 7*n**5/4 + 11*n**4/4 + 35*n**3/6 - 17*n**2 + 168*n. Determine s, given that w(s) = 0.
-1, 1, 34
Suppose b - 10 = -4*b. Suppose b*p + 9*z = 4*z + 5, 0 = -2*p + z + 11. Factor 4 - p*d**3 - d**2 - 4 + 4*d**3.
-d**2*(d + 1)
Let z(r) be the first derivative of r**6/30 + 2*r**5/5 + 3*r**4/2 + 5*r**2/2 - 24. Let a(b) be the second derivative of z(b). Find l, given that a(l) = 0.
-3, 0
Suppose -158 + 382 - 11*n - 5*n**3 - 25*n**2 + n - 184 = 0. Calculate n.
-4, -2, 1
Let p = -57 - -65. Suppose -p*b = -4*b - 8. Factor 0*i**3 - 4/5*i**4 + 0 + 4/5*i**b + 2/5*i - 2/5*i**5.
-2*i*(i - 1)*(i + 1)**3/5
Factor 16820*k**2 + 23180*k**2 - 6000*k**3 + 0*k**5 - 5*k**5 + 300*k**4.
-5*k**2*(k - 20)**3
Let p(w) be the first derivative of -w**6/900 + 2*w**5/75 - 7*w**4/60 - 35*w**3/3 - 27. Let b(x) be the third derivative of p(x). Factor b(u).
-2*(u - 7)*(u - 1)/5
Let x(z) = z**5 + z**4 + z**3 - 1. Let y(j) = 10*j**5 - 35*j**4 + 115*j**3 - 120*j**2 + 45*j - 5. Let r = 100 + -101. Let s(t) = r*y(t) + 5*x(t). Factor s(o).
-5*o*(o - 3)**2*(o - 1)**2
Let m(x) be the second derivative of -1/6*x**3 + 7*x - 13/12*x**4 + 5/2*x**2 + 0. Let g(w) = 4*w**2 - 2. Let j(d) = 14*g(d) + 4*m(d). Factor j(k).
4*(k - 2)*(k + 1)
Let o(g) = g**2 - 69*g - 20. Let u(l) = 7*l**2 - 557*l - 160. Let p(q) = -51*o(q) + 6*u(q). Solve p(r) = 0.
-1/3, 20
Let u be 1*4/(-10) + 22/5. Let k be 9/6 - (-6)/(-4). Factor -6/7*c**3 + k + 2/7*c**u - 2/7*c + 6/7*c**2.
2*c*(c - 1)**3/7
Let j = -34 - -36. Factor 11*v**3 + 15 + 6*v**2 - 15 - j*v**3.
3*v**2*(3*v + 2)
Factor 224/9*k**2 + 350/9 - 60*k - 4*k**3 + 2/9*k**4.
2*(k - 7)*(k - 5)**2*(k - 1)/9
Let l be 1/((8 + -4)/8). Solve 4*n - 1 + 2 + 5*n**3 + n**4 - n**3 + 6*n**l = 0 for n.
-1
Let d(c) be the first derivative of 0*c**3 + 2/85*c**5 + 34 + 0*c**4 + 0*c + 0*c**2 + 1/51*c**6. Factor d(y).
2*y**4*(y + 1)/17
Let q = 92 + -16. Factor 79 + q - 161 + z**3 + 9*z - 4*z**3.
-3*(z - 1)**2*(z + 2)
Suppose -2/3*d**5 - 14/3*d**4 - 10*d**3 - 6*d**2 + 0 + 0*d = 0. Calculate d.
-3, -1, 0
Let q(g) be the third derivative of 4/7*g**3 + 1/630*g**5 + 0 + 1/21*g**4 + 0*g + 20*g**2. Find n, given that q(n) = 0.
-6
Solve -11*r + 6 + r**3 + 0*r**3 - 4*r**3 + 6*r**2 + 2*r**3 = 0.
1, 2, 3
Let c(s) be the first derivative of 3/5*s**5 + 0*s**2 + 0*s + 1/3*s**6 - 5 + 1/4*s**4 + 0*s**3. Factor c(q).
q**3*(q + 1)*(2*q + 1)
Let y(a) be the first derivative of -18*a**5/55 - a**4/2 - 4*a**3/33 + 15. Suppose y(b) = 0. Calculate b.
-1, -2/9, 0
Let p(j) be the second derivative of 1/4*j**4 + 3/2*j**3 + 2*j + 11 + 0*j**2. Determine d so that p(d) = 0.
-3, 0
Let w be -2*(-6)/8*418/(-57). Let q be (-8 - (4 + w))*(-3)/5. Factor 0*r - q*r**2 + 3/5*r**3 + 0.
3*r**2*(r - 1)/5
Let p(l) be the second derivative of l**6/45 + 17*l**5/30 + 77*l**4/18 + 127*l**3/9 + 22*l**2 - 638*l. Determine f so that p(f) = 0.
-11, -3, -2, -1
Let -209*g**4 + 2574*g**5 - 40*g - 2553*g**5 + 164*g**2 - 33*g**3 + 7*g**3 = 0. Calculate g.
-1, 0, 2/7, 2/3, 10
Suppose -2*y - 588 = -3*r, 392 = 2*r - y + 4*y. Let z = r - 193. Suppose -2/5*d + 0 + 2/5*d**z + 3/5*d**2 = 0. What is d?
-2, 0, 1/2
Find g, given that 32/7*g**4 - 72/7*g**2 - 216/7 - 64/7*g**3 + 324/7*g - 4/7*g**5 = 0.
-2, 1, 3
Suppose 0*d - 16/3*d**3 + 0 + 2/9*d**4 + 0*d**2 = 0. What is d?
0, 24
Let u = -2601 - -5205/2. Determine o, given that -3/4*o - u*o**2 + 21/4*o**3 - 3*o**4 + 0 = 0.
-1/4, 0, 1
Let d(r) = 5*r**4 - r**3 - 7*r**2 + 3*r. Let k(p) = p**4 - p**3 - p**2 + p. Suppose -1 = -z - 0. Let h(t) = z*d(t) - 3*k(t). Factor h(m).
2*m**2*(m - 1)*(m + 2)
Let k = -27/70 - -11/14. Let m(v) = v**3 - 41*v**2 - 46*v + 3440. Let c be m(40). Find a, given that 0 + k*a**3 + c*a - 2/5*a**2 = 0.
0, 1
Suppose 10*f = 77 + 23. Suppose -5*o + 5 = r, f*r + o - 1 = 8*r. Factor 2/5*b**4 - 2/5*b**3 + r*b + 0 + 0*b**2.
2*b**3*(b - 1)/5
Let s(c) = -c**3 - 6*c**2 - 14*c - 7. Let g be s(-2). Suppose 6*p - g*p = 4*p. Suppose 0*j**2 - 1/3*j**4 + 1/3*j**3 + 0*j + p = 0. What is j?
0, 1
Let t(b) be the third derivative of 1/60*b**4 - 2/75*b**6 + 0 + 0*b**3 + 0*b - 1/300*b**5 + 1/70*b**7 - 15*b**2. Let t(k) = 0. Calculate k.
-1/3, 0, 2/5, 1
Let y(i) be the third derivative of -i**7/42 - 3*i**6/4 - 4*i**5 + 400*i**4/3 + 2560*i**3 + 664*i**2. Solve y(v) = 0.
-8, 6
Let j = 40 + -16. Let u be 134/j + (-3)/(-4). Let -8/3 - 7/3*c**4 + 2*c**2 - 28/3*c + u*c**3 = 0. What is c?
-1, -2/7, 2
Let w(f) be the second derivative of -2*f**6/15 - 11*f**5/4 + 23*f**4/2 - 95*f**3/6 + 8*f**2 + 67*f. Find z, given that w(z) = 0.
-16, 1/4, 1
Let z = 80469/4 + -20116. Factor 3/2*y**3 - 1/4*y + 0 + z*y**2.
y*(y + 1)*(6*y - 1)/4
Suppose 2*r - 5*n - 263 = 0, -3*n + 239 = 5*r - 3*r. Let a = 127 - r. Determine i so that -1/3 - 11/3*i - 35/3*i**2 - 25/3*i**a = 0.
-1, -1/5
Let a be 20/5*1230/(-40). Let m = a + 616/5. Factor -m*g**5 - 2/5*g**2 - 2/5*g**3 + 3/5*g + 3/5*g**4 - 1/5.
-(g - 1)**4*(g + 1)/5
Suppose 20/21*o**4 + 2/21*o**5 + 36/7*o**2 + 0 + 24/7*o**3 + 18/7*o = 0. What is o?
-3, -1, 0
Let n(m) be the second derivative of -4*m**7/7 - 14*m**6/3 - 36*m**5/5 + 43*m**4/3 + 28*m**3 - 16*m**2 - 4*m + 12. Solve n(a) = 0.
-4, -2, -1, 1/6, 1
Let c = 47 + -68. Let k(n) = -n**3 - 22*n**2 - 19*n + 42. Let y be k(c). Let 0*z + y + 2/7*z**2 - 2/7*z**3 = 0. Calculate z.
0, 1
Let y(q) be the third derivative of 0 + 1/72*q**4 + 0*q - 1/360*q**5 + 1/12*q**3 - 20*q**2. Solve y(k) = 0 for k.
-1, 3
Let r(p) = 9*p**2 + 27*p. Let g be r(-3). Let t(b) be the first derivative of 5 + 1/8*b**4 + 1/20*b**5 + g*b**3 + 0*b**2 + 0*b. Factor t(k).
k**3*(k + 2)/4
Suppose 0 = -14*x + 18*x. Suppose 5*u + 3*q + 1 - 4 = 0, -5*u + q - 1 = x. Let -2/3*k**2 + u*k - 4/3*k**3 + 0 - 1/6*k**5 - 5/6*k**4 = 0. Calculate k.
-2, -1, 0
Let y(h) = -20*h**2 - 23*h + 8*h**3 + 8*h**3 + 11 - 15*h**3 + h**3. Let k be y(11). Solve k - 4/5*f**2 + 0*f**3 + 2/5*f**5 + 4/5*f**4 - 2/5*f = 0.
-1, 0, 1
Let y(j) be the first derivative of -21 - j - 169/16*j**4 + 6*j**2 - 39/4*j**3. Determine g so that y(g) = 0.
-1, 2/13
Let h(d) = -7*d**4 + 3*d**2 + 8*d - 6. Let g(r) = 2*r**4 - 2*r + 2. Let y(a) = 3*g(a) + h(a). What is p in y(p) = 0?
-1, 0, 2
Let w = -11 - -11. Factor -49 + 41 + 4*q**2 + w*q + 4*q.
4*(q - 1)*(q + 2)
Factor 8/9*s - 16/9 - 1/9*s**2.
-(s - 4)**2/9
Let g be -3 - 3 - 1235/(-195). Factor -2*j**2 + 0 - 7/3*j**3 + 0*j - g*j**4.
-j**2*(j + 1)*(j + 6)/3
Let y(x) = -7*x**3 + 4*x**2 - x + 4. Let n(a) = 2*a**3 - 2*a**2. Let k(u) = 4*n(u) + y(u). Factor k(t).
(t - 4)*(t - 1)*(t + 1)
Find a, given that -8 + 7*a**4 - 11*a**2 + 31*a