, 1, 2
Factor 0 + 4/3*n**3 + 2/3*n**2 + 2/3*n**4 + 0*n.
2*n**2*(n + 1)**2/3
Let y(h) be the first derivative of 9 + 1/5*h**3 + 9/5*h**2 + 27/5*h. Factor y(g).
3*(g + 3)**2/5
Let u(g) be the second derivative of -g**5/10 + 19*g**4/6 - 50*g**3/3 + 32*g**2 - 98*g. What is y in u(y) = 0?
1, 2, 16
Let z be (56/(-210))/(4/(-30)). Let m(b) be the first derivative of -18/5*b - 5 - 2/15*b**3 - 6/5*b**z. Factor m(p).
-2*(p + 3)**2/5
Let h = 3/200 - -69/400. Let s(g) be the first derivative of -h*g**4 - 3/2*g**3 - 1 + 0*g - 27/8*g**2. Factor s(w).
-3*w*(w + 3)**2/4
Suppose 145 = -14*y + 43*y. Let w(k) be the first derivative of 0*k**3 - 2/35*k**5 - y + 1/7*k**4 + 2/7*k - 2/7*k**2. Factor w(a).
-2*(a - 1)**3*(a + 1)/7
Let f(t) be the second derivative of 25*t**6/4 + 135*t**5/8 - 195*t**4/4 + 43*t**3 - 18*t**2 - 330*t. Determine a, given that f(a) = 0.
-3, 2/5
Let r(d) = 59*d**2 + 1117*d - 73. Let w be r(-19). Factor 3/7*m + 1/7*m**w - 3/7*m**2 - 1/7.
(m - 1)**3/7
Let k(p) be the second derivative of -p**8/2352 - p**7/490 - p**6/420 + p**5/210 + p**4/2 + 8*p. Let t(z) be the third derivative of k(z). Factor t(x).
-4*(x + 1)**2*(5*x - 1)/7
Let x = -6/1385 - -22178/4155. Let -8/3 - 10/3*m**2 - 2/3*m**3 - x*m = 0. What is m?
-2, -1
Let x be (8/6)/(2/72). Suppose 2*n - g = 6*n - 19, 3*n = -2*g + 18. Determine v so that -x*v**4 + v**2 - 3*v**2 + 52*v**n - 2 + 5*v - v**5 - 4*v**3 = 0.
-1, 1, 2
Let d(v) be the second derivative of -v**8/1008 + v**7/630 + 9*v**2/2 - 16*v. Let q(t) be the first derivative of d(t). What is r in q(r) = 0?
0, 1
Suppose 7*a = -61 + 96. Let y(s) be the third derivative of 6*s**2 + 0*s**3 + 0 + 0*s - 1/30*s**a - 1/6*s**4. Factor y(m).
-2*m*(m + 2)
Let b(j) be the first derivative of 40 + 8/45*j**5 + 1/27*j**6 + 0*j + 0*j**3 + 0*j**2 + 1/6*j**4. Suppose b(d) = 0. Calculate d.
-3, -1, 0
Let u = -98 + 100. Let g be (1/2)/(2/8). Factor -4*d**4 - 2*d**5 + 7*d**4 + 2*d**4 - 4*d**g + u*d - d**4.
-2*d*(d - 1)**3*(d + 1)
Determine z so that -1/2*z**3 + 1/2*z**4 + 1/4*z**5 - z**2 + 1/2 + 1/4*z = 0.
-2, -1, 1
Let t(m) be the first derivative of -m**7/168 - m**6/60 - m**5/80 + 13*m - 10. Let f(u) be the first derivative of t(u). Solve f(q) = 0 for q.
-1, 0
Let t(m) be the third derivative of m**7/2310 + m**6/120 + 19*m**5/660 + 3*m**4/88 + 162*m**2. Solve t(b) = 0 for b.
-9, -1, 0
Suppose -12*f = -2*f. Let k(h) be the second derivative of f*h**2 + 0 + 1/6*h**3 + 10*h + 1/12*h**4. Factor k(w).
w*(w + 1)
Find m, given that -3*m**3 + 15*m**4 - 3*m**2 + 2*m**2 - 16*m**4 + 2*m**2 + 3*m = 0.
-3, -1, 0, 1
Let p be (-7 - (7 + -15)) + 522/(-524). Let m = p + 517/1834. Factor 0 - 6/7*d**2 + m*d.
-2*d*(3*d - 1)/7
Let v(m) be the third derivative of 1/16*m**4 + 1/240*m**5 + 0*m - 32 - m**2 + 0*m**3. Determine s so that v(s) = 0.
-6, 0
Let p(j) be the first derivative of -1/4*j**4 + 2*j**3 + 8*j - 16 + 15/2*j**2. Factor p(t).
-(t - 8)*(t + 1)**2
Let l = 28 + -24. Solve -l*m - 2 + 7*m + 3*m**2 - 4*m**2 = 0.
1, 2
Let w(t) = -t**3 - 19*t**2 + 20*t + 32. Let k be w(-20). Let f be (-66)/44*2*k/(-18). What is y in 1/3*y**2 - 8/3*y + f = 0?
4
Factor 0 - 6/11*i + 2/11*i**3 + 4/11*i**2.
2*i*(i - 1)*(i + 3)/11
Suppose 3*j = 5*y - 0*j - 249, -4*y + 212 = 4*j. Let m = -48 + y. Factor -3/4*d + 9/4*d**2 + 0 + 3/4*d**4 - 9/4*d**m.
3*d*(d - 1)**3/4
What is s in -8/5*s**2 - 68/5*s - 32/5 = 0?
-8, -1/2
Factor 0 + 1/5*u**2 - u.
u*(u - 5)/5
Suppose -16 = -4*k + 4. Let w(r) = -k*r + 5 + 4*r - 9*r**2 + 4*r + 2*r - r**3. Let h(b) = b**3 + 5*b**2 - 3*b - 3. Let m(y) = -5*h(y) - 3*w(y). Factor m(s).
-2*s**2*(s - 1)
Suppose 19 = 5*n - 4*r + r, -2 = 5*n + 4*r. Suppose 3*i - 31 = -4*q, -2*i = 5*q - i - 25. Solve 3*w**4 + 3*w**n - 2*w**q - 2 + w - w**3 + 3*w**4 - 5*w**4 = 0.
-2, -1, 1
Factor 2/7*x**3 + 1400 + 1440*x + 282/7*x**2.
2*(x + 1)*(x + 70)**2/7
Let c = 563/3354 + -2/1677. Let d(m) be the third derivative of 0*m - 1/15*m**5 + c*m**4 + 13*m**2 + 0*m**3 + 0. Factor d(h).
-4*h*(h - 1)
Let l(d) be the first derivative of 10 - 1/9*d**4 - 2/9*d + 0*d**2 + 2/9*d**3. Let l(s) = 0. What is s?
-1/2, 1
Let u = -4 - -9. Suppose -4*x = 3*d - 4*d + 14, 5*d - u*x - 25 = 0. Find a such that -d + 0 - 3*a**3 + 8*a**2 + 0*a**3 - 2*a - a = 0.
-1/3, 1, 2
Let h(q) be the first derivative of 170*q**2 + 200*q + q**5 + 70*q**3 + 55/4*q**4 + 2. Factor h(w).
5*(w + 2)**3*(w + 5)
Let v(z) be the third derivative of -z**6/120 - z**5/24 - z**4/24 + 43*z**2. Find q such that v(q) = 0.
-2, -1/2, 0
Let k(v) be the second derivative of -v**6/345 + 3*v**5/230 - v**4/46 + v**3/69 - 56*v. What is t in k(t) = 0?
0, 1
Let f(s) be the first derivative of 3*s**4/4 - 3*s**3 - 9*s**2 + 24*s - 180. Factor f(p).
3*(p - 4)*(p - 1)*(p + 2)
Factor 0 + 648*y**2 - 2*y**3 + 2 - 650*y**2 + 0 + 2*y.
-2*(y - 1)*(y + 1)**2
Suppose -5*d - 109 = -9. Let z be (2 + -4)/(16/d). Find u, given that -z*u**3 + 3/2*u**2 + 0 + u = 0.
-2/5, 0, 1
Suppose 3*g + 7 = 46. Suppose 6*k = 5*k + g*k. Factor 4/5*l**2 + 0 - 2/5*l**3 + k*l.
-2*l**2*(l - 2)/5
Suppose 2*k + 53 = 5*h - 0*k, 4*k = 3*h - 43. Let n be 12/10*30/h. Factor -2*f**2 + n*f**3 - 5*f**2 - 8*f**4 - 22*f**3 + 3*f**2.
-2*f**2*(f + 2)*(4*f + 1)
Let x = 219/4 + -641/12. Let y(t) be the first derivative of -36*t + 6 - 12*t**2 - x*t**3. Solve y(c) = 0 for c.
-3
Suppose -9*j - 33 = -51. Let v(w) be the first derivative of 3/4*w + 2 + 0*w**j - 1/4*w**3. Let v(h) = 0. Calculate h.
-1, 1
Let z = 1/504 - -59807/504. Let i = -118 + z. Factor -i*q + 1/3*q**3 + 1/3*q**2 + 0.
q*(q - 1)*(q + 2)/3
Let h be (1 + (-4)/2)/(37/(-111)). Let c(r) be the second derivative of 2/147*r**7 + 0*r**2 + 0*r**4 + 4/105*r**6 - 12*r + 0*r**h + 0 + 0*r**5. Factor c(o).
4*o**4*(o + 2)/7
Let m be (-208)/72 + (-9)/(-3). Factor m*q**2 - 4/9*q + 0.
q*(q - 4)/9
Suppose -p = -2*c, -5*c + 7 = -2*p + 3*p. Let v be (-3 - (-3 + (-3)/15))*2. Suppose -v*a**p - 2/5 + a = 0. What is a?
1/2, 2
Let k(z) be the third derivative of 5/24*z**4 - 1/42*z**7 + 0*z**3 + 1/8*z**6 - 13*z**2 - 1/4*z**5 + 0 + 0*z. Let k(f) = 0. Calculate f.
0, 1
Let n(i) be the second derivative of 29*i + 2*i**2 - 1/40*i**5 + 1/4*i**4 + 5/4*i**3 + 0. Factor n(o).
-(o - 8)*(o + 1)**2/2
Let u be 88/160 - -2*(-1)/(-10). Factor 0 + 0*d + 63/4*d**3 + u*d**5 - 6*d**4 - 27/2*d**2.
3*d**2*(d - 3)**2*(d - 2)/4
Suppose -2*z + 10 - 6 = 0. Factor -19*j**4 - 10*j - 55*j**2 + 10*j**4 + 20*j**z - 5*j**5 - 45*j**3 - 16*j**4.
-5*j*(j + 1)**3*(j + 2)
Suppose -2*g + 9 = 3. Let p be ((-3)/4)/g + (-117)/(-52). Factor 2/9*y + 0 - 4/9*y**3 + 0*y**p + 0*y**4 + 2/9*y**5.
2*y*(y - 1)**2*(y + 1)**2/9
Let h be (-1)/3 - 44/(-33). Let p(d) = -d**4 - 1. Let x(u) = 20*u**4 + 35*u**3 - 20*u + 5. Let z(l) = h*x(l) + 5*p(l). Factor z(f).
5*f*(f + 1)*(f + 2)*(3*f - 2)
Let i(s) be the first derivative of 3*s**4/8 + 55*s**3/9 + 41*s**2/4 + 11*s/3 + 248. Factor i(t).
(t + 1)*(t + 11)*(9*t + 2)/6
Let u = -20 + 38. Let h = 22 - u. Factor -3*b**2 + 4*b + b - b**h + 6*b**2 + 8 - b**3 - 6.
-(b - 2)*(b + 1)**3
Let -24*z**2 + 3*z**2 - 12*z + 18*z**2 = 0. What is z?
-4, 0
Let j(z) = -2*z - 4. Let d be j(-3). Factor -t + 5*t**d - 27 - 17*t - 8*t**2.
-3*(t + 3)**2
Let h be (1/(-9) + 104/(-117))*0. Factor -1/3*v**4 + 1/3*v**3 + 0*v + 0*v**2 + h.
-v**3*(v - 1)/3
Factor -1352/9 - 2/9*x**2 - 104/9*x.
-2*(x + 26)**2/9
Let z(i) be the first derivative of 125*i**6/9 + 370*i**5/3 - 195*i**4/2 + 238*i**3/9 - 8*i**2/3 + 46. Determine a, given that z(a) = 0.
-8, 0, 1/5
Let g(u) = 2*u**4 - 4*u**3 + 22*u**2 + 16*u + 12. Let y(x) = 5*x**4 - 8*x**3 + 45*x**2 + 32*x + 26. Let n(v) = -13*g(v) + 6*y(v). Suppose n(l) = 0. What is l?
-2, -1, 0, 2
Let l = -10274 + 10276. Factor 2/5*x - 2/5*x**3 - 1/5*x**4 + 0 + 1/5*x**l.
-x*(x - 1)*(x + 1)*(x + 2)/5
Let s(u) be the first derivative of -u**6/6 + 4*u**5/5 + 2*u**4 - 10*u**3/3 - 23*u**2/2 - 10*u + 113. Factor s(n).
-(n - 5)*(n - 2)*(n + 1)**3
Let x(l) be the third derivative of 15*l**6/11 + 62*l**5/11 + 11*l**4/12 + 2*l**3/33 + 339*l**2. Factor x(k).
2*(k + 2)*(30*k + 1)**2/11
Suppose 3*g - 1 = 68. Suppose -105*r**4 + 103*r**4 - 3*r + g*r - 6 + 12*r**3 - 24*r**2 + 0 = 0. Calculate r.
1, 3
Let c(r) = -r**3 - 7*r**2 + 2*r + 2. Let d(h) = -4*h**3 - 22*h**2 + 5*h + 7. Let z(t) = -14*c(t) + 4*d(t). Factor z(v).
-2*v*(v - 4)*(v - 1)
Let y(f) be the second derivative of -f**4/6 - 2*f**3/3 + 15*