n**4 - m*n**3 + 2*n**4 + 3*n**4 = 0. What is n?
0, 1, 2
Let k(f) = 405*f**2 - 125*f + 55. Let u(d) = 29*d**2 - 9*d + 4. Let q(i) = -4*k(i) + 55*u(i). Factor q(l).
-5*l*(5*l - 1)
Let z = 161/10 - 73/5. Factor 3/4*f**4 - z*f**3 + 0 + 0*f + 3/4*f**2.
3*f**2*(f - 1)**2/4
Let g(w) be the first derivative of -w**4/2 - 2*w**3 + 8*w - 8. Suppose g(p) = 0. What is p?
-2, 1
Let h(x) be the first derivative of -x**2 + 0*x**4 + 1/60*x**6 + 0*x**3 + 2 + 1/30*x**5 + 0*x. Let y(g) be the second derivative of h(g). Factor y(n).
2*n**2*(n + 1)
Let y(p) = 84*p**2 + 376*p + 228. Let o(t) = -13*t**2 - 58*t - 35. Let v(z) = -32*o(z) - 5*y(z). Determine h so that v(h) = 0.
-5, -1
Let t(q) be the third derivative of -q**8/560 + q**7/56 - q**6/20 - q**5/10 + 7*q**4/24 + 5*q**2. Let i(h) be the second derivative of t(h). Factor i(d).
-3*(d - 2)**2*(4*d + 1)
Suppose 5*b - 2*n - 70 = 0, 5 = -b - 3*n + 2. Factor -b*v**3 - 19*v**2 + 24 - 32*v + 52*v - 13*v**2.
-4*(v - 1)*(v + 3)*(3*v + 2)
Let g = 133 + -261/2. Let b(y) be the first derivative of -g*y**2 + 4/3*y**3 + 1 + y. Factor b(h).
(h - 1)*(4*h - 1)
Let q(d) be the second derivative of -25*d**7/42 + d**6/2 + d**5/2 - 42*d. Solve q(j) = 0 for j.
-2/5, 0, 1
Let t(a) be the third derivative of -1/96*a**4 + 0*a - 1/240*a**6 + 0 + 3*a**2 - 1/80*a**5 + 0*a**3. Let t(d) = 0. What is d?
-1, -1/2, 0
Let n be (1560/(-175))/(-6) - 6/21. Factor -8/5*w**2 + 26/5*w - n.
-2*(w - 3)*(4*w - 1)/5
Suppose 4*u - 7 = 1. Let d(n) be the third derivative of -1/75*n**6 + 1/15*n**3 + 0*n - 7/150*n**5 - u*n**2 - 1/30*n**4 + 0. Factor d(p).
-2*(p + 1)**2*(4*p - 1)/5
Let a(c) be the third derivative of c**8/1680 - c**6/180 + c**4/24 + c**3/3 - 4*c**2. Let b(x) be the first derivative of a(x). Factor b(d).
(d - 1)**2*(d + 1)**2
Let t be -1*(-8)/(-6)*2/(-12). Factor -2/9*l + 4/9 - t*l**2.
-2*(l - 1)*(l + 2)/9
Let n = -24 + 26. Factor 5/3*r**n + 1/3*r + r**3 - 1/3.
(r + 1)**2*(3*r - 1)/3
Suppose 3*k + 8 = 7*k. Suppose 2*o + k - 6 = 0. Factor 0 + 0*j**3 + 0*j**o - 1/4*j**5 - 1/4*j**4 + 0*j.
-j**4*(j + 1)/4
Let l(c) be the first derivative of -3*c**4 + 15*c**3 - 18*c**2 - 12*c - 68. Solve l(f) = 0.
-1/4, 2
Let h(o) be the first derivative of -o**3 - 6*o**2 - 12*o + 9. Factor h(a).
-3*(a + 2)**2
Let s be (2/34)/((-67)/(-134)). Factor 0 + s*r**2 + 4/17*r.
2*r*(r + 2)/17
Let q(v) = v**3 - 4*v**2 + 3*v + 2. Let y(b) = -b**2 - 1. Let m(a) = -q(a) + y(a). Let t(o) be the first derivative of m(o). Find x, given that t(x) = 0.
1
Let x(y) be the first derivative of -y**3/18 + y**2/12 + y/3 + 2. Determine h so that x(h) = 0.
-1, 2
Let v be 3*(-4)/12*0. Let y(m) be the third derivative of v - 1/120*m**5 + 0*m**4 + 0*m**3 + 3*m**2 + 0*m. Factor y(w).
-w**2/2
Let f(c) be the third derivative of -c**7/700 + c**6/900 + c**5/150 - c**3/2 + 3*c**2. Let q(s) be the first derivative of f(s). Factor q(h).
-2*h*(h - 1)*(3*h + 2)/5
Let o(c) be the second derivative of -2*c**7/189 - 14*c**6/135 - 19*c**5/45 - 25*c**4/27 - 32*c**3/27 - 8*c**2/9 + c - 22. What is u in o(u) = 0?
-2, -1
Let o(x) be the third derivative of 1/105*x**7 + 0*x**3 + 3*x**2 - 1/30*x**5 + 0*x**4 + 1/60*x**6 + 0 - 1/168*x**8 + 0*x. Determine f, given that o(f) = 0.
-1, 0, 1
Let s(u) be the third derivative of -u**5/100 + 13*u**4/20 - 169*u**3/10 + 22*u**2. Factor s(y).
-3*(y - 13)**2/5
Let a(s) be the first derivative of 4 + 1/4*s**4 + s**3 + 0*s + 1/6*s**6 - 3/5*s**5 - s**2. Factor a(l).
l*(l - 2)*(l - 1)**2*(l + 1)
Let h = -223 - -129. Let i = h - -286/3. Let -2/3 + 1/3*v**3 + 5/3*v - i*v**2 = 0. What is v?
1, 2
Let b be 4 + (1 - 0 - 3). Factor 0*n**2 + 5*n**b + 16 + 10*n + 7*n**2 + 14*n + 2*n**3.
2*(n + 2)**3
Determine c, given that 5*c**2 - c + 3*c + c**2 - 5*c**2 + 1 = 0.
-1
Let r be 9 + 0/(2 + 1). Let h(k) = -r*k**3 + 0 + 3 - 4*k**4 + 2. Let g(s) = -6*s**4 - 14*s**3 + 8. Let u(b) = 5*g(b) - 8*h(b). Find w, given that u(w) = 0.
-1, 0
Let y(v) be the second derivative of -v**6/360 + v**5/60 - 2*v**3/9 + v**2/2 - 2*v. Let w(g) be the first derivative of y(g). Factor w(u).
-(u - 2)**2*(u + 1)/3
Let m = -29 + 33. Let u(p) be the second derivative of 1/40*p**5 + 1/30*p**6 + 0 + 3*p + 1/84*p**7 + 0*p**2 + 0*p**m + 0*p**3. Factor u(k).
k**3*(k + 1)**2/2
Let s = -1/581 + 125501/2905. Let s*t**3 + 8*t + 4/5 + 108/5*t**4 + 144/5*t**2 = 0. Calculate t.
-1, -1/3
Let r(n) be the first derivative of -n**6/3 - 2*n**5/7 + 9*n**4/14 + 10*n**3/21 - 2*n**2/7 - 28. Suppose r(p) = 0. Calculate p.
-1, 0, 2/7, 1
Let o(i) be the second derivative of 1/3*i**2 - 7/9*i**3 + 7/18*i**4 + 0 - 8/45*i**6 + 23/30*i**5 + i - 16/63*i**7. Determine w, given that o(w) = 0.
-1, 1/4, 1
Let r(a) be the third derivative of -a**7/1260 + a**5/120 + a**4/72 - 4*a**2. Suppose r(z) = 0. Calculate z.
-1, 0, 2
Let d(h) = h**3 + 10*h**2 + 8*h - 4. Let l be d(-9). Factor 0*o + 0 + 0*o**2 + 1/3*o**l - 1/3*o**4 + 0*o**3.
o**4*(o - 1)/3
Solve -6040 + 4*b**3 + 12*b + 16*b**2 + 6040 = 0.
-3, -1, 0
Let v = -2 + 3. Solve 4*z + 2*z - 2*z - z**2 - 6*z - v = 0 for z.
-1
Find l such that 1/6*l**5 + 2/3*l**3 + 1/3*l**2 - 2/3*l**4 + 1/3 - 5/6*l = 0.
-1, 1, 2
Let -50/9 + 20/9*q - 2/9*q**2 = 0. Calculate q.
5
Let q = -34 - -37. Let x(t) be the first derivative of 0*t**2 + 1/16*t**4 + 1 - 1/20*t**5 - 1/24*t**6 + 1/12*t**q + 0*t. Factor x(h).
-h**2*(h - 1)*(h + 1)**2/4
Let q be ((-2)/2)/(12 + -1). Let v = 25/33 + q. Suppose -v*a + 7/3*a**2 + 0 + 4/3*a**3 = 0. Calculate a.
-2, 0, 1/4
Let w(x) = -x - 18. Let b be w(-18). Let f(t) be the first derivative of 2/15*t**3 - 2/5*t**2 - 2 + b*t. Let f(g) = 0. Calculate g.
0, 2
Let j(t) be the first derivative of 1/9*t**3 + 3 + 4/3*t + 2/3*t**2. Factor j(h).
(h + 2)**2/3
Factor -9*g + 2*g**2 + 3*g - 7*g + g.
2*g*(g - 6)
Let c be (-3 - -3) + 66/55. Factor 2/5*m**2 + 4/5 - c*m.
2*(m - 2)*(m - 1)/5
Let b(x) be the second derivative of 1/84*x**7 + 1/12*x**3 + 1/36*x**4 + 0 - 1/12*x**2 - 1/20*x**5 - 1/180*x**6 + 6*x. Let b(g) = 0. What is g?
-1, 1/3, 1
Let r = -1295 + 1295. Let w(q) = q**3 - 6*q**2 + 6*q - 5. Let m be w(5). Factor m + r*d - 3/2*d**2.
-3*d**2/2
Let v(s) be the second derivative of -s**5/130 - s**4/39 - 30*s. Factor v(j).
-2*j**2*(j + 2)/13
Let q = 2/33 + 20/33. Solve -1/3*p - q*p**2 + 0 - 1/3*p**3 = 0.
-1, 0
Let g(k) = k**2 - 6*k + 7. Let w be 64/12 - (-2)/(-6). Let q be g(w). What is c in 2*c**5 - 6*c**q + 0 + 2*c - 4*c**3 - 2 + 10*c**2 - 2*c**4 = 0?
-1, 1
Let v(p) be the second derivative of -p**7/42 + p**6/15 + p**5/20 - p**4/6 + 6*p. Find t such that v(t) = 0.
-1, 0, 1, 2
Let b = -27 + 38. Let i = b - 7. Determine c, given that -1/3*c**3 + 0 + 1/3*c**i - 1/3*c**2 + 1/3*c = 0.
-1, 0, 1
Let a(b) be the third derivative of 1/4*b**4 + 0*b**5 - 1/70*b**7 + 0 + 0*b - 1/20*b**6 + 6*b**2 + 1/2*b**3. Solve a(f) = 0.
-1, 1
Factor -3*p**3 - 2*p**2 - 2*p**2 + 9*p**3 - 2*p**3.
4*p**2*(p - 1)
Let d be ((-4)/(-6))/((-5)/(-15)). Factor -1/2*o**d - o - 1/2.
-(o + 1)**2/2
Suppose 5*a - 3 - 12 = 0. Let g(b) be the second derivative of -1/6*b**2 - b + 0*b**a + 1/36*b**4 + 0. Suppose g(u) = 0. Calculate u.
-1, 1
Determine d so that -23*d + 45*d**2 + 24 + 3*d**3 - 22*d - 27*d**2 = 0.
-8, 1
Suppose 20 = -4*j, -4*t + 3*j = -2*t - 15. Let 1/2*v**2 + 0*v + 1/2*v**3 + t = 0. Calculate v.
-1, 0
Let o(l) = -2*l**3 + 13*l**2 - 7*l + 8. Let h be o(6). Factor 4/9 - 2/9*a**h + 2/9*a.
-2*(a - 2)*(a + 1)/9
Suppose -q = -5*m + 14, 4 = -3*m - 5*q - 10. Factor n**m - n**4 - n**4 - 3*n**2 + 4*n**4.
2*n**2*(n - 1)*(n + 1)
Let y(h) be the second derivative of -h**6/360 + h**5/40 - h**4/12 - h**3/6 - 2*h. Let i(c) be the second derivative of y(c). Factor i(d).
-(d - 2)*(d - 1)
Suppose 0 = -0*m + 8*m + 48. Let j = m + 19/3. Let 1/3*k**2 + j - 2/3*k = 0. What is k?
1
Let t(a) = -100*a**3 - 85*a**2 - 16*a + 5. Let f(m) = -250*m**3 - 212*m**2 - 40*m + 12. Let p = -1 - 11. Let g(d) = p*t(d) + 5*f(d). Factor g(n).
-2*n*(5*n + 2)**2
Suppose 32 = h + 3*h. Let n be (h/6)/((-1)/(-3)). What is l in n*l**2 + 4*l**4 + 2*l**2 - l**4 + 6*l**3 - 3*l**2 = 0?
-1, 0
Factor 27*a**2 + 43*a - 16*a**4 - 3 - 22*a + 19*a**4 + 9 + 15*a**3.
3*(a + 1)**3*(a + 2)
Determine h so that 21*h + 29*h + 144*h**3 - 20*h**4 + 20*h**2 - 2*h**5 - 192*h**3 = 0.
-5, -1, 0, 1
Suppose -g + 6 - 4 = 0. Suppose -12 = -x + 2*u, -u - u - g = 4*x. Factor 0 + 2/5*h + 2/5*h**x.
2*h*(h + 1)/5
Let 