0.
-2, -1
Let y(h) be the first derivative of 1/2*h**2 + 0*h + 2 - 1/3*h**3. Find x such that y(x) = 0.
0, 1
Let i = 2/107 - -493/2247. Let n(r) be the second derivative of 0 - 2/7*r**2 + i*r**3 + 2*r - 1/14*r**4. Factor n(x).
-2*(x - 1)*(3*x - 2)/7
Let a(h) be the second derivative of -2*h**7/189 + 4*h**6/135 - h**5/45 + 20*h. Factor a(y).
-4*y**3*(y - 1)**2/9
Let c(n) be the second derivative of -n**9/12096 + n**8/6720 + n**7/3360 - n**6/1440 + 5*n**3/6 - 3*n. Let g(w) be the second derivative of c(w). Factor g(t).
-t**2*(t - 1)**2*(t + 1)/4
Factor 13*b**2 + 0*b**2 - 8*b**2 + 20 - 20*b.
5*(b - 2)**2
Let c(a) be the second derivative of -a**4/3 - 4*a**3/3 + 6*a**2 + 3*a. Factor c(b).
-4*(b - 1)*(b + 3)
Let z(h) be the first derivative of 0*h**4 + 2/15*h**5 + 0*h**3 + 1 + 0*h + 0*h**2. Determine i, given that z(i) = 0.
0
Let t(k) be the first derivative of 4/25*k**5 + 0*k - 4/5*k**2 + 2/5*k**4 - 7 - 4/15*k**3. Find w such that t(w) = 0.
-2, -1, 0, 1
Suppose 6/5*x**2 + 27/5*x**5 + 0 + 0*x - 6/5*x**4 - 27/5*x**3 = 0. Calculate x.
-1, 0, 2/9, 1
Let f(n) be the first derivative of 1 + 5/36*n**4 - 2/45*n**5 - n**2 + 0*n - 2/9*n**3 + 1/180*n**6. Let g(s) be the second derivative of f(s). Factor g(d).
2*(d - 2)*(d - 1)**2/3
Let b(n) = 7*n**2 + 11*n - 1. Let f(h) = 4*h**2 + 6*h - 1. Let c be (-2)/4*(8 - -2). Let s(x) = c*f(x) + 3*b(x). Factor s(t).
(t + 1)*(t + 2)
Let o be 56 + -44 + (0 - 8). Determine m so that -16/9 - 346/9*m**3 - 812/9*m**o - 98/3*m**5 + 76/3*m**2 + 40/9*m = 0.
-2, -1, -1/3, 2/7
Suppose l - 3*b = 4*l - 3, 2*l - 16 = 5*b. Let -2*a**2 - 8*a**2 + 11*a**2 - 2*a - 2 + l = 0. What is a?
1
Let l be 3 + 2 + (1 - -9). Find i such that 25/4*i**5 - 2 + l*i - 83/2*i**2 + 209/4*i**3 - 30*i**4 = 0.
2/5, 1, 2
Let b = 875 - 873. Solve -1/3*h + 0 - h**3 + 1/3*h**4 + h**b = 0 for h.
0, 1
Let w(n) be the second derivative of -45*n**7/14 - 11*n**6 - 19*n**5/3 - 10*n**4/9 - n. Let w(f) = 0. What is f?
-2, -2/9, 0
Suppose -5*m - 15 = -10*m. Find g, given that -g**m + 5/4*g**2 + 0 - 1/4*g = 0.
0, 1/4, 1
Let i = -567 - -127574/225. Let k = 1793/1575 - i. Factor -k - 8/7*b - 2/7*b**2.
-2*(b + 2)**2/7
Let n be 7 + (-8)/2 + (-6)/16. Let y(h) be the first derivative of -3/2*h + n*h**2 - 2*h**3 + 9/16*h**4 + 2. Factor y(j).
3*(j - 1)**2*(3*j - 2)/4
Factor -1/6*g**2 + 1/6*g**3 + 1/6 - 1/6*g.
(g - 1)**2*(g + 1)/6
Suppose 0 = -o + 2, -5*s - 2*o = -2*s + 44. Let x be (-44)/s - (-2)/8. Factor -1/4*a + 0 + 1/4*a**x + 1/4*a**4 - 1/4*a**2.
a*(a - 1)*(a + 1)**2/4
Let w = -58 + 41. Let c = -13 - w. Solve 0 - 2/7*f**5 + 2/7*f**3 + 2/7*f**2 - 2/7*f**c + 0*f = 0.
-1, 0, 1
Suppose -4*o**3 + 1/2*o**5 + o**4 + 16 - 8*o**2 + 8*o = 0. Calculate o.
-2, 2
What is t in 2/21*t**2 + 2/21*t + 0 = 0?
-1, 0
Let b(i) be the second derivative of i**7/420 + i**6/360 - i**5/60 - i**4/24 - i**3/6 - 3*i. Let n(q) be the second derivative of b(q). Factor n(u).
(u - 1)*(u + 1)*(2*u + 1)
Factor -2*s**5 + 0*s - 20*s**3 + 10*s**4 + 43*s**2 + 2 - 10*s - 23*s**2.
-2*(s - 1)**5
Let h = -22 + 31. Let t(l) = l**2 - 1. Let n(z) = 3*z**2 - 3. Let q(j) = h*t(j) - 4*n(j). Factor q(r).
-3*(r - 1)*(r + 1)
Let r be (-3)/12 - (-13)/4. Suppose 9*u + 6 = 12*u. Suppose r + 2*h**u - 1 + 2 - 6*h = 0. What is h?
1, 2
Suppose -w = 13*w - 28. Let p = -9/10 - -67/30. Factor 2/3*s**w + p - 2*s.
2*(s - 2)*(s - 1)/3
Let l(z) = -120*z**5 + 45*z**4 - 55*z**3 + 65*z**2 - 65*z. Let m(r) = 11*r**5 - 4*r**4 + 5*r**3 - 6*r**2 + 6*r. Let a(t) = -6*l(t) - 65*m(t). Factor a(d).
5*d**3*(d - 1)**2
Let 3*m**2 + 2 - 8*m**2 + 2*m**2 - m + 2*m**2 = 0. Calculate m.
-2, 1
Let w be 20/8*(-32)/(-20). Suppose -t + w*o + 14 = 2*o, -3*o = 2*t. Factor t*l + 7/2*l**2 - 2.
(l + 2)*(7*l - 2)/2
Let h be (-3)/6 + 203/294. Let v(z) be the third derivative of 0*z + h*z**3 + 0 + 2*z**2 + 27/70*z**5 - 3/7*z**4. Determine l, given that v(l) = 0.
2/9
Let j be 15/(-2)*32/(-1128). Let y = j - -118/329. Determine m so that 2/7*m**4 + 2/7*m + 2/7*m**5 + 2/7 - 4/7*m**3 - y*m**2 = 0.
-1, 1
Factor 8*c + 1/4*c**4 + 6*c**2 + 2*c**3 + 4.
(c + 2)**4/4
Let m(j) = 85*j**2 - 25*j + 15. Let l(v) = 21*v**2 - 6*v + 4. Let b(g) = 15*l(g) - 4*m(g). Factor b(o).
-5*o*(5*o - 2)
Let x(p) be the first derivative of -p**4/20 - 2*p**3/15 - p**2/10 + 12. Factor x(n).
-n*(n + 1)**2/5
Find r, given that -3*r**3 - 8*r**4 + 0*r**3 - 5*r**4 + r**2 + 15*r**4 = 0.
0, 1/2, 1
Let a(f) be the second derivative of 0*f**2 + 1/18*f**4 + 1/60*f**5 + 0 + 2*f + 1/18*f**3. Suppose a(v) = 0. Calculate v.
-1, 0
Suppose 4*h - 3*q - 2 = -q, -2*q = 2*h - 16. Determine b, given that 9 - 9 + 2*b**5 + 2*b - 4*b**h = 0.
-1, 0, 1
Let g(f) be the second derivative of 1/12*f**2 + 1/72*f**4 + 0 - 1/18*f**3 - 4*f. Factor g(c).
(c - 1)**2/6
Factor -2/3 + 1/3*a**2 - 1/3*a.
(a - 2)*(a + 1)/3
Suppose 3 - 7 = -2*u. Let c = -2 + 2. Solve 0 - 1/2*q**5 - 1/2*q + 0*q**4 + q**3 + c*q**u = 0.
-1, 0, 1
Let m(g) be the third derivative of g**9/75600 - g**8/16800 + g**4/6 + 3*g**2. Let q(w) be the second derivative of m(w). Find o, given that q(o) = 0.
0, 2
Let y = -706/3 + 236. Find k such that 0*k**3 - 2/3*k**2 + 0*k + y*k**4 + 0 = 0.
-1, 0, 1
Let g(d) be the second derivative of -d**5/10 + 5*d**4/6 + 2*d**3 + 12*d. Find y, given that g(y) = 0.
-1, 0, 6
Let s(x) be the third derivative of -1/24*x**4 + 0*x + 0 + 0*x**3 - 1/210*x**7 + x**2 + 1/120*x**6 + 1/60*x**5. Factor s(c).
-c*(c - 1)**2*(c + 1)
Let v = 1897/6 + -316. Determine t, given that 0*t**2 + v*t + 0 - 1/6*t**3 = 0.
-1, 0, 1
Let o(g) be the third derivative of -g**8/3528 + g**6/630 - g**4/252 - 6*g**2. Let o(c) = 0. What is c?
-1, 0, 1
Let a(f) be the third derivative of -5*f**2 + 0*f**3 + 0*f + 0 - 1/60*f**5 + 0*f**4. Find c such that a(c) = 0.
0
Factor 15*g**2 - 5*g**3 - 30 - 15*g**2 + 35*g.
-5*(g - 2)*(g - 1)*(g + 3)
Factor 6*w**2 + 10*w + 4 - 2*w**4 - 8*w**3 + 13*w**3 - 7*w**3.
-2*(w - 2)*(w + 1)**3
Factor -1/3*x**2 + x + 4/3.
-(x - 4)*(x + 1)/3
Let i = 78 - 78. Let i*l**3 + 1/3*l**4 - 2/3*l**2 + 1/3 + 0*l = 0. Calculate l.
-1, 1
Find p, given that 5*p**3 + 2*p**2 + 4*p**5 - 2*p**5 - 2*p**4 - 7*p**3 = 0.
-1, 0, 1
Let k be 4284/1122 - (-2)/11. Solve 0*x + 2*x**k + 2/3*x**5 + 0 + 2/3*x**2 + 2*x**3 = 0 for x.
-1, 0
Factor 6*j**2 + 63*j + 67*j - 18 - 115*j - 3*j**3.
-3*(j - 3)*(j - 1)*(j + 2)
Factor 1/7*a**3 + 0*a + 0 - 2/7*a**2.
a**2*(a - 2)/7
Let z(n) = -n**2 - 7*n - 4. Let d be z(-5). Suppose 2*y - 6 = x, -x + 3*y - 8 - 2 = 0. Suppose p - 8*p**2 - 2*p + d*p**x = 0. What is p?
-1/2, 0
Let w be 6/8 + (-18)/(-8). Suppose 4*z = w*z + 4. Determine p so that 1/4*p**5 + 1/4*p**z - 1/4*p**3 - 1/4*p**2 + 0 + 0*p = 0.
-1, 0, 1
Factor 9*l**2 + 0*l**2 - 4*l - 6 + l**2.
2*(l - 1)*(5*l + 3)
Let v(a) be the first derivative of -63/5*a**5 - 6*a**2 + 87/4*a**4 + 0*a - 4 - 4*a**3. Find g, given that v(g) = 0.
-2/7, 0, 2/3, 1
Let v(x) = x**2 - 4*x - 5. Let w(j) = -3*j**2 + 11*j + 14. Suppose a = -a + 22. Let u(m) = a*v(m) + 4*w(m). Suppose u(n) = 0. Calculate n.
-1, 1
Let m(k) be the first derivative of -3*k**5/5 - 3*k**4 - 2*k**3 + 6*k**2 + 9*k - 36. Suppose m(v) = 0. What is v?
-3, -1, 1
Let g be 8/5 - 4/(-10). Suppose -g*i = 3*m - 2, -i - 5*m - 6 = -0*m. Factor 0*d - 2/3*d**i + 4/3*d**3 - 2/3*d**2 + 0.
-2*d**2*(d - 1)**2/3
Let h(y) be the first derivative of -2 + 1/15*y**5 + 1/3*y - 2/9*y**3 + 0*y**4 + 0*y**2. Factor h(n).
(n - 1)**2*(n + 1)**2/3
Let s be 9/(-6) + (84/7 - 9). Factor -9/4*j**2 - 1/4 - s*j.
-(3*j + 1)**2/4
Let g be ((-464)/(-290))/(1/(10/4)). Solve -2/13*x**3 - 2/13*x**2 + 2/13*x**g + 2/13*x**5 + 0*x + 0 = 0 for x.
-1, 0, 1
Let a(f) be the second derivative of -f**5/60 - f**4/8 - f**3/3 + 2*f**2 + 4*f. Let u(p) be the first derivative of a(p). Factor u(i).
-(i + 1)*(i + 2)
Let o be 0 - (1 - (4 - 3))/1. Let w(j) be the first derivative of -1/3*j**3 + o*j + 3 + 0*j**2. Factor w(q).
-q**2
Suppose -4*d = -17 + 5. Solve 0 - 2/9*i + 0*i**2 + 2/9*i**d = 0 for i.
-1, 0, 1
Solve 2/9*c + 4/9*c**2 - 4/9 - 2/9*c**3 = 0 for c.
-1, 1, 2
Let t(k) be the third derivative of k**7/1155 - k**6/330 - k**5/110 + k**4/33 + 4*k**3/33 + 10*k**2. Factor t(s).
2*(s - 2)**2*(s + 1)**2/11
Suppose -j - 1 = -0*j + 4*n, 2*j + 4*n = 2. Let p(c) be the first derivative of 0*c**2 + 0*c + 1/12*c**j - 2 + 0*c**4 - 1/20*c**5. Factor p(k).
-k**2*(k - 1)*(k + 1)/4
Let i(v) be the first derivati