h(i) = 0. What is i?
0, 2
Let j(d) = d**2 - d + 1. Let v be (4/3)/(2/3). Let l be j(v). Factor 2*g**5 + 0*g**l - 4*g**5 - 5*g**4 - 2*g**3 + g**4.
-2*g**3*(g + 1)**2
Let o(l) be the first derivative of -l**3/3 - l**2 + 10. Factor o(f).
-f*(f + 2)
Let s(x) be the second derivative of -x**9/68040 + x**8/30240 + x**4/6 + x. Let q(r) be the third derivative of s(r). Factor q(w).
-2*w**3*(w - 1)/9
Let l = -9 - -13. Find c, given that -3*c**4 + 5 - 2*c - c + 2*c**3 - l + c**5 + 2*c**2 = 0.
-1, 1
Let s = -101/99 - -10/9. Let x(t) be the first derivative of 0*t**3 - 1/33*t**6 + 0*t**5 + 0*t - 3 - s*t**2 + 1/11*t**4. Factor x(o).
-2*o*(o - 1)**2*(o + 1)**2/11
Let y(f) be the second derivative of 2*f**7/189 - 2*f**6/45 + f**5/15 - f**4/27 - 18*f. Determine v, given that y(v) = 0.
0, 1
Let q(b) = -b**3 + 3*b**2 + 4*b. Let i(t) = 2*t**3 - 4*t**2 - 6*t. Let j(a) = 2*i(a) + 3*q(a). Factor j(l).
l**2*(l + 1)
Let y(h) be the second derivative of 0 - 1/15*h**2 - 1/150*h**5 + 1/90*h**4 + 5*h + 1/45*h**3. Factor y(v).
-2*(v - 1)**2*(v + 1)/15
Let b(w) = w + 7. Let o be b(-6). Let z = 3 - o. Factor -4*h**3 + 2*h**4 - 2*h**4 + z*h**2 + 2*h**4.
2*h**2*(h - 1)**2
Let m(s) be the second derivative of s**6/20 + 29*s**5/120 + 11*s**4/24 + 5*s**3/12 + s**2/6 + 8*s. Factor m(w).
(w + 1)**3*(9*w + 2)/6
Factor -3/2*c**4 + 0 + 3/2*c**2 - 1/4*c**3 + 1/4*c.
-c*(c - 1)*(c + 1)*(6*c + 1)/4
Let o(a) be the first derivative of a**4/26 + 10*a**3/39 + 7*a**2/13 + 6*a/13 + 6. Find v, given that o(v) = 0.
-3, -1
Let o(t) = -t**2 + t - 1. Let z(f) = -5*f**5 - 10*f**4 - 4*f**2 + 4*f - 4. Let h(v) = -4*o(v) + z(v). Suppose h(k) = 0. What is k?
-2, 0
Suppose -8*i + 3 = -7*i. Let t be (6 - 2)*2/5. Find f, given that 22/5*f**2 - t + 16/5*f - 6*f**i = 0.
-2/3, 2/5, 1
Let h = 1232 + -1229. Solve 3 - 3/2*m**h + 3/2*m - 3*m**2 = 0 for m.
-2, -1, 1
Let b(x) be the first derivative of x**8/1680 - x**7/1050 - x**6/200 + x**5/60 - x**4/60 - 4*x**2 - 10. Let a(o) be the second derivative of b(o). Factor a(s).
s*(s - 1)**3*(s + 2)/5
Let b(w) = w + 206. Let l be b(0). Factor l*j**2 + 108 + 324*j + 154*j**2 + 4*j**5 + 19*j**4 + 25*j**4 + 184*j**3.
4*(j + 1)**2*(j + 3)**3
Let o = 47 - 45. Factor -12*d**3 - 20/9*d + 8*d**o + 6*d**4 + 2/9.
2*(d - 1)*(3*d - 1)**3/9
Find a such that -28*a**4 + 4*a - 21*a**4 - 18*a**2 + 60*a**3 + 16*a**5 - 3*a**4 - 10*a**2 = 0.
0, 1/4, 1
Let w = -10587 + 74243/7. Let y = -132/7 + w. Factor -4/7*n - y - 2/7*n**2.
-2*(n + 1)**2/7
Let v(w) = 109*w**4 - 76*w**3 + 12*w**2 + 4. Let q(t) = 108*t**4 - 75*t**3 + 12*t**2 + 3. Let r(s) = -4*q(s) + 3*v(s). Factor r(h).
-3*h**2*(5*h - 2)*(7*h - 2)
Let k(x) be the second derivative of x**5/20 - 3*x**4/8 + x**3 - x**2/2 + 5*x. Let s(a) be the first derivative of k(a). Factor s(t).
3*(t - 2)*(t - 1)
Let v(m) = 6*m**3 + 2*m**2 + 2*m**2 - 5*m**2 - m**2. Let b(g) = -7*g**3 + 3*g**2 - g. Let c(t) = 4*b(t) + 5*v(t). Factor c(w).
2*w*(w - 1)*(w + 2)
Let p(o) be the first derivative of 9*o**4/8 + 13*o**3/2 + 12*o**2 + 6*o - 7. Factor p(g).
3*(g + 2)**2*(3*g + 1)/2
Let b = 1 - 1. Suppose -2*h = -b - 4. Factor 4*z**4 - z**3 + h*z**3 - z**3 - 10*z**5.
-2*z**4*(5*z - 2)
Let y = 3/109 - -315/436. Let i(q) = q**3 + 10*q**2 + 12*q + 27. Let b be i(-9). Suppose 0*k + 1/4*k**5 - 1/4*k**2 + b - y*k**4 + 3/4*k**3 = 0. Calculate k.
0, 1
Suppose 5*q = 2*q + 12. Let h be ((-6)/(-2))/(6/q). Factor g**3 - g**5 - 2*g**2 + 3*g**2 - g**4 + 0*g**h.
-g**2*(g - 1)*(g + 1)**2
Let t = -965 - -6773/7. Factor 10/7*n**2 + 2/7*n + t*n**3 + 0 + 2*n**4 + 4/7*n**5.
2*n*(n + 1)**3*(2*n + 1)/7
Let r(n) = 2*n**4 - 2*n**3 - 3*n**2 - 3*n. Let h(f) = f**4 - f**3 - f**2 - f. Let z(y) = 6*h(y) - 2*r(y). Solve z(u) = 0.
0, 1
Let f(v) be the third derivative of -7/32*v**4 - 1/20*v**5 + 1/4*v**3 + 0*v + 3*v**2 + 0. Factor f(u).
-3*(u + 2)*(4*u - 1)/4
Let t(a) be the third derivative of a**8/151200 + a**7/9450 + a**6/1800 - a**5/10 - 4*a**2. Let v(p) be the third derivative of t(p). Let v(j) = 0. What is j?
-3, -1
Let o(h) be the first derivative of 5*h**6/6 + 11*h**5 + 115*h**4/2 + 150*h**3 + 405*h**2/2 + 135*h - 26. Find x such that o(x) = 0.
-3, -1
Let w(p) = 8*p**5 + 8*p**4 - 4*p + 4. Let l(m) = -9*m**5 - 9*m**4 - m**3 - m**2 + 5*m - 5. Let g(t) = -4*l(t) - 5*w(t). Factor g(o).
-4*o**2*(o - 1)*(o + 1)**2
Let z(h) be the third derivative of h**8/616 + 2*h**7/385 - h**5/55 - h**4/44 - 25*h**2. Factor z(y).
6*y*(y - 1)*(y + 1)**3/11
Let w(t) be the third derivative of t**5/160 + t**4/64 - t**3/8 - 8*t**2. Solve w(c) = 0.
-2, 1
Factor 4/9*x**4 - 2/9*x**3 + 0*x**2 + 0*x - 2/9*x**5 + 0.
-2*x**3*(x - 1)**2/9
Let b(q) be the first derivative of 3 - 20/3*q**3 - 2*q + 5*q**4 + 5*q**2 + 1/3*q**6 - 2*q**5. What is p in b(p) = 0?
1
Let i(b) be the second derivative of 0 - 3/40*b**5 + 0*b**2 + 1/8*b**4 + 1/60*b**6 - 1/12*b**3 - 3*b. Factor i(o).
o*(o - 1)**3/2
Let o(w) be the second derivative of w**4/36 + w**3/6 + 5*w. Factor o(l).
l*(l + 3)/3
Let l be (-6)/21 + 639/(-140). Let g = l - -21/4. Find p such that 0*p + 0 - g*p**5 + 0*p**2 + 0*p**4 + 0*p**3 = 0.
0
Let y(w) = 4*w**4 - 6*w**3 + 10*w - 6. Let q(s) be the second derivative of s**5/20 - s**3/6 - s**2/2 - 5*s. Let k(a) = -6*q(a) + y(a). Factor k(t).
4*t*(t - 2)**2*(t + 1)
Suppose -3*v - 6 = -2*v. Let o = v + 8. Suppose -2*f**4 - o*f**5 - f**3 - 1 - 1 - 2*f + 4*f**2 + 5*f**3 = 0. Calculate f.
-1, 1
Let x be 1 - (-2)/((-2)/(-1)). Find p such that -3*p + 4*p**4 + 5*p**3 - x*p**4 + 3*p**2 - 2*p**3 - 5*p**4 = 0.
-1, 0, 1
Suppose -d + 11 = 3*l, d + l - 2*l = -1. Factor -c**2 - 2 + d*c**2 + 4 + 0*c**2 - 3*c.
(c - 2)*(c - 1)
Let d(l) = 3*l - 15. Let q be d(6). Suppose 2*v + v + 2*y = 14, 2 = v - 2*y. Factor k**q + 2*k**5 + 0*k**3 - v*k**4 + k**3.
2*k**3*(k - 1)**2
Suppose 0 = -4*h - 0*h - 140. Let l be (-8)/(-28) - 4/h. Factor l + 2/5*g**2 + 4/5*g.
2*(g + 1)**2/5
Let j(n) be the third derivative of n**8/141120 - n**7/11760 + n**6/2520 - 7*n**5/60 + 5*n**2. Let h(a) be the third derivative of j(a). Factor h(g).
(g - 2)*(g - 1)/7
Let u(x) = 4*x**3 - 4*x. Let r(f) = 3*f**3 - 3*f. Let y(h) = 5*r(h) - 4*u(h). Factor y(t).
-t*(t - 1)*(t + 1)
Let c = -510 - -513. Solve -2/7*x - 2/7*x**5 + 0 + 8/7*x**2 - 12/7*x**c + 8/7*x**4 = 0 for x.
0, 1
Let a(m) be the first derivative of -5*m**3/9 + 5*m**2/6 + 16. Factor a(r).
-5*r*(r - 1)/3
Let i(q) = -q + 2. Let r be i(-2). Let p = r - 0. Let 2*b**2 - p*b - 1 + 3 + 0*b = 0. What is b?
1
Let o(r) = -r + 11. Let d be o(8). Suppose 5*j + d*l - 6 = 0, l - 12 = 5*l. Find c such that -2*c**j + c**4 + 3 - 3 + c**2 = 0.
0, 1
Let x(b) be the third derivative of -b**7/105 + b**6/12 - 3*b**5/10 + 7*b**4/12 - 2*b**3/3 - 6*b**2. Let x(s) = 0. Calculate s.
1, 2
Let v be (-1)/(-1*3/30). Suppose 0 = -2*i + 4*i - v. Factor 2/7*a**i + 4/7*a**2 - 2/7*a**4 + 2/7*a - 2/7 - 4/7*a**3.
2*(a - 1)**3*(a + 1)**2/7
Suppose -i = 5*o - o + 37, 3*i - 1 = 2*o. Let x be o/(-20) - (-12)/(-80). Suppose x*c**4 + 1/4*c + 3/4*c**3 + 3/4*c**2 + 0 = 0. What is c?
-1, 0
Let k(i) = -i**2 - 12*i - 36. Let j be k(-6). Determine y, given that j + 3/4*y**2 + 0*y + 3/4*y**4 + 3/2*y**3 = 0.
-1, 0
Let m = 5 + -2. Factor -1 + 0 - 12*q**2 + 6*q + 4*q**3 + m*q**2.
(q - 1)**2*(4*q - 1)
Let i be -3*(-1184)/2448 - (-4)/(-34). Determine j so that i - 2/3*j - 2/3*j**2 = 0.
-2, 1
Let r(a) = 6*a**3 - 2*a**2 - 3*a + 3. Let d(b) = -6*b**3 + 2*b**2 + 4*b - 4. Let m be (-18)/(-4)*4/6. Let o(k) = m*d(k) + 4*r(k). Factor o(u).
2*u**2*(3*u - 1)
Factor -377*h**4 + 0*h**3 + 2*h**3 - 2*h**2 + 379*h**4 - 2*h.
2*h*(h - 1)*(h + 1)**2
Let u(n) be the first derivative of n**7/420 - n**6/360 - n**5/60 + n**4/24 - 4*n**3/3 + 1. Let z(g) be the third derivative of u(g). Find a such that z(a) = 0.
-1, 1/2, 1
Let y(p) = -2*p**3 + 6*p**2 - 2*p. Suppose 11 = 3*o - 7. Let f(d) = 3*d - 2*d**2 - 10*d**2 + 3*d**3 + 6*d**2. Let z(w) = o*y(w) + 5*f(w). What is i in z(i) = 0?
-1, 0
Let p(y) be the second derivative of -y**5/72 - 7*y**4/144 - y**3/18 - 3*y**2 - y. Let z(c) be the first derivative of p(c). Determine k, given that z(k) = 0.
-1, -2/5
Find h, given that -3/2*h**2 + 3/2*h**3 + 0 - 3*h = 0.
-1, 0, 2
Let p = 2/137 + 951/548. Let q = -3/2 + p. Determine g, given that -1/4*g**2 + 0 + q*g = 0.
0, 1
Suppose -2*z - 4*g = 60, -2*z = -3*z + 3*g - 5. Let p = z - -20. Factor p + 2/9*c**2 - 2/9*c.
2*