+ 1/40*h**5 + 0 + h + 1/2*h**2. Suppose i(o) = 0. What is o?
-2, 1
Let l(g) be the third derivative of 0*g**6 + 0*g**5 + 0 + 0*g**4 + 3*g**2 + 1/2520*g**7 + 1/6*g**3 + 0*g. Let u(m) be the first derivative of l(m). Factor u(c).
c**3/3
Suppose 0 = -3*a + 5 + 1. Let f(w) be the third derivative of 0*w + 1/72*w**4 - 2*w**a - 1/630*w**7 + 0 + 1/120*w**6 - 1/60*w**5 + 0*w**3. Solve f(q) = 0.
0, 1
Factor 32/7*t + 2/7*t**2 + 128/7.
2*(t + 8)**2/7
Let p(o) = 31*o**2 - 60*o + 14. Let t(f) = 30*f**2 - 60*f + 15. Let d(x) = -5*p(x) + 6*t(x). Let d(n) = 0. What is n?
2/5, 2
Let u be ((-1)/2)/((-27)/(-12) - 3). Find x such that -4/3 + 4/3*x**2 - 2/3*x + u*x**3 = 0.
-2, -1, 1
Let h(o) = -20*o**5 + 20*o**4 - 15*o**3 - 20*o**2 - 15*o - 25. Let u(m) = -m**5 + m**4 - m**2 - m - 1. Let c(x) = h(x) - 25*u(x). Factor c(b).
5*b*(b - 2)*(b - 1)*(b + 1)**2
Let y = -19 + 24. Let x(v) be the second derivative of 2*v + 1/6*v**3 + 0 + 0*v**2 - 1/20*v**y + 0*v**4. Factor x(g).
-g*(g - 1)*(g + 1)
Factor 6*r + 5*r**4 - r**2 - 4*r**2 - 6*r - 20*r**3 + 20*r.
5*r*(r - 4)*(r - 1)*(r + 1)
Let r = -125/6 - -45/2. Let i(u) be the first derivative of 2*u**2 + 1/2*u**4 - u - r*u**3 - 2. Let i(o) = 0. What is o?
1/2, 1
Let g(q) = 2*q**2 + 8*q + 6. Let c be g(-5). Let p = c - 13. Factor 0*r**2 - 1/4*r + 1/4*r**p + 0.
r*(r - 1)*(r + 1)/4
Let i = -31 + 34. Let t be (-9)/i + (-39)/(-9). What is n in 2/3*n**5 + 0*n**3 + 0 - 2/3*n + 4/3*n**2 - t*n**4 = 0?
-1, 0, 1
Solve -4*r**2 + r**2 + 2*r**3 - 2*r**4 - r**2 + 4*r**3 = 0.
0, 1, 2
Let o be 9/(-6)*(-4)/(36/3). Solve -1/2 - o*u**2 - u = 0 for u.
-1
Let o = 274/81 - 4/81. Suppose 0 = -5*q + 3*q + 10. Determine y so that -6*y**q + 4/3*y**2 - o*y + 28/3*y**3 + 2/3 - 2*y**4 = 0.
-1, 1/3, 1
Suppose -5*o + 12*o - 14 = 0. Factor 0*i - 1/5 + 1/5*i**o.
(i - 1)*(i + 1)/5
Let i(r) be the second derivative of -r**6/1080 + r**5/60 - r**4/8 + r**3/3 - 4*r. Let x(a) be the second derivative of i(a). Let x(f) = 0. What is f?
3
Let v = 9 + -4. Let 4*c**2 + 15*c**4 + 3*c**v + 3*c**5 - 19*c**4 + 2*c - 8*c**3 = 0. What is c?
-1, -1/3, 0, 1
Let j(v) = -371*v**4 - 83*v**3 + 203*v**2 - 79*v - 7. Let u(p) = 186*p**4 + 42*p**3 - 102*p**2 + 39*p + 3. Let k(s) = -6*j(s) - 13*u(s). Factor k(b).
-3*(b + 1)*(4*b - 1)**3
Determine z so that -2/5*z**2 + 1/5*z**3 + 2/5 - 1/5*z = 0.
-1, 1, 2
Factor 6/5*n**3 - 8/5 + 24/5*n - 22/5*n**2.
2*(n - 2)*(n - 1)*(3*n - 2)/5
Let g(n) be the second derivative of -n**4/18 + n**2/3 + 6*n. Factor g(u).
-2*(u - 1)*(u + 1)/3
Let l(u) be the third derivative of u**8/840 - 2*u**7/525 + u**5/75 - u**4/60 - 10*u**2. Let l(p) = 0. Calculate p.
-1, 0, 1
Let o(l) be the third derivative of -l**6/96 + l**5/30 - l**4/96 - l**3/12 + 10*l**2. Factor o(k).
-(k - 1)**2*(5*k + 2)/4
Let s(c) be the first derivative of 0*c**5 + 1/180*c**6 + 0*c**3 + 0*c + 0*c**4 + 1/2*c**2 + 2. Let x(g) be the second derivative of s(g). Factor x(m).
2*m**3/3
Let y(o) = -o**2 - 7*o - 6. Let d be y(-5). Suppose -j**3 - 6*j - 2*j**3 + j**d + 4*j**3 + 5*j - j**2 = 0. Calculate j.
-1, 0, 1
Factor -6 + 2127*n**2 - 2177*n**2 - 2*n**5 - 2 - 32*n - 14*n**4 - 38*n**3.
-2*(n + 1)**3*(n + 2)**2
Suppose -a - 241 = -4*a + v, -405 = -5*a + 5*v. Let p be 6/21 - a/(-14). Factor -4*h**5 - p*h**3 + 5*h**2 - 10*h**4 - 2*h**5 - 3*h**2 + 4*h**3.
-2*h**2*(h + 1)**2*(3*h - 1)
Let o(y) be the second derivative of y**7/84 + y**6/20 + y**5/20 - 8*y. Factor o(b).
b**3*(b + 1)*(b + 2)/2
Suppose 2*s - 48 = -3*f, -f + 24 = s - 3*s. Let y = f - 16. Factor 4/3*i - 2/3 - 2/3*i**y.
-2*(i - 1)**2/3
Let n be 7/35 + (-4)/(-5). Let 0 + c**2 - n + c**2 - c**4 = 0. Calculate c.
-1, 1
Let b(q) = -q + 6. Let t be b(4). Solve -2/7*o**3 + 4/7*o**t + 2/7*o - 4/7 = 0.
-1, 1, 2
Let r(s) be the second derivative of s**6/40 + 3*s**5/20 + 3*s**4/16 - s**3/2 - 3*s**2/2 + 5*s. Factor r(q).
3*(q - 1)*(q + 1)*(q + 2)**2/4
Let p(h) be the second derivative of -h**7/10080 - h**6/1440 - h**5/480 - h**4/3 + 8*h. Let x(o) be the third derivative of p(o). Factor x(v).
-(v + 1)**2/4
Suppose 2*w + 6 = -4*c + 2, c + 3 = 0. Let a be 1 + -4 + (-36)/(-10). Solve 3/5*r**2 + a*r**3 + 1/5*r + 1/5*r**w + 0 = 0.
-1, 0
Let i = -8 + 14. Suppose -3*j - 9 = 3*w, i + 11 = -4*j - 5*w. Solve -6/7*b + 4/7 + 2/7*b**j = 0.
1, 2
Let q(r) = -3*r**5 + 7*r**4 + 8*r**3 - 7*r**2 - 5*r - 5. Let d(y) = -2*y**5 + 3*y**4 + 4*y**3 - 3*y**2 - 2*y - 2. Let g(v) = -5*d(v) + 2*q(v). Factor g(k).
k**2*(k - 1)*(k + 1)*(4*k - 1)
Let h = 12 - 8. Factor 3*v**4 + 7*v**3 - 19*v**3 - 8*v**2 - 7*v**h.
-4*v**2*(v + 1)*(v + 2)
Let a(m) be the second derivative of 2*m**7/21 + m**6/15 - m**5/5 - m**4/6 + 7*m. Solve a(p) = 0.
-1, -1/2, 0, 1
Factor 3*h**3 + 8*h - 5*h**2 + 2*h + 3*h**2 - 6 - 5*h**3.
-2*(h - 1)**2*(h + 3)
Let m(r) = -r**3 - 4*r**2 + 4. Let h be m(-3). Let i(l) = l**2 - l + 3. Let k be i(h). Factor 2*j**2 - j - k*j**4 + 32*j**4 - 3 + 2 + 2*j**3 - j**5.
-(j - 1)**2*(j + 1)**3
Suppose 6*n = -16 + 40. Let m(u) be the third derivative of 0 + 0*u**6 - 1/70*u**7 + 0*u**n + 0*u + 3*u**2 + 1/20*u**5 + 0*u**3. Factor m(p).
-3*p**2*(p - 1)*(p + 1)
Let t(i) = 5*i - 7. Let m be t(9). Let q = m + -35. Factor -1/5*n**q + 0 + 0*n + 1/5*n**2.
-n**2*(n - 1)/5
Determine t, given that -t**2 + 4*t**4 - 3*t**2 + 4*t**3 - 2*t**5 - 5*t**5 + 3*t**5 = 0.
-1, 0, 1
Let g(i) be the third derivative of 0*i**6 - 1/24*i**4 - 1/420*i**7 + 0*i + 0 + 0*i**3 - 3*i**2 + 1/40*i**5. Factor g(r).
-r*(r - 1)**2*(r + 2)/2
Let v be (-116)/(-32) - (-3 - -5 - 1). Find s such that 0 - 3/4*s + 27/8*s**3 - v*s**2 = 0.
-2/9, 0, 1
Let b(k) be the second derivative of k**7/5880 - k**6/2520 - k**5/840 + k**4/168 + k**3/6 + 8*k. Let h(g) be the second derivative of b(g). Factor h(d).
(d - 1)**2*(d + 1)/7
Let g(a) = -5*a**3 + 7*a**2 + 5*a - 7. Let n(r) = 6*r**3 - 8*r**2 - 6*r + 8. Let d(i) = 7*g(i) + 6*n(i). What is b in d(b) = 0?
-1, 1
Let j(u) = u + 2 + 2*u**2 - 3 - 2*u. Let a be j(-1). Determine x so that -3/4*x**3 - 1/4*x**4 - 1/4*x + 0 - 3/4*x**a = 0.
-1, 0
Let q be -1 + -1 - 2097/(-45). Let d = 45 - q. Factor -14/5*p**2 - 6/5*p**3 - 2*p - d.
-2*(p + 1)**2*(3*p + 1)/5
Let o(z) = z**5 - 2*z**4 - 2*z**3 + z - 2. Let y(i) = i**3 + i**2 - i + 1. Let x(a) = o(a) + 2*y(a). Suppose x(h) = 0. What is h?
-1, 0, 1
Let c(h) be the first derivative of h**4/8 - 3*h**2/4 + h + 28. Determine x, given that c(x) = 0.
-2, 1
Suppose 3*v = -3*p + 15, -2*p + 5*p - 5*v = -9. Factor 0 - 6/11*n**3 + 0*n**p + 8/11*n - 2/11*n**4.
-2*n*(n - 1)*(n + 2)**2/11
Let j = -13 + 9. Let l be -4 + 196/24 + j. Determine x so that 0 + 0*x**2 - 1/6*x**3 + l*x = 0.
-1, 0, 1
Let n = -80 + 82. What is w in -2/11*w**3 + 0 + 2/11*w**5 + 0*w + 2/11*w**n - 2/11*w**4 = 0?
-1, 0, 1
Suppose 6*p - 364 + 9*p + 346 + 3*p**2 = 0. What is p?
-6, 1
Let b(a) be the second derivative of a**6/630 + a**5/420 - a**3/6 + a. Let w(p) be the second derivative of b(p). Factor w(o).
2*o*(2*o + 1)/7
Let c = 599 + -2991/5. Factor c*s**2 - 2/5 + 2/5*s - 4/5*s**3 - 2/5*s**4 + 2/5*s**5.
2*(s - 1)**3*(s + 1)**2/5
Let j(c) = 3*c - 15. Let g be j(7). Let p(f) be the third derivative of 0 - f**2 + 0*f + 0*f**3 + 1/24*f**4 + 1/120*f**g + 1/30*f**5. Find x such that p(x) = 0.
-1, 0
Let t(p) be the first derivative of -1 + 1/3*p - 1/6*p**2 - 1/9*p**3 + 1/12*p**4. Factor t(g).
(g - 1)**2*(g + 1)/3
Let y = 4/27 - -61/135. Determine b so that y*b**2 - b - 2/5 = 0.
-1/3, 2
Let a(w) = w**2 - 8*w + 9. Let t be a(7). Determine n so that 5*n**5 + 0*n**5 - 3*n**5 + 0*n**5 - t*n**3 = 0.
-1, 0, 1
Let z(u) = -u**2 + 7*u - 1. Suppose -h = -o - 6, 24 = 4*h + o + 4*o. Let k be z(h). Factor 76*q**4 + 95*q**3 + 9*q**3 + 19*q**k + 2*q**5 + 2 + 19*q + 66*q**2.
(q + 1)**3*(3*q + 1)*(7*q + 2)
Let t be 10/(-12)*3*4/(-5). Let v(q) be the first derivative of 0*q - 5/24*q**4 - 1 + 1/6*q**t + 1/18*q**3 + 1/12*q**6 - 1/30*q**5. Solve v(x) = 0.
-1, -2/3, 0, 1
Factor -50/3 + 20/3*o - 2/3*o**2.
-2*(o - 5)**2/3
Factor -3/5*l + 1/5*l**2 + 0.
l*(l - 3)/5
Let c = -7 - -10. Factor -41*i - 4*i**4 - 12*i**2 + 21*i + 4*i + 16*i**c + 16.
-4*(i - 2)**2*(i - 1)*(i + 1)
Let s(j) be the second derivative of -j**8/2240 - j**7/480 - j**6/288 - j**5/480 - 2*j**3/3 + 7*j. Let z(b) be the second derivative of s(b). Factor z(h).
-h*(h + 1)**2*(3*h + 1)/4
Let z(v) be the third derivative of v**5/180 - 2*v**4/9 + 32*v**3/9 + 22*v**2. Fact