
-p*(p - 1)*(p + 1)*(2*p + 1)/4
Let v(l) be the third derivative of l**7/70 - l**6/40 - l**5/20 + l**4/8 + 5*l**2. Let v(a) = 0. Calculate a.
-1, 0, 1
Suppose o - 4*o = 0. Let j(d) be the second derivative of o*d**2 - 3/20*d**5 - 4*d - 1/4*d**4 + 0 + 0*d**3. Factor j(q).
-3*q**2*(q + 1)
Let v(c) = -c. Let a(i) = -i**2 - 2*i. Let d(g) = -5*a(g) + 5*v(g). Factor d(m).
5*m*(m + 1)
Let o(z) be the third derivative of z**5/24 + 14*z**2. Factor o(a).
5*a**2/2
Let k(p) be the third derivative of p**2 + 0*p - 1/12*p**4 - 1/20*p**5 + 0 + 1/6*p**3. Factor k(a).
-(a + 1)*(3*a - 1)
Let i(s) be the third derivative of -s**6/50 - s**5/100 - 45*s**2. Factor i(y).
-3*y**2*(4*y + 1)/5
Let i = -1/26 + 7/13. Let o = i - 1/6. What is z in -z**2 + 0 - z**3 - o*z - 1/3*z**4 = 0?
-1, 0
Let t(w) be the first derivative of 1/3*w**3 + 0*w**4 + 0*w - 2 + 0*w**2 - 1/1440*w**6 + 1/480*w**5. Let i(p) be the third derivative of t(p). Factor i(f).
-f*(f - 1)/4
Let a(w) = -w**3 + w**2 + w - 1. Let s(y) = 6*y**3 + 2*y**2 - 15*y + 7. Let l(b) = 21*a(b) + 3*s(b). Factor l(n).
-3*n*(n - 8)*(n - 1)
Suppose -3*a - 14 = -t, 4 = -2*t - a - 3. Let r be (-13)/26*1*t. Factor 0*d**3 + r*d**4 + 0 - 3/2*d**2 - d.
d*(d - 2)*(d + 1)**2/2
Let f(w) = w**2 + w - 2. Let n be f(2). Suppose n = -s + 3*s. Factor 1/5*g + 1/5*g**4 + 0 - 1/5*g**s - 1/5*g**3.
g*(g - 1)**2*(g + 1)/5
Let r(v) = v**3 - 8*v**2 + 17*v - 10. Let a be r(5). Let q = -12 + 61/5. Determine y, given that q*y**2 + a - 2/5*y = 0.
0, 2
Let i(j) be the first derivative of -3*j**6/2 + 34*j**5/5 - 23*j**4/2 + 8*j**3 - j**2/2 - 2*j + 10. Factor i(a).
-(a - 1)**4*(9*a + 2)
Let r(l) = -5*l**3 - 15*l**2 - 10*l + 11. Let m(z) = 2 - z**3 + 2*z - 10*z**2 - 4*z + 7*z**2. Let a(t) = -33*m(t) + 6*r(t). Find u such that a(u) = 0.
-2, -1, 0
Suppose -2/3*s + 0 - 2/3*s**3 - 4/3*s**2 = 0. What is s?
-1, 0
Let i(j) be the third derivative of -1/60*j**5 + 0 + 0*j + 0*j**3 + 0*j**4 + 4*j**2. What is s in i(s) = 0?
0
Let z = 7 + -4. Suppose 3*w = -3*s + 9, -5*w + z*s + 2*s = -5. Let -6*o**2 - 1 - 5*o**2 + 5*o**w - o**4 - 4*o - 4*o**3 = 0. What is o?
-1
Let r = -157 + 159. Factor 2/13*h**3 + 0*h**r - 6/13*h + 4/13.
2*(h - 1)**2*(h + 2)/13
Factor 0 - 2/7*h**2 + 2/7*h - 2/7*h**3 + 2/7*h**4.
2*h*(h - 1)**2*(h + 1)/7
Let f(v) = v**2 + 11*v - 5. Let x(d) = -d + 1. Let g(z) = -f(z) - 5*x(z). Let g(m) = 0. Calculate m.
-6, 0
Let n(q) be the second derivative of -3*q**5/20 + q**4/4 + q**3/2 - 3*q**2/2 - 35*q. Let n(h) = 0. Calculate h.
-1, 1
Let 0 - 5*z**3 + 0*z - 5/4*z**4 - 5*z**2 = 0. Calculate z.
-2, 0
Let k(t) be the second derivative of t**6/10 + 9*t**5/20 - 3*t**4/4 - 7*t**3/2 + 9*t**2 - 10*t. Factor k(d).
3*(d - 1)**2*(d + 2)*(d + 3)
Let z(t) be the third derivative of -1/15*t**3 + 1/60*t**4 + 1/75*t**5 + 0*t + 0 + 1/840*t**8 - 1/150*t**6 + 4*t**2 - 1/525*t**7. Solve z(m) = 0.
-1, 1
Let t(l) be the second derivative of 7*l**5/180 + 5*l**4/108 - 8*l**3/27 + 2*l**2/9 - l. Factor t(m).
(m - 1)*(m + 2)*(7*m - 2)/9
Factor -2/13*g**3 + 2/13*g**4 + 0*g + 0*g**2 + 0.
2*g**3*(g - 1)/13
Let o be 2 + 2 - (-1 - (-3 + -2)). Factor o + 1/3*u**2 - 1/3*u.
u*(u - 1)/3
Suppose 2*y + 9 = p - 10, 4*y - 5*p + 41 = 0. Let s = y - -11. Factor -2/9*t + 4/9 - 10/3*t**s.
-2*(3*t - 1)*(5*t + 2)/9
Let k(t) be the first derivative of t**3 + 24*t**2 + 192*t + 30. Suppose k(f) = 0. Calculate f.
-8
Let -19*o**4 + 8*o**4 - 30*o**2 + 6*o**4 - 35*o**3 = 0. What is o?
-6, -1, 0
Determine i so that 19 - 3*i**2 + 5*i**2 - 40 - 4*i + 15 = 0.
-1, 3
Let l(w) = -2*w**2 + 205*w - 1089. Let m(r) = -r**2 + 68*r - 363. Let o(d) = -2*l(d) + 7*m(d). Factor o(g).
-3*(g - 11)**2
Suppose d - 6 = 3*d. Let n be 3*(-1)/d*3. Factor 0*o**2 + 2/3*o**n - 2/3*o - 1/3 + 1/3*o**4.
(o - 1)*(o + 1)**3/3
Suppose 2*m + 32 = -2*m. Let w be 29/9 - (-24)/m. Factor 0*l + w*l**2 + 0.
2*l**2/9
Let y be 7/((-70)/4)*-10. Suppose 2*m - y = -0. Suppose 2/7*p**m + 0*p + 0 = 0. What is p?
0
Suppose 0 = j + 4*j - 20. Let z(u) be the second derivative of -1/6*u**j + u + 0*u**3 + 0*u**2 + 0. Let z(d) = 0. Calculate d.
0
Let v = 4 - -22. Let o be 3 - (-3)/((-30)/v). Factor o - 12/5*n + 18/5*n**2.
2*(3*n - 1)**2/5
Let w(c) be the second derivative of -4*c**7/105 + 13*c**6/75 - 7*c**5/50 - 11*c**4/30 + 11*c**3/15 - 2*c**2/5 - 11*c. What is u in w(u) = 0?
-1, 1/4, 1, 2
Let o(u) be the first derivative of -u**6/8 - 9*u**5/20 - 3*u**4/8 + u**3/2 + 9*u**2/8 + 3*u/4 + 1. Find s, given that o(s) = 0.
-1, 1
Let q = -9 - -52. Let d = q - 127/3. Factor 0 + 8/3*w**5 + 0*w**4 - 2*w**3 + 0*w + d*w**2.
2*w**2*(w + 1)*(2*w - 1)**2/3
Let p = 0 + 2. Solve d + 0*d + 4*d**p - 2*d**2 = 0.
-1/2, 0
Let q(v) = -v**2 - 11*v + 3. Let c = -11 - 0. Let r be q(c). Suppose 0*k**3 + k**2 + k**3 + 0*k**r = 0. Calculate k.
-1, 0
Let v(c) = -2 + 4*c**2 + 5 + 0*c**2. Let r(y) be the third derivative of -y**5/30 - y**3/3 + 2*y**2. Let q(a) = -7*r(a) - 4*v(a). Suppose q(x) = 0. What is x?
-1, 1
Let w(h) be the third derivative of -h**10/50400 - h**9/10080 - h**8/6720 - h**5/12 - h**2. Let f(z) be the third derivative of w(z). What is c in f(c) = 0?
-1, 0
Let c = -441 - -441. Factor c + 2/5*z**2 - 4/5*z.
2*z*(z - 2)/5
Let m = -428/85 - -24/5. Let u = m - -70/153. Find p such that -2/3*p**2 + u*p**3 + 2/3*p - 2/9 = 0.
1
Suppose 5*i - i - 22 = n, 0 = 4*n + 8. Let u(x) be the second derivative of 0 - x - 1/18*x**3 + 1/20*x**i + 0*x**2 + 1/18*x**4. Factor u(b).
b*(b + 1)*(3*b - 1)/3
Let b(c) be the first derivative of c**3/24 + 23. Factor b(k).
k**2/8
Let -m - 1/2*m**3 + 0 - 3/2*m**2 = 0. What is m?
-2, -1, 0
Let -16/13*x - 2/13*x**3 + 8/13 + 10/13*x**2 = 0. Calculate x.
1, 2
Let u be 0/(-2 + 4) - -4. Factor -u*m**3 + 15*m - 35*m - 16*m**2 - 2 - 6.
-4*(m + 1)**2*(m + 2)
Factor -3/4*w + 0 - 3/4*w**2.
-3*w*(w + 1)/4
Suppose p = 3*p - 8. Suppose -2 - 8*s**2 + 0*s + 5*s + p*s**2 + s**3 = 0. Calculate s.
1, 2
Let b(y) be the third derivative of -y**6/180 - 2*y**5/15 - 7*y**4/12 + 98*y**3/9 + 47*y**2. Let b(i) = 0. Calculate i.
-7, 2
Let l(t) = 53*t**3 - 68*t**2 - 52*t - 8. Let w(i) = -35*i**3 + 45*i**2 + 35*i + 5. Let b(s) = -5*l(s) - 8*w(s). Solve b(q) = 0 for q.
-2/3, 0, 2
Let y(x) be the first derivative of 3 + 0*x**5 + 1/40*x**6 + 0*x**3 + 3/2*x**2 - 1/8*x**4 + 0*x. Let a(n) be the second derivative of y(n). Factor a(p).
3*p*(p - 1)*(p + 1)
Suppose 3*s + 7*u = 2*u + 11, -2*s = 2*u - 6. Suppose -s*i + 3 = -1. Find j, given that -7 - i - 1 + 2 - 18*j**2 + 24*j = 0.
2/3
Let w(n) = n + 8. Let t be w(-5). Factor -4*u**2 - t*u**3 - 2*u**4 - u**3 + 2*u**2.
-2*u**2*(u + 1)**2
Let v = 14 + -14. Let p(k) be the first derivative of -1/4*k**2 + 2 + v*k - 1/3*k**3 - 1/8*k**4. Let p(i) = 0. Calculate i.
-1, 0
Let k(w) be the first derivative of -w**4/16 - w**3/4 - 3*w**2/8 - w/4 + 5. Factor k(r).
-(r + 1)**3/4
Let g(b) = -b**2 - 6*b - 1. Let v be g(-5). Let -51*h + 2*h**v + 51*h - 2*h**3 = 0. Calculate h.
0, 1
Let n(a) = -4*a**3 + 6*a**2 + 6*a + 14. Let g(p) = 4*p**3 - 7*p**2 - 5*p - 15. Let x(r) = -6*g(r) - 7*n(r). Find z, given that x(z) = 0.
-1, 2
Let o be 6/((-9)/(-48)*4). Determine m so that 2*m**5 + 4*m - 3*m**5 - 4*m**2 + 9*m**3 - o*m**2 - 2*m**5 + 2*m**4 = 0.
-2, 0, 2/3, 1
Let n be (1/3)/((-3)/(-27)). Suppose -4*a + 40 = -2*y, n*a + 0*y - 2*y = 28. Factor -c**3 + c**2 + 12*c - a*c.
-c**2*(c - 1)
Let v(d) be the first derivative of 1/5*d**3 + 3/10*d**2 - 3 + 0*d. Let v(i) = 0. What is i?
-1, 0
Let a(v) be the third derivative of -v**7/840 + v**5/240 - 4*v**2. Solve a(x) = 0.
-1, 0, 1
Let x be (42/(-28))/(2 - (-165)/(-24)). Factor 4/13 + x*u**3 + 14/13*u**2 + 14/13*u.
2*(u + 1)*(u + 2)*(2*u + 1)/13
Let f = 35 - 137/4. Determine h so that 8*h**3 + 1/2 + 13/4*h + 4*h**4 + f*h**5 + 15/2*h**2 = 0.
-2, -1, -1/3
Let b(s) be the first derivative of 7*s**4/10 + 2*s**3/3 - 2*s**2/5 + 4. Find c, given that b(c) = 0.
-1, 0, 2/7
Let q(t) = -t**2 - t. Let v(w) = 7*w**2 + 3. Let r(y) = 6*q(y) + v(y). Let j be r(6). Determine u so that -u**3 + 2*u**2 + 1 - 3*u**2 - u + 2*u**j = 0.
-1, 1
Factor -2*p**3 + 124*p**2 + 32*p - 132*p**2 + p**3 - 3*p**3.
-4*p*(p - 2)*(p + 4)
Let c(z) = z**3 - 6*z**2 - 9*z + 14. Let i be c(7). Let -1/3*u**2 + i + 0*u - 1/3*u**3 = 0. What is u?
-1, 0
Let v(t) be the second derivative of -t**7/75 + t**6/60 + t**5/75 - 2*t**2 - 3*t. Let x(f) be the first derivative of v(f).