Let q(r) be the first derivative of f(r). Solve q(l) = 0.
1, 3
Let a(l) be the second derivative of -54*l**3 + 0 + 36*l**4 + 8*l - 48/5*l**5 + 81/2*l**2. Factor a(i).
-3*(4*i - 3)**3
Let i(a) be the first derivative of 1/2*a**4 - 4 + 0*a + 0*a**2 - 4/3*a**3 + 2/5*a**5. Factor i(f).
2*f**2*(f - 1)*(f + 2)
Let d(a) be the second derivative of 49*a**5/190 - 35*a**4/57 - 52*a**3/57 - 8*a**2/19 + 12*a. Factor d(g).
2*(g - 2)*(7*g + 2)**2/19
Let m(d) be the first derivative of 1/18*d**3 + 1/20*d**5 + 1/90*d**6 + 0*d**2 + 1/12*d**4 + 2*d + 3. Let h(j) be the first derivative of m(j). Factor h(c).
c*(c + 1)**3/3
Let w(c) = -2*c**3 + 2*c + 3. Let f(v) = 13*v**3 - v**2 - 12*v - 17. Suppose -22 = -z + 12. Let s(x) = z*w(x) + 6*f(x). Factor s(g).
2*g*(g - 1)*(5*g + 2)
Let m = 45/4 + -11. Factor 3/2*y - 9/4 - m*y**2.
-(y - 3)**2/4
Let o(f) be the third derivative of 0*f**3 - 1/600*f**6 + 0 + 1/120*f**4 + 0*f**5 + f**2 + 0*f. Suppose o(p) = 0. Calculate p.
-1, 0, 1
Let v(s) be the third derivative of s**8/336 - s**6/60 + s**4/24 - 18*s**2. Factor v(y).
y*(y - 1)**2*(y + 1)**2
Let m(q) be the third derivative of -q**5/36 - 35*q**4/72 - 25*q**3/9 + q**2 - 65. Suppose m(n) = 0. Calculate n.
-5, -2
Let o be 13 - ((-4)/2)/2. Let h = o + -11. Let 0 + 0*z + 1/2*z**h + z**4 - 1/2*z**2 = 0. Calculate z.
-1, 0, 1/2
Let v(j) be the second derivative of 5*j**7/168 - j**6/6 + 23*j. Factor v(i).
5*i**4*(i - 4)/4
Let f(z) = -9*z**2 - 3*z - 3. Let a(k) = 10*k**2 + 3*k + 2. Let m(j) = -3*a(j) - 2*f(j). Suppose m(r) = 0. What is r?
-1/4, 0
Let k(u) be the second derivative of -u**10/90720 + u**8/6720 - u**7/3780 + u**4/4 + 2*u. Let y(s) be the third derivative of k(s). Suppose y(f) = 0. What is f?
-2, 0, 1
Let -7*m**4 - 10*m**3 + 23*m**4 - 6*m**4 + 15*m**2 - 15*m**4 = 0. What is m?
-3, 0, 1
Let r = 10 + -68/7. Let r*q - 2/7 + 2/7*q**2 - 2/7*q**3 = 0. Calculate q.
-1, 1
Let j(l) = -24*l. Let s be j(-1). Find x, given that -s*x**3 + 9*x**3 + 6*x**2 + 11*x**3 - 2 = 0.
-1/2, 1
Let w be ((-66)/(-231))/((-27)/(-21)). Suppose -2/3*h - w*h**2 + 2/3*h**3 + 2/9*h**4 + 0 = 0. What is h?
-3, -1, 0, 1
Factor -27/4 + 27/4*p - 9/4*p**2 + 1/4*p**3.
(p - 3)**3/4
Suppose 109*u**2 - 37*u**2 + 789 + 432*u + 75 + 4*u**3 = 0. What is u?
-6
Let p(b) = -29*b**2 - 29*b - 17. Let d(r) = -5*r**2 - 5*r - 3. Let w be 34/(2 + 0)*-2. Let l(s) = w*d(s) + 6*p(s). Let l(o) = 0. What is o?
-1, 0
Determine s so that -10/19*s**4 + 14/19*s - 12/19*s**3 - 2/19*s**5 + 4/19*s**2 + 6/19 = 0.
-3, -1, 1
Let d = 4/43 + 58/301. Determine k so that -4/7*k + 0 - d*k**2 = 0.
-2, 0
Let u(s) be the third derivative of 1/12*s**3 - 1/120*s**5 + 0*s**4 + 0*s + 0 + 2*s**2. What is i in u(i) = 0?
-1, 1
Let q(l) be the first derivative of l**4/14 + 4*l**3/21 + l**2/7 + 7. Factor q(u).
2*u*(u + 1)**2/7
Let v(n) be the third derivative of -n**6/180 - n**5/72 - n**4/144 + n**2. Factor v(c).
-c*(c + 1)*(4*c + 1)/6
Suppose 17 = 5*g - f, 2*g - 6*g + 6 = 3*f. Let j(h) be the first derivative of -1/2*h**4 + 1 - 4/21*h**g + h**2 + 4/7*h. Suppose j(z) = 0. What is z?
-1, -2/7, 1
Find a, given that -1 - 2*a**4 + 3/2*a**2 - 5/2*a + 4*a**3 = 0.
-1/2, 1, 2
Let v be 11/5 + 108/30 + -4. Suppose -3*b + 9 = -0*b. Suppose 1/5*n**4 + v*n**2 + 7/5*n + 2/5 + n**b = 0. What is n?
-2, -1
Let b(h) be the first derivative of 2/3*h + h**2 + 1/6*h**4 + 4 + 2/3*h**3. Determine f so that b(f) = 0.
-1
Let n(t) be the first derivative of -4*t + 9*t**3 - 13/2*t**4 + 7/5*t**5 - 2*t**2 + 6. Factor n(z).
(z - 2)*(z - 1)**2*(7*z + 2)
Let j = 10 - 6. Suppose -5*f + 30 = 5*m - 0*m, -4*m = -2*f - 12. Determine d so that m*d**3 - 4*d**3 + 2*d**2 + j*d**4 - 8*d**4 + 2*d**3 = 0.
-1/2, 0, 1
Suppose -8*j = -10*j + 8. What is f in 0*f**2 + 1/4*f**j + 0*f - 1/4*f**3 + 0 = 0?
0, 1
Let n = 2/57 - -167/114. Let w(o) be the first derivative of n*o**4 + 0*o - 2/5*o**5 - 1 - 2*o**3 + o**2. Solve w(x) = 0.
0, 1
Let x(r) = r**3 - 7*r**2 + 4. Let d be x(7). Factor 2*h**3 + 2*h**2 - 2*h - 2*h**2 - 2*h**2 + 2*h**4 + 0*h**d.
2*h*(h - 1)*(h + 1)**2
Let c(j) = -j**4 + j + 1. Suppose -40 + 100 = -5*a. Let l(i) = 2*i**5 - 8*i**4 - 4*i**2 + 10*i + 12. Let r(y) = a*c(y) + l(y). Factor r(n).
2*n*(n - 1)*(n + 1)**3
Let g(i) be the second derivative of -i**7/14 + i**6/10 + 3*i**5/10 - i**4/2 - i**3/2 + 3*i**2/2 + i. Factor g(z).
-3*(z - 1)**3*(z + 1)**2
Let w(i) = 16*i**3 + 12*i**2 - 7*i + 5. Let k(o) = 32*o**3 + 23*o**2 - 14*o + 9. Let c = 23 + -16. Let l(n) = c*w(n) - 4*k(n). Factor l(g).
-(g + 1)*(4*g - 1)**2
Let d = -107/7 + 601/21. Let j be (-1)/4 + (-5 - (-132)/16). Factor -d*f**j + 8/3*f**2 + 0*f + 0 + 50/3*f**4.
2*f**2*(5*f - 2)**2/3
Solve -3*u**3 + 11*u**2 + 20*u + 0*u**3 - 26*u = 0 for u.
0, 2/3, 3
Let p(h) be the first derivative of h**4/42 + h**3/21 + h + 4. Let o(r) be the first derivative of p(r). Solve o(q) = 0.
-1, 0
Factor -41*d**3 + d**2 + 37*d**3 - 13*d**2.
-4*d**2*(d + 3)
Solve 2/3*y**2 + 20/3*y + 50/3 = 0 for y.
-5
Let f(p) = p**5 - 10*p**4 - p**3 + 10*p**2. Let b(q) = q**5 - 5*q**4 - q**3 + 5*q**2. Let o(g) = -9*b(g) + 4*f(g). Factor o(s).
-5*s**2*(s - 1)**2*(s + 1)
Suppose 5*w = 5, -4*w = 4*j - 15 + 3. Factor j*x + 0*x**2 + 16*x + 4 + 14*x**2.
2*(x + 1)*(7*x + 2)
Let s(w) = 10*w**5 - 5*w**4 - 5*w**3 + 10*w**2. Let g(t) = -5*t**5 + 2*t**4 + 2*t**3 - 5*t**2. Let z(p) = -5*g(p) - 3*s(p). Factor z(q).
-5*q**2*(q - 1)**2*(q + 1)
Let a be 1/4 - 132/16. Let n be (-12)/a*12/9. Factor -4/7*q + 0 + 2/7*q**3 + 2/7*q**n.
2*q*(q - 1)*(q + 2)/7
Factor 0*g - g**4 + 3/4*g**3 + 0*g**2 - 7/4*g**5 + 0.
-g**3*(g + 1)*(7*g - 3)/4
Let d = -55/6 + 223/24. Let z(k) be the first derivative of d*k**4 + 5/4*k**2 + 3 + 2/3*k**3 + k. Determine w, given that z(w) = 0.
-2, -1
Let v(d) be the second derivative of d**4/48 + d**3/24 - d**2/4 - 5*d. Solve v(c) = 0.
-2, 1
Let r(o) = o**2 + 7*o - 5. Let t be r(-8). Factor 0 - 16/5*z**t + 7/5*z**4 - 2/5*z + 11/5*z**2.
z*(z - 1)**2*(7*z - 2)/5
Determine f so that 20*f - 2*f**3 + 4*f + 15*f**2 + 12 + 5*f**3 = 0.
-2, -1
Solve 0 - 6/5*a - 2/5*a**2 = 0.
-3, 0
Factor -50/3*s**3 + 6*s - 10*s**2 - 2/3.
-2*(s + 1)*(5*s - 1)**2/3
Let s = -108 + 64. Let i be 4*2/s*-1. Suppose 0*c**2 - 4/11*c**3 + i*c + 0 + 2/11*c**5 + 0*c**4 = 0. Calculate c.
-1, 0, 1
Let w(k) be the first derivative of -1/3*k**2 + k + 2/9*k**3 - 1/18*k**4 + 2. Let r(y) be the first derivative of w(y). Solve r(g) = 0 for g.
1
Let y(i) be the first derivative of -i**3 + 10 + 1/3*i**5 + 0*i + 1/18*i**6 + 0*i**2 + 1/4*i**4. Suppose y(n) = 0. Calculate n.
-3, 0, 1
Suppose 3 + 7 + 5*w**2 - w**2 + 2 + 16*w = 0. What is w?
-3, -1
Suppose 2*g = -17 + 21. Let w(j) be the second derivative of 1/12*j**3 + 0 - 1/24*j**4 - g*j + 0*j**2. What is r in w(r) = 0?
0, 1
Let h(s) be the second derivative of 0 - 1/18*s**4 + 2/3*s**2 + 3*s + 1/9*s**3. Suppose h(z) = 0. Calculate z.
-1, 2
Let z(a) be the first derivative of 2 + 2/3*a**3 + 0*a + 0*a**2. Factor z(k).
2*k**2
Let w(n) = -n**3 + 6*n**2 - n - 3. Let h be w(4). Suppose 2*x - 2*f + 4*f = -4, -5*x + 2*f = -h. Let 0 + 0*t - 1/3*t**x + 1/3*t**2 = 0. What is t?
0, 1
Let g(v) = -v**3 - 5*v**2 + 2. Let x be g(-5). Let z = 12 + -5. Factor -x*i**2 - 8 - i - z*i + 0.
-2*(i + 2)**2
Let s(z) be the first derivative of z**5/90 + z**4/9 + 4*z**3/9 + 8*z**2/9 - 9*z - 7. Let a(m) be the first derivative of s(m). Factor a(n).
2*(n + 2)**3/9
Determine j, given that -22*j - 12*j**2 + 17*j**2 + 4 + 18*j**3 + 19*j**2 = 0.
-2, 1/3
Let k(h) = 7*h**4 - 9*h**3 - h + 3. Let m(a) = -4*a**3 - 1 + 3*a**4 + 3 - 1. Let u = 1 - 6. Let i(g) = u*m(g) + 2*k(g). Determine r, given that i(r) = 0.
-1, 1
Let f(o) be the second derivative of -o**8/13440 - o**7/5040 + o**6/1440 + o**5/240 - o**4/4 - 3*o. Let h(m) be the third derivative of f(m). Factor h(t).
-(t - 1)*(t + 1)**2/2
Let w = -38/9 - -284/63. Factor -4/7*h**2 + w*h**3 + 0 - 6/7*h.
2*h*(h - 3)*(h + 1)/7
Solve -4/3*h + 40/3*h**3 + 14/3*h**2 + 22/3*h**4 + 0 = 0.
-1, 0, 2/11
Suppose -4*w = -2*w + 2*w. Suppose -2/7*m**2 - 2/7*m + w = 0. Calculate m.
-1, 0
Suppose 0 = -108*h + 102*h + 18. Let a(o) be the first derivative of -1/15*o**h - 2/5*o**2 + 4 - 4/5*o. Determine i, given that a(i) = 0.
-2
Let g = 616/3 + -205. Let 0*c + 1/3*c**4 - g*c**2 - 1/3*c**3 + 1/3*c**5 + 0 = 0. What is c?
-1, 0, 1
Let t(l) be the first derivative of -1/21*l**3 + 1/14*l