hird derivative of -f*g**3 + 0 + 0*g - 1/24*g**4 + 2*g**2 - 1/80*g**5. Factor k(s).
-(s + 1)*(3*s + 1)/4
Let y be ((-6)/(-4))/(3/8). Suppose -4*j + y*k - 12 = 0, 3*k - 1 = 8. Factor 2/5 - 4*n**2 - 6*n**4 + 8*n**3 + 8/5*n**5 + j*n.
2*(n - 1)**4*(4*n + 1)/5
Find c such that 10/7*c**2 - 2*c**4 - 18/7*c**3 + 4/7 + 18/7*c = 0.
-1, -2/7, 1
Suppose -u - 2*w = -7, 5*u - 56 = u - w. Let -30*k**2 - 3 - 3*k**4 + 3*k**5 - k**4 + 30*k**3 + u*k - 11*k**4 = 0. What is k?
1
Suppose -10 = -5*x + 5. Let i be x/(-2)*(-4)/3. Factor -2*r**4 + 0*r - 6*r**2 + 0*r**4 + 6*r**3 + i*r.
-2*r*(r - 1)**3
Suppose 0*c - 7*c = 0. Let w(i) be the first derivative of c*i - 2/3*i**3 + 2/5*i**5 + i**2 - 1/2*i**4 - 3. Let w(y) = 0. What is y?
-1, 0, 1
Let n = -21 + 21. Find s such that n*s**2 + 1/4*s**3 + 0 + 1/4*s**5 - 1/2*s**4 + 0*s = 0.
0, 1
Suppose -2*u + 13 = 3*u + 3*d, 0 = -u - 4*d + 6. Suppose s - 1 = u*h, h - 4 = -3. Let -m + 3*m**5 - 4*m**5 - 2*m**s + 4*m**3 = 0. What is m?
-1, 0, 1
Suppose -5*v - 22*r = -23*r - 8, -5*v = r - 12. Factor -3/5*w + 3/5*w**3 - 3/5*w**v + 3/5.
3*(w - 1)**2*(w + 1)/5
Let v be (2 + 1/(-2))*2. Suppose v*y - 5 = 5*c - 2*y, -5*y + 5 = -3*c. Factor 0 + c*d + 1/5*d**2.
d**2/5
Let j(l) be the second derivative of 0*l**2 - 1/40*l**5 - 3*l - 1/12*l**3 - 1/12*l**4 + 0. Factor j(q).
-q*(q + 1)**2/2
Let i = 37 - 37. Let k(l) be the third derivative of 0*l**4 + 0*l**3 + i*l**5 - 1/60*l**6 + 0*l + 0 + l**2. Factor k(g).
-2*g**3
Suppose 0 = 17*g - 44 - 24. What is k in -26/5*k**3 + 2/5*k - 18/5*k**2 + 4/5 - 2*k**g = 0?
-1, 2/5
Let s = -14 - -16. Let u**3 + 3 - 104*u - u**2 - s*u**2 + 2*u**3 + 101*u = 0. What is u?
-1, 1
Let h(q) be the second derivative of 0*q**4 + 0 + 1/18*q**3 - 1/180*q**5 + 2*q + 1/2*q**2. Let t(b) be the first derivative of h(b). Factor t(a).
-(a - 1)*(a + 1)/3
Determine z so that 2/5*z**2 - 2/5*z**4 + 6/5*z**3 - 2/5*z**5 - 4/5*z + 0 = 0.
-2, -1, 0, 1
Let v(f) be the first derivative of -f**6/45 + f**4/6 - 2*f**3/9 + f + 2. Let s(q) be the first derivative of v(q). Determine x, given that s(x) = 0.
-2, 0, 1
Suppose 18*u + 5 = 59. Suppose 20 = -4*g + 8*g. Suppose 3/2*a + 9/2*a**g - 3*a**4 + 3*a**2 + 0 - 6*a**u = 0. Calculate a.
-1, -1/3, 0, 1
Factor -j**3 + 2*j + 3/2*j**2 - 1/2*j**4 - 2.
-(j - 1)**2*(j + 2)**2/2
Let p(a) = a**3 - 10*a**2 + 10*a - 3. Let t be p(9). Let f = t - 11/2. Factor 0 + 1/2*c**2 - f*c.
c*(c - 1)/2
Factor -1/2*b - 3/4*b**2 - 1/4*b**3 + 0.
-b*(b + 1)*(b + 2)/4
Let f(w) be the second derivative of -w**6/100 + 4*w**5/75 - w**4/20 - 2*w**3/15 + 2*w**2 - 3*w. Let u(v) be the first derivative of f(v). Solve u(s) = 0.
-1/3, 1, 2
Let f(n) be the first derivative of -2*n**3/33 + 2*n**2/11 + 9. Solve f(a) = 0.
0, 2
Let z(n) be the third derivative of -2*n**2 + 0*n + 1/300*n**6 + 0*n**3 - 1/75*n**5 + 1/525*n**7 + 0*n**4 + 0. Determine q so that z(q) = 0.
-2, 0, 1
Let x(p) be the first derivative of 0*p**4 + 0*p**2 - 1 + 4/15*p**3 - 2/25*p**5 - 2/5*p. Factor x(s).
-2*(s - 1)**2*(s + 1)**2/5
Suppose 0 = -29*l - 6 + 64. Let 2/9 - 4/9*y + 2/9*y**l = 0. What is y?
1
Suppose 3*n = 16 - 4. Suppose 4*m = -n*u + 5*m + 4, -4*u - 4*m - 16 = 0. Suppose 1/4*y**2 + u + 1/4*y = 0. What is y?
-1, 0
Let g(l) be the first derivative of 5*l**3 - 33*l**2/2 + 6*l - 5. Factor g(q).
3*(q - 2)*(5*q - 1)
Let y(x) be the first derivative of -2*x**3/45 + 4*x**2/3 - 40*x/3 - 53. Factor y(p).
-2*(p - 10)**2/15
Factor j**3 + 0*j**2 + 6*j + 5*j**2 - 5*j + 3*j.
j*(j + 1)*(j + 4)
Let a be (-22)/(-6) + (-2)/(-6). Suppose 12 = 2*k + 4*r, -a*k + 2*r = -2*r. Suppose 6/7*n**k - 2/7*n**3 - 6/7*n + 2/7 = 0. What is n?
1
Factor -12*f - 54*f**4 - 4*f**2 + 32*f**4 + 12*f**3 + 26*f**4.
4*f*(f - 1)*(f + 1)*(f + 3)
Let z(m) be the second derivative of m**8/40320 + m**7/1680 + m**6/160 + 3*m**5/80 - 5*m**4/12 + 5*m. Let g(k) be the third derivative of z(k). Factor g(b).
(b + 3)**3/6
Let w(x) be the second derivative of 5*x**4/12 + 20*x**3/3 + 40*x**2 - 8*x. Find g, given that w(g) = 0.
-4
Let w(c) be the third derivative of -c**6/240 + c**5/120 + c**4/6 - c**3 + 37*c**2. Suppose w(s) = 0. Calculate s.
-3, 2
Let m = -12051/20 + 603. Let a(i) be the first derivative of -3/5*i + m*i**4 - 9/10*i**2 + 1/5*i**3 + 1. Find k, given that a(k) = 0.
-1, -1/3, 1
Let t(q) be the second derivative of 1/21*q**4 - 2/7*q**2 - 4*q + 1/21*q**3 - 1/70*q**5 + 0. Factor t(b).
-2*(b - 2)*(b - 1)*(b + 1)/7
Let f(c) be the first derivative of -c**6/4 - 9*c**5/10 - 9*c**4/8 - c**3/2 - 5. Factor f(d).
-3*d**2*(d + 1)**3/2
Let d(z) be the third derivative of -1/420*z**6 - 1/210*z**5 - 7*z**2 + 5/84*z**4 + 0*z - 1/7*z**3 + 0. Factor d(x).
-2*(x - 1)**2*(x + 3)/7
Let k(b) be the first derivative of 5*b**6/2 - 24*b**5/5 - 3*b**4 + 10*b**3 - 3*b**2/2 - 6*b + 2. Find x, given that k(x) = 0.
-1, -2/5, 1
Find x such that 8*x**3 - 2*x**3 + 2*x**5 - 4*x**2 - 11*x**4 - 6*x**3 + 13*x**3 = 0.
0, 1/2, 1, 4
Suppose 3*k**2 - 30*k + 6*k + 9*k**3 - 3*k**4 + 11*k + 7*k - 3*k**5 = 0. Calculate k.
-2, -1, 0, 1
Let t = -2/51 + 7/34. Let q(k) be the first derivative of 0*k**3 + t*k**4 + 1 + 0*k**2 - 2/15*k**5 + 0*k. Solve q(u) = 0.
0, 1
Suppose -5*c + 5 = 4*k, -6*c - 2*k = -c - 15. Suppose 5*a = 16 + 4. Factor l**5 - l**c + 2*l**4 - 2*l**5 + a*l**3.
-2*l**3*(l - 2)*(l + 1)
Let j(l) = 2*l - 7. Let b be j(5). Factor 4/3*p**b - p**2 - 3*p - 2/3.
(p - 2)*(p + 1)*(4*p + 1)/3
Let y(f) be the second derivative of f**4/72 - f**3/9 + f**2/3 + 5*f. Find q such that y(q) = 0.
2
Let j(t) be the third derivative of 0*t + t**2 + 0 + 1/40*t**4 + 0*t**3 - 1/100*t**5. Factor j(l).
-3*l*(l - 1)/5
Let y(q) = 36*q**2 - 4*q - 24. Let l(n) = -7*n**2 + n + 5. Let g(f) = -16*l(f) - 3*y(f). Determine k, given that g(k) = 0.
-1, 2
Let t = 781472132/765 - 1021532. Let u = t + 2/85. Factor u*y**2 + 2/9*y**3 - 2/9 - 2/9*y.
2*(y - 1)*(y + 1)**2/9
Suppose 5*j + 0*r - 25 = r, -2*r - 14 = -j. Factor 0 - 6/5*d**2 - 2/5*d - 2/5*d**j - 6/5*d**3.
-2*d*(d + 1)**3/5
Let c(m) = -m**3 + 5*m**2 - 3*m + 3. Let y(s) = -s**2 - 1. Let w = 3 - 4. Let l(v) = w*c(v) - 2*y(v). Suppose l(k) = 0. Calculate k.
1
Let k be ((-2)/(-24)*-2)/(-2). Let u(f) be the first derivative of 1/15*f**5 + 2/3*f - k*f**4 + 1/6*f**2 - 1/3*f**3 - 1. Factor u(y).
(y - 2)*(y - 1)*(y + 1)**2/3
Let k(y) be the second derivative of y**5/75 + y**4/10 + 4*y**3/15 - y**2/2 + y. Let o(w) be the first derivative of k(w). Find t such that o(t) = 0.
-2, -1
Let n be 18/5 + (-2)/(-5). Let h(i) = -i**2 - 1. Let v(l) = 3*l**2 - 3*l + 2. Suppose 6*w = -w + 7. Let s(f) = n*h(f) + w*v(f). Factor s(y).
-(y + 1)*(y + 2)
Factor -1/6 - 1/6*r**3 + 1/6*r + 1/6*r**2.
-(r - 1)**2*(r + 1)/6
Let z(s) = 2*s**2 - 12*s + 12. Let a(q) = -2*q**2 + 12*q - 13. Let f = -2 - -7. Let u(c) = f*z(c) + 6*a(c). Factor u(o).
-2*(o - 3)**2
Let n(k) be the third derivative of -k**5/420 - k**4/84 + k**3/14 - 9*k**2. Find m such that n(m) = 0.
-3, 1
Let s(p) = 5*p**2 - 7*p + 5. Let o(q) = q**2 - q + 1. Let k(n) = -3*o(n) + s(n). What is c in k(c) = 0?
1
Let j be ((-8)/(-12))/2*81. Determine n, given that j*n**4 - 26*n**4 - 6*n**2 + 4*n**2 + 1 = 0.
-1, 1
Let k(d) be the first derivative of 12*d**5/55 + 3*d**4/22 - 6*d**3/11 - 3*d**2/11 + 6*d/11 - 12. Find y such that k(y) = 0.
-1, 1/2, 1
Let j(q) be the third derivative of -1/40*q**4 + 1/50*q**5 + 0*q**3 + q**2 - 1/200*q**6 + 0*q + 0. Factor j(o).
-3*o*(o - 1)**2/5
Let x(r) = -r**2 - 4*r + 81. Let g be x(7). Suppose 0*w + 2/11*w**g - 2/11*w**2 + 0 + 0*w**3 = 0. What is w?
-1, 0, 1
Factor -11*p - 5*p + 16 + 10*p**2 - 6*p**2.
4*(p - 2)**2
Let g be (-4)/2 - (-20 - -12). Factor g*b**2 - 2*b**3 + 0*b - 4*b + 0*b.
-2*b*(b - 2)*(b - 1)
Let x(v) = v**4 - 5*v**3 - 15*v**2 - 15*v - 6. Let i(c) = -5*c**4 + 26*c**3 + 75*c**2 + 74*c + 30. Let z(g) = 2*i(g) + 11*x(g). Factor z(j).
(j - 6)*(j + 1)**3
Factor 1/5*j**4 - 12/5*j**3 + 5 - 12*j + 46/5*j**2.
(j - 5)**2*(j - 1)**2/5
Let p(k) be the second derivative of k**5/120 - 7*k**3/36 + k**2/2 + 48*k. Factor p(y).
(y - 2)*(y - 1)*(y + 3)/6
Let t(q) be the second derivative of -q**4/84 - 9*q. Factor t(u).
-u**2/7
Factor -63*u**2 + 2*u**4 + 12*u - 2*u**3 + u**3 - 3*u**3 + 53*u**2.
2*u*(u - 3)*(u - 1)*(u + 2)
Let o(a) be the second derivative of 1/16*a**4 - 3*a + 0 + 0*a**2 + 0*a**3. Factor o(w).
3*w**2/4
Let o(j) be the second derivative of 0 + 1/5*j**3 - 1