*d**2 - 2*d**4 - 12*d**3.
-2*(d - 1)**2*(d + 1)*(d + 7)
Determine u, given that -16/9*u - 2/9*u**4 + 4/9*u**3 + 2/3*u**2 + 8/9 = 0.
-2, 1, 2
Let k(j) be the second derivative of -13/36*j**3 + 0 + 23*j + 1/3*j**2 + 1/8*j**4. Find a such that k(a) = 0.
4/9, 1
Let q(c) = 45*c**2 + 65*c + 55. Let a(i) = -19*i**2 - 33*i - 28. Let t(h) = -5*a(h) - 2*q(h). Find j such that t(j) = 0.
-6, -1
Let p be ((22 - 1)/21)/((-1)/(-2)). Find n, given that 2/5*n**p + 0 - 4/5*n + 2/5*n**3 = 0.
-2, 0, 1
Let x(d) = -15*d + 15. Let g = -45 + 41. Let u(v) = v**2 - 16*v + 15. Let w(j) = g*x(j) + 3*u(j). Factor w(a).
3*(a - 1)*(a + 5)
Let h = -18 - -15. Let k be ((-9)/15)/(h/15). Factor 3*a**3 - 2*a**3 + 2*a**4 - 5*a**k.
2*a**3*(a - 2)
Let b(a) be the third derivative of -29*a**2 - 1/36*a**4 + 0 + 0*a + 1/18*a**3 + 1/180*a**5. Find w, given that b(w) = 0.
1
Let o = 15413 - 200367/13. Let 14/13*h**2 + 28/13*h + 16/13 + o*h**3 = 0. What is h?
-4, -2, -1
Let x = -191 + 196. Suppose -3*q - 5*v = -x*q + 16, q + 1 = -2*v. Solve 4/11*g - 10/11*g**2 + 10/11*g**4 - 4/11*g**q + 0 = 0 for g.
-1, 0, 2/5, 1
Let t(o) be the first derivative of -o**6/48 + o**5/8 + o**4/32 - 5*o**3/24 + 844. Determine r, given that t(r) = 0.
-1, 0, 1, 5
Let d(h) be the first derivative of h**6/900 + h**5/150 - h**4/20 + 2*h**3 + 14. Let o(t) be the third derivative of d(t). Solve o(w) = 0.
-3, 1
Let h(c) = -3*c**4 + 7*c**3 - 7*c**2 - 3*c + 12. Let x(a) = -6*a**4 + 15*a**3 - 12*a**2 - 7*a + 20. Let v(f) = 5*h(f) - 3*x(f). Factor v(l).
l*(l - 3)*(l - 1)*(3*l + 2)
Let m(p) be the third derivative of 1/60*p**4 + 0*p + 38*p**2 - 1/300*p**5 + 0 - 1/30*p**3. Suppose m(n) = 0. Calculate n.
1
Let x(c) be the first derivative of 2/9*c**3 + 14 + 2/15*c**5 - 1/3*c**4 + 0*c + 0*c**2. Factor x(a).
2*a**2*(a - 1)**2/3
Let m(b) be the first derivative of -b**3/6 + 29*b**2/2 - 841*b/2 - 33. Solve m(a) = 0.
29
Suppose 228 - 15 = 3*v + 3*z, 2*v - 137 = -z. Let l = 68 - v. What is p in 0 - 3/7*p**l - 6/7*p = 0?
-2, 0
Let r(t) = -4*t**4 - 10*t**3 + 22*t**2 - 12*t - 2. Let j(w) = w**4 + w**3 + 1. Let q(l) = -2*j(l) - r(l). Solve q(m) = 0.
-6, 0, 1
Let v(z) be the second derivative of -z**8/504 - z**7/105 - z**6/90 - 7*z**2 + 25*z. Let b(s) be the first derivative of v(s). Find y such that b(y) = 0.
-2, -1, 0
Let r(d) be the second derivative of -d**6/180 - d**5/30 + 2*d**4/3 - 4*d**3/3 - 11*d. Let v(o) be the second derivative of r(o). Solve v(l) = 0 for l.
-4, 2
Suppose 4*d = -6*d. Let p(s) be the third derivative of -1/175*s**7 + 0 + 0*s**3 + 1/100*s**6 + s**2 - 1/150*s**5 + 0*s**4 + 1/840*s**8 + d*s. Factor p(y).
2*y**2*(y - 1)**3/5
Let l(w) be the first derivative of -w**4/12 - 55*w**3/9 - 364*w**2/3 + 784*w/3 - 46. Solve l(q) = 0 for q.
-28, 1
Factor 49/4*v**2 + 126*v + 324.
(7*v + 36)**2/4
Let k = 2791/44 - 253/4. Let r(z) = -2*z**2 + 26*z - 44. Let a be r(2). Find g, given that k + a*g - 2/11*g**2 = 0.
-1, 1
Let m = -3134 + 12537/4. Solve -h + 1 + 1/4*h**3 - m*h**2 = 0 for h.
-2, 1, 2
Suppose 21*r = 27*r - 18. Let y(v) be the third derivative of 0*v + 0 + 0*v**r + 1/48*v**4 - 7*v**2 + 1/120*v**5. Factor y(l).
l*(l + 1)/2
Factor -104 + 4*z**4 - 12*z**2 + 104 + 8*z.
4*z*(z - 1)**2*(z + 2)
Let t(l) be the first derivative of 0*l - 4/3*l**3 + 17 + 4*l**2. Factor t(w).
-4*w*(w - 2)
Let t be 14 - (-126)/(-11 + 2). Factor -2/9*h**3 + t*h**2 - 1/9*h**4 + 0*h + 0.
-h**3*(h + 2)/9
Suppose b + g = 1, 3*b - 2*g - 3*g - 19 = 0. Let -6*c**b + 12*c**5 - 3*c**5 - 2 + 2 - 3*c**4 = 0. What is c?
-2/3, 0, 1
Let n be 2/(-4) - (-52)/91. Let u(j) be the second derivative of 0 + 2/21*j**3 - 1/35*j**5 + 0*j**2 - n*j**4 + j + 1/35*j**6. Solve u(a) = 0.
-1, 0, 2/3, 1
Factor -22/3*m**3 - 40/3*m - 7/6*m**4 - 8/3 - 16*m**2.
-(m + 2)**3*(7*m + 2)/6
Let w(j) be the second derivative of j**7/105 - j**6/45 + j**5/90 + 5*j**2 + 4*j. Let a(t) be the first derivative of w(t). Solve a(o) = 0.
0, 1/3, 1
Let y(a) be the first derivative of 2*a**3/39 + 314*a**2/13 + 49298*a/13 - 441. Factor y(z).
2*(z + 157)**2/13
Let n(f) = f**3 - 7*f**2 - 5*f + 3. Let b be n(7). Let j = b + 36. Solve 1 + 649*h**2 + 22*h - 112*h + j - 244*h**2 = 0 for h.
1/9
Let j(z) be the third derivative of 9*z**7/280 - 9*z**6/80 + 3*z**5/20 - z**4/12 + z**2 - 91. Let j(b) = 0. What is b?
0, 2/3
Suppose 0 = 6*l - l - 15. Let n(x) = -19*x**3 + 39*x**2 - 24*x + 7. Let k(s) = 56*s**3 - 116*s**2 + 72*s - 20. Let a(d) = l*k(d) + 8*n(d). Factor a(r).
4*(r - 1)**2*(4*r - 1)
Factor -5/2*p**3 + 1 + 1/2*p**4 - 7/2*p + 9/2*p**2.
(p - 2)*(p - 1)**3/2
Suppose -3/2*n**2 - 867/2 - 51*n = 0. What is n?
-17
Let o(f) be the third derivative of 5*f**8/336 - 4*f**7/21 + 5*f**6/24 + 25*f**5/6 - 2*f**2 - 158. Find u, given that o(u) = 0.
-2, 0, 5
Let a(t) = -4*t - 18. Let l be a(-7). Let c(d) = d**2 - 4*d**2 + 3*d - 2*d**2 + 7*d**3. Let p(q) = 3*q**3 - 2*q**2 + q. Let k(j) = l*p(j) - 4*c(j). Factor k(v).
2*v*(v - 1)*(v + 1)
Let 0*d**3 - 16/11*d + 12/11*d**2 + 0 - 1/11*d**4 = 0. Calculate d.
-4, 0, 2
Let k(b) be the first derivative of -2*b**6/3 + 4*b**5 - 8*b**4 + 16*b**3/3 + 19. Factor k(o).
-4*o**2*(o - 2)**2*(o - 1)
Let l = 98/25 - 244/75. Find g such that -2/3*g + 0*g**2 + 0 + l*g**3 = 0.
-1, 0, 1
Suppose 47*b - 43*b - 10 = h, -5*b = h - 8. Factor 0*j**3 + 0*j + 0 - 2/9*j**4 + 0*j**b.
-2*j**4/9
Let q(o) = -54*o - 702. Let l be q(-13). What is b in 1/3*b**5 - 1/3*b**4 - 2*b**3 + 4/3*b**2 + l + 8/3*b = 0?
-2, -1, 0, 2
Let h(k) be the first derivative of -4*k - 1/36*k**4 - 3/2*k**2 + 4 + 1/3*k**3. Let f(x) be the first derivative of h(x). Suppose f(t) = 0. Calculate t.
3
Suppose a + 0*a - 7 = -2*x, -a + 1 = -4*x. Let p(l) be the third derivative of -5*l**2 + 0*l**3 + 0 + 3/100*l**a + 0*l - 1/40*l**4. Factor p(j).
3*j*(3*j - 1)/5
Let i(d) be the third derivative of -d**7/1050 + d**6/900 + d**4/12 + 12*d**2. Let z(a) be the second derivative of i(a). Factor z(k).
-4*k*(3*k - 1)/5
Let r(l) be the third derivative of -l**7/1400 + 3*l**5/200 + l**4/20 + 7*l**3/6 - l**2. Let d(z) be the first derivative of r(z). Factor d(t).
-3*(t - 2)*(t + 1)**2/5
Let v(a) = a**2 - 18*a + 17. Let f(i) = 3*i**2 - 36*i + 33. Let n(c) = -6*f(c) + 14*v(c). Factor n(x).
-4*(x - 1)*(x + 10)
Let v(y) = y**3 + y**2 + y. Let d = -24 + 19. Let p(i) = -10*i**2 - 10*i - 5. Let z(c) = d*v(c) + p(c). Factor z(g).
-5*(g + 1)**3
Let s be ((-2)/(-10))/(21384/1644 - 13). Suppose 49/5*j**5 - 168/5*j**4 - 8/5 + 26/5*j**2 - 36/5*j + s*j**3 = 0. What is j?
-2/7, 1, 2
Let a be 5353/22 - (-4 + (-126)/(-33)). Let n = -3397/14 + a. Factor -4/7*p + n*p**3 + 0 - 10/7*p**2.
2*p*(p - 2)*(3*p + 1)/7
Let y(n) be the third derivative of n**6/420 - n**5/70 - n**4/21 - 2*n**2 + 8*n. Determine g so that y(g) = 0.
-1, 0, 4
Let d(c) = 5*c**4 - c - 8*c**2 - 1 + 9*c**2 - 6*c**4. Let y(o) = -o**5 + 3*o**4 + 2*o**3 - o**2 + 4*o + 3. Let g(n) = 15*d(n) + 3*y(n). Let g(f) = 0. What is f?
-2, -1, 1
Let p(f) be the third derivative of -f**6/24 + 25*f**5/12 - 85*f**4/6 + 110*f**3/3 - 596*f**2. Factor p(k).
-5*(k - 22)*(k - 2)*(k - 1)
Let o(m) be the third derivative of m**8/2352 + m**7/1470 + 20*m**2 - m. Factor o(v).
v**4*(v + 1)/7
Let o(l) = 27*l**4 + 67*l**3 - 9*l**2 - 36*l + 13. Let q(c) = c**4 + c**3 + c**2 - 1. Let i = -17 + 16. Let f(x) = i*o(x) - 5*q(x). Let f(w) = 0. Calculate w.
-2, -1, 1/4, 1/2
Suppose 3*y - 21 = -0*y. Suppose -10*n**4 - y*n**4 + 9*n**3 + 14*n**4 = 0. What is n?
0, 3
Suppose 0 = 3*v + 5*u, -8 = -4*v - 5*u - 3. Suppose 0 = 2*p - 7*p + 5*x, -4*p - v*x + 27 = 0. Factor -7*g**5 + 29*g**3 - p*g**4 - 26*g**3 + g**5.
-3*g**3*(g + 1)*(2*g - 1)
Let g(u) = -10 - 7*u**2 - u**3 + 0*u**3 - 12*u + 4*u. Let x be g(-6). Factor -6*q**2 - q**2 - x*q**3 + 0*q**2 + 4*q + 5*q**2.
-2*q*(q - 1)*(q + 2)
Let g = -3607 - -3607. Factor 3/5*r**3 - 6/5*r**2 + 3/5*r**4 + g*r + 0.
3*r**2*(r - 1)*(r + 2)/5
Suppose -n = n - 10*n. Let z(l) be the second derivative of 9*l**2 + 6*l + n - 2*l**3 + 1/6*l**4. Let z(f) = 0. What is f?
3
Suppose -12*a + 3*a + 153 = 0. Let -12*u**2 + 4 - u**2 + 10*u + a*u**2 = 0. What is u?
-2, -1/2
Let r(t) be the second derivative of t**7/420 - t**6/60 - t**5/15 - 5*t**3/3 - 22*t. Let l(o) be the second derivative of r(o). Factor l(p).
2*p*(p - 4)*(p + 1)
Let v(q) be the first derivative of q**6/10 - 21*q**5/25 - 6*q**4/5 - 73. Factor v(r).
3*r**3