 1/4*r**4 + 32 + 57/2*r**2.
(r - 8)**2*(r - 2)*(r - 1)/4
Let w(u) be the first derivative of u**3/6 - 9*u**2/4 + 4*u - 549. Let w(r) = 0. Calculate r.
1, 8
What is l in 258/13*l**2 + 2/13*l**3 + 630*l - 650 = 0?
-65, 1
Let w(i) be the first derivative of -4*i**3/15 - 12*i**2/5 - 4*i + 47. Factor w(u).
-4*(u + 1)*(u + 5)/5
Let r = -988 + 990. Determine z, given that 2/13*z**3 + 2/13*z + 0 + 4/13*z**r = 0.
-1, 0
Let h be (5 - (-44)/(-8))/(2/(-12)). Suppose 5*o - 7 = h*w - 2*w, 5*w = o + 13. Solve -1 - 2*k**o - 5/2*k - 1/2*k**3 = 0.
-2, -1
Let n(g) = g**3 + 4*g**2 + 3*g - 1. Let s(r) be the second derivative of -r**4/12 - r**3/6 + r**2/2 - 12*r. Let a(z) = -2*n(z) - 2*s(z). Factor a(h).
-2*h*(h + 1)*(h + 2)
Let m(c) be the first derivative of 7*c - 1/3*c**3 - 12 - 1/4*c**4 + 0*c**2. Let o(h) be the first derivative of m(h). What is j in o(j) = 0?
-2/3, 0
Suppose -j + 0*j - 3*r + 12 = 0, -3*j = r - 20. Let i = j + -4. Factor -3*y**4 + y**4 + 6*y**4 - i*y**4.
2*y**4
Let h(s) be the third derivative of -s**8/840 + 3*s**7/175 - s**6/20 - 29*s**5/150 + 6*s**4/5 - 12*s**3/5 + 5*s**2 + 21. Solve h(n) = 0 for n.
-2, 1, 3, 6
Let j(u) be the second derivative of -2*u**4 - 4/3*u**3 + 5*u + 0*u**2 + 0 - 9/10*u**5. Let j(g) = 0. What is g?
-2/3, 0
Let w = 189 - 185. Let h(t) be the third derivative of 1/4*t**4 - 1/2*t**3 + 0 - 1/20*t**6 + 1/70*t**7 - w*t**2 + 0*t**5 + 0*t. Factor h(j).
3*(j - 1)**3*(j + 1)
Let c be (-5 - 240/(-56) - 8) + (-16 - -25). Let l(f) = -f**3 - 2*f**2 + 3*f + 4. Let w be l(-3). Factor 2/7*q**3 + 2/7*q**2 + 0*q - c*q**w + 0 - 2/7*q**5.
-2*q**2*(q - 1)*(q + 1)**2/7
Factor 4/7*i**4 - 144/7*i + 0*i**3 - 80/7 - 68/7*i**2.
4*(i - 5)*(i + 1)*(i + 2)**2/7
Let k(m) be the third derivative of m**9/7560 - m**8/1400 + m**7/700 - m**6/900 + 13*m**3/3 - 27*m**2. Let p(c) be the first derivative of k(c). Factor p(q).
2*q**2*(q - 1)**3/5
Let z(d) be the third derivative of -d**6/120 + d**4/8 - d**3/3 + 84*d**2. Solve z(c) = 0 for c.
-2, 1
Let t(j) = -3*j**2 - 76*j + 75. Let u(x) = -5*x**2 - 75*x + 75. Let o(d) = 5*t(d) - 4*u(d). Factor o(r).
5*(r - 15)*(r - 1)
Let -6*x**4 - 2*x**3 + 40*x - 35*x**2 - 46*x**2 + 5*x**4 + 44*x**3 = 0. What is x?
0, 1, 40
Factor 12 + 5954*v + 5*v**2 - 6004*v - 67.
5*(v - 11)*(v + 1)
Let f(n) be the first derivative of 7*n**6/2 - 107*n**5/5 + 34*n**4 + 24*n**3 - 88*n**2 + 16*n - 438. Solve f(p) = 0 for p.
-1, 2/21, 2
Let d be (24/40)/((-27)/15 + 2). What is h in -3*h**2 + 13/3*h**d + 2/3 - 5/3*h**4 - 1/3*h = 0?
-2/5, 1
Find d such that -48*d - 33*d**5 - 419*d**3 + 45*d**5 - 84*d**4 + 108*d**5 + 336*d**2 - 157*d**3 + 27*d**5 = 0.
-2, 0, 2/7, 2
Let v(l) be the second derivative of 5*l**4/12 + 220*l**3/3 + 4840*l**2 - 13*l. Suppose v(z) = 0. Calculate z.
-44
Let f(v) = -v - 21. Let k be f(-21). Let y(s) be the second derivative of 2/3*s**3 + s**2 + k + 1/6*s**4 + 4*s. Factor y(a).
2*(a + 1)**2
Let l(t) = 8*t**3 + 8*t**2 + 4*t - 4. Let b(g) = -g**5 - g**4 + 7*g**3 + 7*g**2 + 3*g - 3. Let n(p) = 4*b(p) - 3*l(p). What is j in n(j) = 0?
-1, 0, 1
Let p(o) = -o - 12. Let y be p(-14). Let k(q) = 37*q + 37. Let d be k(-1). What is w in -2/13*w**5 + 4/13*w**3 + 0 - 2/13*w + d*w**4 + 0*w**y = 0?
-1, 0, 1
Let y be (2 - -6)/((-124)/(-308) + 1/7). Factor -16/3*g**3 - 2/3*g**4 - 16*g - y*g**2 - 6.
-2*(g + 1)**2*(g + 3)**2/3
Determine f so that -1 - 38*f - 54*f**2 + 88*f - 17 - 2*f**4 + 2 + 22*f**3 = 0.
1, 8
Let -3/2*b**4 + 0 - 525/2*b**2 + 1323/2*b + 69/2*b**3 = 0. What is b?
0, 7, 9
Let d(i) be the first derivative of i**4/26 + 8*i**3/39 + 4*i**2/13 - 5. Factor d(n).
2*n*(n + 2)**2/13
Let n(q) be the first derivative of q**3 + 27*q**2/4 + 6*q - 118. Factor n(w).
3*(w + 4)*(2*w + 1)/2
Suppose 0 + 1293/2*s**3 + 372*s**2 + 288*s**4 - 81/2*s**5 + 54*s = 0. What is s?
-1, -2/3, -2/9, 0, 9
Let m be 12/(-22) + 508/44. Suppose -32 = -m*t - 5*t. Solve 1/3 - 14/9*b**t + 4/9*b**3 + 1/3*b**4 + 4/9*b = 0.
-3, -1/3, 1
Suppose -69 - 5 = -50*c + 26. Find w such that -1/3*w**3 - 2/9*w + 1/9*w**5 - 5/9*w**c + 0 + 1/9*w**4 = 0.
-1, 0, 2
Let b = -194 + 196. Let l(m) be the first derivative of -64*m + 16*m**b + 7 - 4/3*m**3. Determine x so that l(x) = 0.
4
Suppose 0 = 3*g - 5*q - 16, 3*q + 18 - 2 = 5*g. Solve -2 + 12*k**3 + 7*k**g - 23*k**2 - 20*k + 10 = 0.
-1, 1/3, 2
Let g be (-2 + -1)*(-2)/3. Suppose -g*w + 7 - 1 = -3*r, -2*w - 5*r + 6 = 0. Factor b**4 + 7*b - 273*b**2 + 0*b**4 + 282*b**2 + 5*b**w + 2.
(b + 1)**3*(b + 2)
Let k be 2/16 - (-141)/376. Let c(n) be the first derivative of -k*n**3 + 9/4*n**2 - 3*n - 2. Factor c(p).
-3*(p - 2)*(p - 1)/2
Factor 3*a**5 + 9*a**2 + 3*a**3 - 9*a**4 + 2*a - 40 - 8*a + 40.
3*a*(a - 2)*(a - 1)**2*(a + 1)
Let t(d) be the second derivative of 0*d**4 + 0*d**3 - 1/420*d**7 + 0 + 1/200*d**5 + 0*d**2 + 0*d**6 - 18*d. Factor t(m).
-m**3*(m - 1)*(m + 1)/10
Suppose -5 = -3*p - 2*p. Suppose 4 = l + p. Factor 3*x**3 + 3*x - 3*x + x**2 - 4*x**l.
-x**2*(x - 1)
Let z = -2919 - -2919. Factor 8/13*b**3 + 0*b + z*b**2 - 10/13*b**5 + 0 - 16/13*b**4.
-2*b**3*(b + 2)*(5*b - 2)/13
Suppose 0 = 6*a - 2*a + 4*n - 12, -4*a + 2*n = 0. Suppose -t + 4 = 5*j - a, -5 = -t. Factor 0*q**2 + 0 + 1/5*q**5 - 3/5*q**4 + 2/5*q**3 + j*q.
q**3*(q - 2)*(q - 1)/5
Let n(k) be the third derivative of 5/3*k**3 + 5/24*k**4 - 1/12*k**5 + 0 + 0*k - 5*k**2. Factor n(y).
-5*(y - 2)*(y + 1)
Let t(x) be the second derivative of 4/21*x**4 + 18*x - 16/21*x**3 + 0 - 1/70*x**5 + 0*x**2. Find r, given that t(r) = 0.
0, 4
Let x(d) be the first derivative of 2*d**5/45 - 7*d**4/18 + 4*d**3/9 - 61. Solve x(u) = 0 for u.
0, 1, 6
Let t(j) = -j**3 + 3 - j**3 + 0 + 4*j**3 - 8*j. Let m(x) = -2*x**3 + 8*x - 2. Let g(h) = -3*m(h) - 2*t(h). Factor g(n).
2*n*(n - 2)*(n + 2)
Factor 72*m**2 + 19008*m + 1/11*m**3 + 1672704.
(m + 264)**3/11
Let b(i) = -i**3 - 5*i. Let j(r) = -r**3 - 15*r**2 + 20*r + 20. Let y(h) = 4*b(h) + j(h). Factor y(q).
-5*(q - 1)*(q + 2)**2
Suppose -3*i = 2*g - 5*i - 12, -2*g + 12 = 6*i. Let y be 1/((-15)/9 - -2). Let -3*k**y - g*k + 21/2*k**2 - 6 = 0. What is k?
-1/2, 2
Let a be 0/2 + (-45)/(-9). Suppose 2*g + 3*u = 6*g - 2, 0 = -a*g + 5*u. Factor 3*m + 4*m**2 - g - 2*m - 3*m + 4*m.
2*(m + 1)*(2*m - 1)
Factor 4/7*d**2 - 2/7*d**3 + 0 + 6/7*d.
-2*d*(d - 3)*(d + 1)/7
Let q(g) = -g**2 - g - 1. Let b(i) = -i. Let h(c) = -c**2 - 2*c + 3. Let p be h(0). Let f(u) = p*b(u) - q(u). Solve f(k) = 0 for k.
1
Suppose 0 = -2*v - 3*g - 16 - 2, 0 = 4*v + 3*g + 18. Factor v + 0*o - 12/7*o**2 - 2/7*o**3.
-2*o**2*(o + 6)/7
Suppose 5*z = z + 16. Let j = -91 + 109. Let 25*h**5 + j*h**2 + z*h**3 - 18*h**2 - 24*h**4 + 4*h**4 = 0. Calculate h.
0, 2/5
Let k(i) be the first derivative of i**6/40 - i**4/2 - 8*i**2 + 37. Let l(h) be the second derivative of k(h). Determine r, given that l(r) = 0.
-2, 0, 2
Let y = -2089 + 2091. Solve y*m**2 - 4/7 + 10/7*m = 0 for m.
-1, 2/7
Let o = 1489/24 - 62. Let n(h) be the second derivative of o*h**4 + 3/4*h**2 + 0 - 1/3*h**3 - 2*h. Determine u, given that n(u) = 0.
1, 3
Let q(m) be the second derivative of 5*m**4/12 - 5*m**3/6 - 80*m. Factor q(z).
5*z*(z - 1)
Let s(g) = g**5 + 3*g**3 - 4*g**2 - 4*g + 4. Let v(k) = -k**3 + k**2 + k - 1. Let i(w) = s(w) + 4*v(w). Suppose i(p) = 0. What is p?
-1, 0, 1
Let r be 6/(-5)*(3 + (-38)/6). Factor -55*o**r + 10*o + 53*o**4 + 18*o**2 + 2*o**3 + 4*o**3.
-2*o*(o - 5)*(o + 1)**2
Let k(g) be the first derivative of 1/30*g**4 + 0*g - 5 - 1/3*g**3 - 7/300*g**5 + 0*g**2 - 1/225*g**6. Let d(a) be the third derivative of k(a). Factor d(h).
-2*(h + 2)*(4*h - 1)/5
Let o = 145 - 143. Find f such that -1/4*f - 1/4*f**o + 0 = 0.
-1, 0
Let n(d) be the third derivative of 0*d - 5*d**2 + 0*d**3 + 0 + 1/120*d**5 - 1/420*d**7 - 1/60*d**6 + 1/12*d**4. Factor n(q).
-q*(q - 1)*(q + 1)*(q + 4)/2
Let l = 8 - 3. Factor 15*p - 39*p + 14*p**3 + 18*p**2 - 13 + l.
2*(p - 1)*(p + 2)*(7*p + 2)
Solve 3/2*b**2 + 3*b**3 - 9/4 - 3*b + 3/4*b**4 = 0.
-3, -1, 1
Find r, given that -121/4*r**3 - r + 11*r**2 + 0 = 0.
0, 2/11
Let u(k) be the third derivative of 1/6*k**4 + 1/480*k**6 + 1/30*k**5 + 0*k - 5*k**2 + 0*k**3 + 0. Factor u(v).
v*(v + 4)**2/4
Let c(p) be the first derivative of -7*p**6/3 - 32*p**5/5 + 3*p**4/2 + 32*p**3/3 + 4*p**2 + 1. Let c(b) = 0. Calculate b.
-2, -1, -2/7, 0, 1
Let z(k) be the second derivative of 1/6*k**4 + 0*k**3 + 0 + 1/30*k**5 