Let o = -49 + 54. Suppose -2*x + 1 = -3. Factor 2*s**4 - 4*s**5 - 5*s**x + 3*s**2 - s + o*s**5.
s*(s - 1)*(s + 1)**3
Suppose 530 - 554 = -12*f. Let k = 821/13 + -63. Factor -k*i**f - 4/13 + 6/13*i.
-2*(i - 2)*(i - 1)/13
Let a(c) be the third derivative of -27*c**2 - 107/6*c**5 - 25/6*c**4 + 20*c**3 + c - 35/24*c**6 + 0. Solve a(z) = 0 for z.
-6, -2/5, 2/7
Let a = 1059 - 1057. Let v(p) be the third derivative of 0 + 1/39*p**4 + 1/13*p**3 + 1/390*p**5 - 10*p**a + 0*p. Factor v(c).
2*(c + 1)*(c + 3)/13
Let p(d) be the first derivative of -d**6/18 + 2*d**5/15 - 199. Factor p(x).
-x**4*(x - 2)/3
Let 4391*t - 4*t**2 + 148 - 2112*t - 2135*t = 0. What is t?
-1, 37
Let q be (-2 + (-15)/(-6))/(-4 + 7). Let j(w) be the second derivative of w**2 + 0 - 1/12*w**4 + 2*w - q*w**3. Factor j(p).
-(p - 1)*(p + 2)
Let s(d) be the first derivative of 36/5*d - 42/5*d**2 - 2 + 61/15*d**3 - 7/10*d**4 + 1/25*d**5. Factor s(o).
(o - 6)**2*(o - 1)**2/5
Let b(d) be the second derivative of -11*d + 0 + 1/2*d**3 - 15/8*d**2 + 1/16*d**4. Factor b(m).
3*(m - 1)*(m + 5)/4
Let b(s) be the first derivative of s**7/5040 - s**6/90 + 4*s**5/15 - 32*s**4/9 - 2*s**3/3 + 8. Let x(d) be the third derivative of b(d). Solve x(a) = 0.
8
Let l(d) be the second derivative of -9*d**5/5 + 50*d**4/3 + 58*d**3 + 56*d**2 - 6*d + 20. Factor l(w).
-4*(w - 7)*(w + 1)*(9*w + 4)
Let j be 3/(-63)*291/(-39). Let a = j - 2/91. Factor -a*z + 1/6*z**2 + 1/6.
(z - 1)**2/6
Find u such that u**3 + 5*u**3 - 4*u**3 + 8 + 12*u**2 + 18*u = 0.
-4, -1
Let q(c) = c**4 + c**3 - c**2 + c + 1. Let v(o) = 20*o**4 + 30*o**3 - 10*o**2 + 5. Suppose -t + 3 = 4. Let y(d) = t*v(d) + 15*q(d). Find b, given that y(b) = 0.
-2, -1, 1
Let k(r) be the first derivative of -2*r**5/5 - 3*r**4 - 6*r**3 + 4*r**2 + 24*r - 139. Factor k(c).
-2*(c - 1)*(c + 2)**2*(c + 3)
Let v(k) be the third derivative of k**6/90 - 4*k**5/45 - 2*k**4/3 - 176*k**2. What is t in v(t) = 0?
-2, 0, 6
Let y(o) be the first derivative of -o**6/15 + 4*o**5/5 - 5*o**4/2 - 253. Determine m so that y(m) = 0.
0, 5
Let -152*u**2 + 58*u - 39*u + 65*u + 20*u**3 = 0. What is u?
0, 3/5, 7
Let c(t) be the second derivative of -t**7/168 + t**6/20 - 3*t**5/20 + t**4/6 + 155*t. Factor c(u).
-u**2*(u - 2)**3/4
Let m(l) be the second derivative of -36*l + 0*l**3 + 0 + 5/12*l**4 + 0*l**2 + 1/6*l**6 + 1/2*l**5. Let m(t) = 0. Calculate t.
-1, 0
Factor -68*r + 250*r**2 + 242*r**2 - 494*r**2.
-2*r*(r + 34)
Factor 0*f**2 - 72*f + 3/2*f**3 - 192.
3*(f - 8)*(f + 4)**2/2
Let f(t) be the first derivative of -t**3/3 - t**2/2 + 6*t + 27. Factor f(d).
-(d - 2)*(d + 3)
Let v(a) = 2*a**2 - 3*a + 4. Let g be v(1). Factor -3*c**3 - 405*c + c**g - 2*c**2 - 2*c**4 + 407*c + 4*c**2.
-2*c*(c - 1)*(c + 1)**2
Let f(u) be the first derivative of u**6/20 - 3*u**5/10 + 5*u**4/8 - u**3/2 + 6*u + 3. Let n(i) be the first derivative of f(i). Factor n(h).
3*h*(h - 2)*(h - 1)**2/2
Let m be 14/(-40) - ((-6)/20)/((-7)/(-14)). Factor 3/4*o**4 + m*o**2 - 3/4*o**3 - 1/4*o**5 + 0*o + 0.
-o**2*(o - 1)**3/4
Let s = 67 + -63. Let x(i) be the first derivative of 1/6*i - 1/18*i**3 + 4 - 1/12*i**2 + 1/24*i**s. Find t such that x(t) = 0.
-1, 1
Let g be 36/48 - 2/(-8). Let j be g - 1 - (-2)/4. Factor 0*i**2 - j - 3/4*i + 1/4*i**3.
(i - 2)*(i + 1)**2/4
Suppose -3*b - 3*a = b - 5, -5*b + 5*a = -15. Let z = -10 + 13. Determine o, given that -6/11*o - 2/11*o**z + 2/11 + 6/11*o**b = 0.
1
Let c(a) be the third derivative of -a**9/1008 + 3*a**7/280 - a**6/60 + 3*a**3 - 23*a**2. Let g(z) be the first derivative of c(z). Solve g(y) = 0.
-2, 0, 1
Let v = 16 + -11. Suppose 0*f + 3*l = f - 20, -v*f + 10 = 3*l. Suppose 12*w**4 - 7*w - 3*w**f + 8*w**4 - 22*w**3 + 18*w**2 + 1 - 7*w**4 = 0. Calculate w.
1/3, 1
Let g(t) be the third derivative of 0 + 1/4*t**4 - 1/30*t**5 + 0*t - 2/3*t**3 + 10*t**2. Factor g(l).
-2*(l - 2)*(l - 1)
Let v(q) be the first derivative of q**6/240 + q**5/40 + q**4/16 + q**3/12 + 3*q**2 + 11. Let l(k) be the second derivative of v(k). Factor l(t).
(t + 1)**3/2
Let g = -18113 + 54341/3. Suppose -r**3 + 0*r + 0 - g*r**4 - 1/3*r**2 = 0. Calculate r.
-1, -1/2, 0
Let v(l) be the second derivative of -2/147*l**7 - 10*l + 0*l**6 - 2/7*l**3 - 2/21*l**4 + 4/7*l**2 + 0 + 4/35*l**5. Find j such that v(j) = 0.
-2, -1, 1
Let m(q) be the second derivative of 0 + 2/5*q**2 + 11*q + 1/5*q**3 - 1/75*q**6 - 3/50*q**5 - 1/30*q**4. What is y in m(y) = 0?
-2, -1, 1
Let l = 1/492 - -437/164. Suppose -32/3*q + 14/3*q**2 + l = 0. Calculate q.
2/7, 2
Let k be 48/9 + 2 + 18/27. Factor 4*g - k*g**2 - 8 + 4*g**2 + 8*g.
-4*(g - 2)*(g - 1)
Let o(m) be the first derivative of 0*m - 2/9*m**3 + 2/15*m**5 + 3 + 1/6*m**4 - 1/3*m**2. Find i such that o(i) = 0.
-1, 0, 1
Let l(u) = -u**4 + 3*u**3 - 6*u**2 + 4*u + 4. Let q = -14 + 13. Let i(z) = z**2 - z - 1. Let w(k) = q*l(k) - 4*i(k). Factor w(g).
g**2*(g - 2)*(g - 1)
Let y(c) be the first derivative of c**7/168 + c**6/30 - c**4/3 - 2*c**3/3 - 3*c + 15. Let u(o) be the first derivative of y(o). Suppose u(b) = 0. What is b?
-2, 0, 2
Determine x so that -2809*x**4 + 137*x**2 - 128*x**3 + 15*x**2 + 2849*x**4 - 60*x - 4*x**5 = 0.
0, 1, 3, 5
Let j be (90/(-12))/(1*(-1)/2). Suppose -18 = -11*o + j. Factor -3/4*c + 3/4*c**o - 3/4*c**2 + 3/4.
3*(c - 1)**2*(c + 1)/4
Suppose -99 + 9 = -5*v. Solve 19*z**2 - z**3 - 35*z**3 - v*z**4 - 4*z**2 + 12 - 9*z**4 + 36*z = 0.
-1, -2/3, 1
Let k(c) be the second derivative of 8*c**2 + 11*c + 0 - 1/3*c**4 + 0*c**3. Factor k(j).
-4*(j - 2)*(j + 2)
Let n(x) be the second derivative of x**5/16 - 73*x**4/48 + 5*x**3/3 + 7*x**2/2 + 208*x. Solve n(r) = 0.
-2/5, 1, 14
Let j be 348/(-7) + 5 - (-4)/(-14). Let u = 49 + j. Determine z, given that -2/13*z**3 + 4/13*z**2 + 0 + 2/13*z**5 + 0*z - 4/13*z**u = 0.
-1, 0, 1, 2
Let o = 43 + -39. Factor -72*x**2 - 44*x - o + 7 - 36*x**3 - 11.
-4*(x + 1)*(3*x + 1)*(3*x + 2)
Let q(x) be the second derivative of -x**5/16 + 5*x**4/8 + 198*x. Factor q(p).
-5*p**2*(p - 6)/4
What is p in -8*p + 1/2*p**4 - 5/6*p**5 - 4/3*p**2 - 8/3 + 16/3*p**3 = 0?
-2, -1, -2/5, 2
Let m(f) be the second derivative of -f**6/1440 - f**5/160 + f**3/3 - 13*f. Let o(q) be the second derivative of m(q). Find x such that o(x) = 0.
-3, 0
Let r = 8 - 12. Let u = r + 8. Solve k - k - u*k**2 + k = 0.
0, 1/4
Let l(k) = -4*k**5 - k**4 - 6*k**3 - 3. Let i(c) = 7*c**5 + 3*c**4 + 11*c**3 + 5. Let z(v) = -3*i(v) - 5*l(v). Factor z(n).
-n**3*(n + 1)*(n + 3)
Let r(w) be the third derivative of -w**6/600 + 7*w**5/300 - w**4/30 - 2*w**3/5 + w**2 - 3. Find c such that r(c) = 0.
-1, 2, 6
Let g = 171 - 102. Let f = 75 - g. Determine q so that -f + 10*q - 14/3*q**2 + 2/3*q**3 = 0.
1, 3
Let z(m) = -m**2 - 9*m. Let v be z(-4). Determine o, given that 4*o**4 - 4*o**4 + 32*o - 28*o**3 - 4*o**5 - 16 + v*o**4 - 4*o**2 + 0 = 0.
-1, 1, 2
Let j be -6 + 44/7 - 3797/35. Let h = -107 - j. Factor 0 - h*r**5 + 0*r - 2*r**4 + 2/5*r**2 - 2/5*r**3.
-2*r**2*(r + 1)**2*(3*r - 1)/5
Let x(d) = 2*d - 1. Let g be x(3). Suppose -2*o - 3 - g = -l, -4*o - 20 = -4*l. Suppose -8*h + 2*h**2 + 2*h**l - 1 + 5 = 0. What is h?
1
Let t = 28033/7 - 4004. Determine x, given that -1/7*x**3 + 3/7 + 1/7*x**2 + t*x = 0.
-1, 3
Let q(l) = -l**3 - 14*l**2 + 12*l - 45. Let c be q(-15). Let p(d) be the second derivative of -1/5*d**2 + c - 1/60*d**4 - 2*d + 1/10*d**3. Solve p(x) = 0 for x.
1, 2
Determine g, given that -4/7*g**4 + 20/7*g**2 - 16/7 - 2/7*g**5 + 10/7*g**3 - 8/7*g = 0.
-2, -1, 1, 2
Let m = -5308 - -5310. Factor 4/9*g**m - 2/9*g**3 - 16/9 + 8/9*g.
-2*(g - 2)**2*(g + 2)/9
Let s(v) = -v**3 - 5*v**2 + 6*v + 2. Let l be s(-6). Let g(j) be the first derivative of -6*j - j**3 - 3 - 9/2*j**l. Factor g(p).
-3*(p + 1)*(p + 2)
Let h(d) = -30*d - 390. Let g be h(-13). Let t(z) be the second derivative of -5/4*z**5 + 25/6*z**3 - 1/2*z**6 - 2*z - 5*z**2 + g + 25/12*z**4. Solve t(i) = 0.
-2, -1, 1/3, 1
Find r, given that 129/2*r + 33/2 - 6*r**2 = 0.
-1/4, 11
Let r be 3 + ((-35)/5 - -4) + 3. Suppose 4*d - 2*d + 2*d**r - 8*d**2 + 4*d = 0. Calculate d.
0, 1, 3
Let n(c) be the first derivative of c**9/3024 - c**8/420 + c**7/280 + 10*c**3/3 + 6. Let j(f) be the third derivative of n(f). Factor j(y).
y**3*(y - 3)*(y - 1)
Suppose -10 = -2*l, l + 7 = 2*p + p. Factor 3*s**5 + 2*s**2 + 0*s**2 + 6*s + s**2 + 2*s**4 - 5*s**p - 9*s**3.
3*s*(s - 2)