d derivative of -t**5/180 - t**4/12 - t**3/2 - 2*t**2. Factor n(d).
-(d + 3)**2/3
Let n(b) be the second derivative of b**5/50 + 12*b. Factor n(w).
2*w**3/5
Let u(f) be the third derivative of -5*f**6/56 + f**4/14 + 8*f**2. Factor u(c).
-3*c*(5*c - 2)*(5*c + 2)/7
Let g(p) be the third derivative of p**8/84 - 2*p**7/35 + p**6/15 + 2*p**5/15 - p**4/2 + 2*p**3/3 + 16*p**2 - 2. Find u such that g(u) = 0.
-1, 1
Suppose 3*f - 9 = -3. Factor 8*x + 38*x**3 + 36*x**3 + 8*x**5 + 10*x**5 + 60*x**4 + 40*x**f.
2*x*(x + 1)**2*(3*x + 2)**2
Suppose 0 = -5*n - y - 2, 2 = -2*n - y - 0. Let d = 2 + n. Factor -4 + 4*p**2 - 5 + 2*p**3 + 5 - d*p.
2*(p - 1)*(p + 1)*(p + 2)
Let k(p) = -2*p**3 + 2*p**2 + 6*p + 6. Let m(d) = -4*d**3 + 5*d**2 + 12*d + 13. Let q(v) = 5*k(v) - 2*m(v). Solve q(y) = 0.
-1, 2
Suppose 5*q = x + 17, 2*q - 2 = -x - x. Factor -4/5*h**2 + 2/5 - 2/5*h**5 + 2/5*h**4 - 2/5*h + 4/5*h**q.
-2*(h - 1)**3*(h + 1)**2/5
Suppose 149*c = 142*c. Suppose 8/3*w**2 - 4/3*w + c + 19/3*w**3 + 7/3*w**4 = 0. Calculate w.
-2, -1, 0, 2/7
Let t(r) be the first derivative of -3*r**5/5 - 15*r**4/2 - 37*r**3 - 90*r**2 - 108*r + 2. Factor t(z).
-3*(z + 2)**2*(z + 3)**2
Let v(x) be the third derivative of 0*x**5 + 0*x**4 + x**2 + 1/120*x**6 + 0*x - 1/210*x**7 + 0*x**3 + 0. Determine i so that v(i) = 0.
0, 1
Factor 1/8*f**2 - 1/8*f**4 + 1/8*f - 1/8*f**3 + 0.
-f*(f - 1)*(f + 1)**2/8
Let c(m) be the third derivative of 0 + 1/12*m**4 + 8*m**2 + 1/60*m**5 + 0*m + 0*m**3. Factor c(v).
v*(v + 2)
Factor 12*i**2 - 10*i**2 - 7*i**2 - 245 + 70*i.
-5*(i - 7)**2
Factor -8/3 - 10/3*a - 2/3*a**2.
-2*(a + 1)*(a + 4)/3
Let u(t) be the third derivative of t**5/20 - t**4/8 - 4*t**2. What is w in u(w) = 0?
0, 1
Let d be (11/12 - (-2)/(-3))*1. Solve -1/4*t**3 + 0*t**2 + 0 + 0*t - d*t**5 + 1/2*t**4 = 0 for t.
0, 1
Solve -9*z**4 - 2*z**3 - 3*z**2 + 11*z**3 + 405*z**5 - 402*z**5 = 0 for z.
0, 1
Let p(r) be the second derivative of r**4/4 - 3*r**2/2 - r. Factor p(c).
3*(c - 1)*(c + 1)
Let i(d) be the second derivative of d**7/2520 - d**6/576 + d**5/480 + d**4/3 - d. Let s(h) be the third derivative of i(h). Determine z so that s(z) = 0.
1/4, 1
Factor 3/8*m**5 - 9/8*m**4 + 0 - 3/8*m**2 + 9/8*m**3 + 0*m.
3*m**2*(m - 1)**3/8
Suppose -10 + 0 = -2*w. Suppose 0 = -0*h + w*h - 20. Factor 0*z - 1/4*z**2 + 1/2*z**h + 0 + 1/4*z**3.
z**2*(z + 1)*(2*z - 1)/4
Let n(t) be the first derivative of t**3/21 + 3*t**2/7 + 9*t/7 + 1. Factor n(r).
(r + 3)**2/7
Factor -11/2*o**4 + 18*o**2 + 12*o**3 + 0 + 0*o + 1/2*o**5.
o**2*(o - 6)**2*(o + 1)/2
Find y, given that -4/5*y**2 + 2/5*y**3 + 16/5 - 8/5*y = 0.
-2, 2
Let s = -1 - -7/4. Suppose -5*j + 31 = -4*d, -3*j + 4*d = d - 21. Factor 1/4 + 1/4*c**j + 3/4*c + s*c**2.
(c + 1)**3/4
Suppose 6 = 3*n - 5*c, 0*n + 3*n = c + 6. Let k(b) be the second derivative of -1/9*b**2 - 1/18*b**4 + n*b + 0 - 1/9*b**3 - 1/90*b**5. Factor k(d).
-2*(d + 1)**3/9
Let q(y) = y**2 - 5*y + 6. Let m be q(8). Let r = -30 + m. What is b in 6*b**5 + b**2 + 0 + r*b - 7/2*b**4 - 7/2*b**3 = 0?
-2/3, 0, 1/4, 1
Determine a so that -125/6 - 13/6*a**4 + 5/3*a**2 - 1/6*a**5 - 23/3*a**3 + 175/6*a = 0.
-5, 1
Suppose -4/5*t**2 - 2/5*t**4 + 0 + 0*t - 6/5*t**3 = 0. What is t?
-2, -1, 0
Let d(v) be the third derivative of -v**8/224 + v**7/140 + v**6/80 - v**5/40 + 8*v**2. Suppose d(r) = 0. Calculate r.
-1, 0, 1
Suppose -2*x - x = 0. Let t be 9/(-3) + (-50)/(-15). Factor 0*p + 0*p**2 + t*p**3 + x.
p**3/3
Let k(z) be the third derivative of z**7/140 + 3*z**6/80 - 14*z**2. Solve k(w) = 0 for w.
-3, 0
Solve -7/8*t**5 + 2*t**2 - 17/4*t**3 + 1/8*t - 1/4 + 13/4*t**4 = 0.
-2/7, 1
Let n(j) be the second derivative of j**8/168 + 4*j**7/105 + j**6/15 - 5*j**2/2 - 4*j. Let o(r) be the first derivative of n(r). Factor o(w).
2*w**3*(w + 2)**2
Suppose -2*j + j = -2. Factor 0 + 1/2*p + 1/2*p**j.
p*(p + 1)/2
Let t = -512/9 + 57. Let j = t + 1/9. Factor 2/9*r**3 + 0*r + 2/9*r**2 + 0 - j*r**4 - 2/9*r**5.
-2*r**2*(r - 1)*(r + 1)**2/9
Let a be 4/(-40) + (-161)/(-210). Factor -a*z + 4/3*z**2 + 0.
2*z*(2*z - 1)/3
Suppose 1 = -4*k + 13. Let y be k/9 + (-94)/(-6). What is f in 0 + f**3 + y*f**5 + 0 + 8*f**4 = 0?
-1/4, 0
Factor -8/21*m + 8/21 + 2/21*m**2.
2*(m - 2)**2/21
Let x(j) = -j**3 + j + 4. Let i be x(0). Let q(p) = -p**3 + 6*p**2 - p + 6. Let s be q(6). What is w in w - i*w + s*w**2 + w - 2*w**2 = 0?
-1, 0
Let 1 + 2923*r**4 + 4*r**3 - 2935*r**4 - 1 - 16*r**5 = 0. Calculate r.
-1, 0, 1/4
Let z(m) = 5*m - 9. Let x be z(5). Let -44*d**2 + x + 112*d**3 + 30*d**3 - 48*d + 100*d**4 - 22*d**3 = 0. Calculate d.
-1, 2/5
Let s = -18 - -25. Let k = s + -2. Factor 2*a + k*a**2 - a**2 + a**3 + a**3.
2*a*(a + 1)**2
Let z(s) be the first derivative of 2*s**5/25 + 3*s**4/10 + 2*s**3/5 + s**2/5 - 9. Factor z(w).
2*w*(w + 1)**3/5
Let u = -9 - -12. Suppose u*r + r - 8 = 0. What is w in 0 + 1/4*w + 1/4*w**r = 0?
-1, 0
Factor 0*d + 0*d**2 + 8/5*d**3 + 4/5*d**4 + 0.
4*d**3*(d + 2)/5
Let t(l) = l**3 - 1. Let f(z) = 8*z**3 - 10 - 3*z + z - 6*z**3 + 10*z**3. Let x(v) = -f(v) + 10*t(v). Solve x(o) = 0.
-1, 0, 1
Let d = 8 - 6. Let s(u) be the second derivative of 0 - 2*u - 1/45*u**6 + 1/18*u**4 + 0*u**d + 0*u**5 + 0*u**3. Let s(q) = 0. Calculate q.
-1, 0, 1
Let g = -39348936 - -33407250628/849. Let z = g + -2/849. Factor 0 - z*f**4 + 0*f - 10/3*f**3 + 4/3*f**2.
-2*f**2*(f + 1)*(7*f - 2)/3
Let b = 161 - 154. Let v(d) be the third derivative of 4*d**2 + 0 + 0*d**4 + 0*d**3 + 0*d**5 + 0*d**6 - 1/1050*d**b + 0*d. Factor v(n).
-n**4/5
Let j(f) = -4*f**5 - 16*f**4 + 4*f**3 - 8*f**2 + 8. Let p(i) = -i**5 - i**4 - i**2 + 1. Let d(b) = -j(b) + 8*p(b). Determine k, given that d(k) = 0.
0, 1
Suppose -4*q = -25 + 9. Find x such that 4*x**2 + 6*x**3 - 4*x**5 - 2*x**3 - 4*x**4 + 0*x**q = 0.
-1, 0, 1
Suppose 2*q + 3*k + 12 = 1, k + 7 = q. Let l(d) be the first derivative of 1/5*d**q - 1 + 0*d + 1/3*d**3. Factor l(m).
m*(5*m + 2)/5
Let q = -6 - -8. Factor -4*p**2 + 6*p - 4*p**3 + 4 - 6 - q*p**5 + 0 + 6*p**4.
-2*(p - 1)**4*(p + 1)
Let l(r) be the first derivative of 3*r**5/10 - 5*r**4/6 + r**3/3 + r**2 - 6*r - 6. Let v(x) be the first derivative of l(x). Factor v(n).
2*(n - 1)**2*(3*n + 1)
Let g(a) be the second derivative of a**5/4 - 5*a**4/4 + 10*a**2 + 13*a. Solve g(w) = 0.
-1, 2
Let q(t) = -6*t - 1. Let y be q(-1). Let w be -1 + y/4 - 0. Factor r**2 + 0 + w*r**4 + 0*r - r**3.
r**2*(r - 2)**2/4
Let t(r) = 16*r**4 - 31*r**3 + 30*r**2 - 20*r + 16. Let n(s) = 3*s**4 - 6*s**3 + 6*s**2 - 4*s + 3. Let q(c) = 22*n(c) - 4*t(c). Factor q(m).
2*(m - 1)**4
Let c be -3 + 3 + (0 - -2 - 2). Factor 1/3*s + c - 1/3*s**3 - 1/3*s**2 + 1/3*s**4.
s*(s - 1)**2*(s + 1)/3
Let y(f) be the second derivative of -3*f**5/40 - 3*f**4/8 + f**3 + 42*f. Factor y(k).
-3*k*(k - 1)*(k + 4)/2
Suppose 15 = -3*h + 6*h. Suppose s - 2 = h. Determine g so that -9*g + 0 - 16*g**3 + 11*g**2 + 7*g**4 + 0 + s*g = 0.
0, 2/7, 1
Let d(b) be the second derivative of -1/36*b**4 + 1/60*b**5 - 6*b + 0 + 0*b**2 + 0*b**3. Determine h so that d(h) = 0.
0, 1
Let n = 7 - 6. Factor -2*l + 3*l + 4*l**2 + n - 1.
l*(4*l + 1)
Let i be 3 - (300/(-66) + 7). Factor 2/11*w**4 + 6/11*w**2 + i*w**3 + 0 + 2/11*w.
2*w*(w + 1)**3/11
Let u(o) = -3*o + 3. Let y be u(0). Let 4/3 - 10/3*c + 8/3*c**2 - 2/3*c**y = 0. Calculate c.
1, 2
Let v(c) = c**3 + 10*c**2 - 10*c + 11. Let k be v(-11). Let 2/3*j**3 - 2*j + k*j**2 + 4/3 = 0. Calculate j.
-2, 1
Let w(o) = o + 10. Let n be w(-6). Factor n*v**2 + 1/2*v**5 + 1 - v**4 - v**3 - 7/2*v.
(v - 1)**4*(v + 2)/2
Let b(d) = -16*d + 4. Let l be b(-2). Let r be (4/10)/(l/45). Factor 0 - 3/2*j**3 - r*j**4 + 5/2*j**2 - j + 1/2*j**5.
j*(j - 1)**3*(j + 2)/2
Let i(c) be the third derivative of -c**5/15 + c**4/3 - 2*c**3/3 - 6*c**2. Factor i(j).
-4*(j - 1)**2
Let l(x) be the first derivative of x**7/420 - x**6/240 - x**5/120 + x**4/48 + x**2 - 3. Let i(g) be the second derivative of l(g). Factor i(h).
h*(h - 1)**2*(h + 1)/2
Suppose t + 3*v - 4 = 5, 2*v = 2*t - 2. Solve -7*z - z**t - 12*z**2 - 2*z**3 + 5*z - 10*z = 0.
-2, 0
Suppose -10 = -4*q - 2*m, m + 4*m + 19 = q. Let c(b) be the second derivative of 4/21*b**3 + 4/21*b**q + 0*b**2 + b + 1/14*b**5 + 1/105*b**6 + 0. Factor c(i).
2*i*(i + 1)*(i + 2)**2/7
Factor 24/5 - 4*q - 4/5*q**2.
-4*(q - 1)*(q + 6)/5
Determine r, given that r**2 + 7*r - 3*r + 0*r**2 = 0.
-4, 0
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