8 + 5*r - 1. Let c(x) be the first derivative of u(x). Factor c(d).
d**2*(d - 1)**3/4
Suppose 2 + 14 = -2*w + 4*u, 2*w - 12 = -3*u. Let l = 737/7 - 105. Suppose w + 0*s - 2/7*s**2 - l*s**3 = 0. Calculate s.
-1, 0
Suppose 12 = 2*p + 2. Suppose 3*n = -n - q + 1, -4*n = -5*q + p. Factor -2/7*m**3 + n - 2/7*m**2 + 0*m.
-2*m**2*(m + 1)/7
Factor 2/7*j + 0 + 0*j**2 - 2/7*j**3.
-2*j*(j - 1)*(j + 1)/7
Let s be (-2)/(1 - 15/9). What is k in 2 + k**s + k**3 - 2*k**2 - 72*k + 70*k = 0?
-1, 1
Let i(s) be the third derivative of s**6/40 + 5*s**5/4 + 21*s**4 + 72*s**3 - 35*s**2. Factor i(r).
3*(r + 1)*(r + 12)**2
Let a(k) be the third derivative of 0*k**3 - 3*k**2 + 0*k + 7/120*k**5 + 0 - 1/24*k**4. Factor a(t).
t*(7*t - 2)/2
Suppose 0 = -3*i - 16 + 67. Let p = -15 + i. Let -1 + 3/2*d + 0*d**p - 1/2*d**3 = 0. Calculate d.
-2, 1
Let h be 13/78*-9 + (-3)/(-2). Solve -2/5*q**2 + h*q + 2/5 = 0 for q.
-1, 1
Factor 1/2*q**4 - 1/2*q**2 + 0 + 1/2*q - 1/2*q**3.
q*(q - 1)**2*(q + 1)/2
Let j(q) be the third derivative of q**8/1120 + q**7/315 + q**6/360 + q**4/8 + 2*q**2. Let c(h) be the second derivative of j(h). Solve c(f) = 0.
-1, -1/3, 0
Let m(o) = 3*o**3 - 2*o**2 - o + 4. Let q(x) = -x**3 - 1. Let v(b) = m(b) + 4*q(b). Solve v(k) = 0 for k.
-1, 0
Let d(j) = 3*j**2 - 8*j + 2. Let t(n) = -2*n**2 + 8*n - 2. Let m(w) = 4*d(w) + 3*t(w). Factor m(b).
2*(b - 1)*(3*b - 1)
Suppose -135 = 4*a - 9*a. Let h = 55/2 - a. Determine y, given that h*y**3 + 0 + 1/4*y**4 + 0*y + 1/4*y**2 = 0.
-1, 0
Let o(d) be the first derivative of -2*d**6/15 + 2*d**5/25 + 7*d**4/10 - 14*d**3/15 - d**2/5 + 4*d/5 - 6. Let o(r) = 0. Calculate r.
-2, -1/2, 1
Let v(t) = 12*t - 1. Let z be v(4). Suppose z + 13 = 5*p. Factor -3*g**5 - 3*g - 9*g**4 - 4*g**3 - 14*g**3 - p*g**2 - 3*g**4.
-3*g*(g + 1)**4
Let b = -35 + 37. Let j(o) be the first derivative of -1/5*o**3 + 0*o + 3/5*o**b - 3 - 3/20*o**4. Factor j(m).
-3*m*(m - 1)*(m + 2)/5
Factor -6/5 + 9/5*o - 3/5*o**2.
-3*(o - 2)*(o - 1)/5
Let p be ((-1)/5 + 2)/(126/60). Factor -p + 2/7*x**2 + 4/7*x.
2*(x - 1)*(x + 3)/7
Let c(b) be the second derivative of 3*b - 1/66*b**4 - 1/11*b**2 + 0 + 2/33*b**3. Factor c(d).
-2*(d - 1)**2/11
Factor a**3 - 6*a**2 + 4*a**3 + 12*a - 5*a**3 - 8 + a**3.
(a - 2)**3
Let v(r) = -r**4 + 5*r**3 + 5*r**2 + 5. Let g = 4 + 1. Let n(a) = 2*a**4 - 6*a**3 - 6*a**2 - 6. Let m(x) = g*n(x) + 6*v(x). Let m(p) = 0. Calculate p.
0
Let b = -9 - -5. Let m = b + 6. Let k(c) = c**3 - c**2 - c. Let j(r) = -4*r**3 + 4*r**2 + 4*r - 1. Let a(p) = m*j(p) + 6*k(p). Factor a(f).
-2*(f - 1)**2*(f + 1)
Let b(a) be the first derivative of -3/2*a**2 + 4 + 3/2*a**6 - 3/2*a**4 + 0*a - 12/5*a**5 + 4*a**3. Determine h so that b(h) = 0.
-1, 0, 1/3, 1
Let r(n) be the first derivative of 0*n**2 + 2 + 2/9*n**3 - 2/3*n. Factor r(c).
2*(c - 1)*(c + 1)/3
Let p(k) be the first derivative of -1/48*k**4 + 1 - 2*k + 0*k**2 - 1/12*k**3. Let b(u) be the first derivative of p(u). Factor b(x).
-x*(x + 2)/4
Let a(l) be the second derivative of -l**4/12 - 5*l**3/6 - l**2 + l. Let h be a(-4). Factor o**2 + o**4 + o**h - o**3 - 4*o**2.
o**2*(o - 2)*(o + 1)
Let u = 781/5 - 155. What is r in -u*r + 0*r**3 + 9/5*r**2 - 3/5*r**4 + 0 = 0?
-2, 0, 1
Let h(k) be the first derivative of k**7/21 - k**6/30 - k**5/10 + k**4/12 + 2*k + 2. Let t(q) be the first derivative of h(q). Let t(l) = 0. What is l?
-1, 0, 1/2, 1
Let d(s) be the third derivative of s**5/180 - s**4/12 + s**3/2 + 4*s**2. Solve d(t) = 0.
3
Let f(q) be the third derivative of q**10/15120 - q**9/7560 - q**8/3360 + q**7/1260 - q**4/12 - q**2. Let c(v) be the second derivative of f(v). Factor c(i).
2*i**2*(i - 1)**2*(i + 1)
Determine n, given that 1/4*n**4 + 1/4 - 1/4*n**5 + 1/2*n**3 - 1/4*n - 1/2*n**2 = 0.
-1, 1
Let m(y) be the first derivative of y**6/15 + 2*y**5/25 - 12. Factor m(x).
2*x**4*(x + 1)/5
Solve 0 + 7/5*s**2 + 2/5*s - 2/5*s**3 - 7/5*s**4 = 0 for s.
-1, -2/7, 0, 1
Let -1/7*m - 1/7*m**2 + 6/7 = 0. Calculate m.
-3, 2
Let k be (1 + -2)/(1/(-6)). Suppose 0 = -2*x + 5*x - k. Let 4*r**x - 4*r**2 - r**2 = 0. What is r?
0
Let k(b) be the third derivative of -3*b**2 + 1/300*b**6 + 0*b**5 + 0*b**3 + 0*b**4 + 0*b - 1/840*b**8 + 0 + 0*b**7. Factor k(h).
-2*h**3*(h - 1)*(h + 1)/5
Suppose 4*m + 2*y + 8 = 4*y, 20 = -3*m - 2*y. Let s be (-7)/14*2/m. Solve 0 + 0*l - s*l**2 - 1/4*l**3 = 0 for l.
-1, 0
Let q = -18 + 14. Let n be 6/(-90) - q/6. Suppose 6/5 + n*s**2 + 9/5*s = 0. Calculate s.
-2, -1
Suppose -y + 20 = -44. Factor 136*l**3 - y*l**2 - 2 + 5 + 28*l**5 + 5 - 103*l**4 - 4*l - l**4.
4*(l - 1)**4*(7*l + 2)
Let s(i) be the third derivative of i**7/630 - i**6/72 + i**5/30 - i**4/24 + i**2. Let f(h) be the second derivative of s(h). Factor f(k).
2*(k - 2)*(2*k - 1)
Let g be (-5)/20 - (-39)/12. Let q(l) be the third derivative of -2*l**2 - 1/12*l**4 - 1/30*l**5 + 0 + 0*l**g + 0*l. Factor q(v).
-2*v*(v + 1)
Let l(y) = y + 1. Let t be l(1). Factor s**3 + 8*s**2 - 3*s**3 + 2*s - 4*s**t - 4.
-2*(s - 2)*(s - 1)*(s + 1)
Let t = 2 + 0. Suppose 0 = -3*v - t + 8. Let u**4 - 4*u + 6*u**2 - 4*u**3 + 1 + 4*u**2 - 4*u**v + 0 = 0. Calculate u.
1
Let i(p) be the second derivative of p**8/3360 + p**7/630 - p**6/360 - p**5/30 - p**4/4 + p. Let z(s) be the third derivative of i(s). Factor z(h).
2*(h - 1)*(h + 1)*(h + 2)
Let f(s) be the second derivative of -5*s**4/24 - s**3/12 - 3*s. Find c, given that f(c) = 0.
-1/5, 0
Let a(i) be the third derivative of i**7/210 - 2*i**6/45 + 2*i**5/15 - i**3/2 + 4*i**2. Let j(r) be the first derivative of a(r). Let j(x) = 0. What is x?
0, 2
Let k = 1405/5856 + -14/61. Let s(q) be the third derivative of -1/480*q**6 - 3*q**2 - k*q**4 + 0 + 0*q**3 + 0*q + 1/120*q**5. Factor s(p).
-p*(p - 1)**2/4
Let p(r) = 5*r + 5. Let i be p(-4). Let w be 8/(-6)*9/i. Suppose 2/5*y**2 + w*y + 0 = 0. What is y?
-2, 0
Let f(b) = b**2 + 2*b + 3. Let r be f(-2). Let x be (-21 - -24)*2/3. Solve -x*q**r - q**2 - 2*q**2 + 5*q**3 = 0.
0, 1
Let f(p) be the second derivative of -p**5/40 - p**4/16 + p**2/8 - 21*p. What is k in f(k) = 0?
-1, 1/2
Factor -1/2*z**4 - 12*z**2 + 4*z**3 - 8 + 16*z.
-(z - 2)**4/2
Suppose 0 = p - 1 - 1. Suppose 2*w + 4 + 16 = 4*q, 0 = 5*q + p*w - 7. Let m**2 - 1 + 0*m + 0*m - m**q + m = 0. Calculate m.
-1, 1
Let x(a) = -a**3 + a**2 + a - 1. Let i(k) = 3*k**3 - 3*k**2 - 4*k + 2. Let l(s) = -i(s) - 2*x(s). Solve l(q) = 0 for q.
-1, 0, 2
Let j = -85 - -89. Factor 0*o - 10/9*o**j + 0 + 2/3*o**3 + 4/9*o**2.
-2*o**2*(o - 1)*(5*o + 2)/9
Suppose 2*f + 5 = 3*y, f - y = 4*f - 9. Factor -d**2 + d**2 + d**f - 3*d**2 - 2*d**3.
-2*d**2*(d + 1)
Let d(i) be the first derivative of i**6/27 - i**4/9 + i**2/9 + 8. Factor d(u).
2*u*(u - 1)**2*(u + 1)**2/9
Factor 19*p**2 + p**3 + 0*p**3 - 20*p**2.
p**2*(p - 1)
Let b(w) = -w**2 + 5*w - 4. Let d be b(3). Factor -t**3 + d*t**2 - 78*t + 82*t - 2*t**2.
-t*(t - 2)*(t + 2)
Let g(b) be the second derivative of b**7/8820 - b**5/420 + b**4/4 - 3*b. Let t(l) be the third derivative of g(l). What is y in t(y) = 0?
-1, 1
Let y(q) be the second derivative of -q**4/48 - q**3/4 + 31*q. Factor y(i).
-i*(i + 6)/4
Let j = -61 - -63. Let c(p) be the third derivative of 0 + 0*p**4 - 4*p**j + 0*p + 1/180*p**5 - 1/18*p**3. Factor c(r).
(r - 1)*(r + 1)/3
Let w(z) be the first derivative of 1/14*z**4 + 0*z + 0*z**2 - 2/35*z**5 + 4/21*z**3 + 1. Determine n, given that w(n) = 0.
-1, 0, 2
Let p(c) = -9*c**5 - 7*c**4 + 4*c**3 - 7*c**2 - 2*c + 7. Let i(r) = -4*r**5 - 3*r**4 + 2*r**3 - 3*r**2 - r + 3. Let u(o) = -7*i(o) + 3*p(o). Factor u(h).
h*(h - 1)**2*(h + 1)**2
Let h = 16 - 14. Let v(z) be the third derivative of 1/672*z**8 + z**h - 1/120*z**6 + 0*z + 0*z**5 + 0*z**3 + 1/48*z**4 + 0*z**7 + 0. Factor v(i).
i*(i - 1)**2*(i + 1)**2/2
Let c(d) be the second derivative of -d**6/660 - d**5/330 - 3*d**2/2 + 2*d. Let j(s) be the first derivative of c(s). Factor j(x).
-2*x**2*(x + 1)/11
Let m(j) = 8*j**2 + 8*j. Let r be m(-1). Factor -2/5*c**3 + r*c + 1/5*c**4 + 1/5*c**2 + 0.
c**2*(c - 1)**2/5
Suppose 2*x = -2*x + 40. Let g be 15/x*8/6. Factor 2/5*m**g + 0*m - 2/5.
2*(m - 1)*(m + 1)/5
Let i = -45 + 80. Suppose f + f + 41*f**2 + 9*f**3 - 3*f**3 + 2*f**4 - i*f**2 = 0. Calculate f.
-1, 0
Let d(a) = -10*a**3 + 12*a**2 - 38*a + 24. Let v(l) = 8*l**3 - 13*l**2 + 37*l - 23. Let k(j) = -3*d(j) - 4*v(j). Factor k(q).
-2*(q - 5)