derivative of 0 + 1/3*s**3 + 0*s - 1/18*s**4 - 1/180*s**5 + s**2 + 1/540*s**6. Let m(t) be the first derivative of k(t). Factor m(p).
2*(p - 2)*(p + 1)/3
Let z(u) = 4*u**2 - 2*u + 1. Let t be z(1). Suppose -t*l = -0*l. Factor -3 - 4*y**2 - 2*y**3 + 3 - 2*y + l.
-2*y*(y + 1)**2
Let d = 4 + -4. Suppose -6*k + 3*k - 2*q = -22, 5*k + 3*q - 36 = d. Find z such that -k*z**3 - 2*z + 2*z**4 + 3*z**3 + 6*z**2 - 3*z**3 = 0.
0, 1
Let v(b) = 6*b**2 - 3*b - 2. Suppose -3*c - 6 - 6 = 0. Let q be v(c). Find s, given that q*s**2 - 1 - 10*s**2 + 128*s**3 + 3 + 24*s = 0.
-1/4
Let y = -7 - -12. Let f(h) be the first derivative of -2/45*h**y + 0*h**3 + 0*h**4 - 1 + 1/27*h**6 + 0*h + 0*h**2. Suppose f(a) = 0. Calculate a.
0, 1
Let q be 6/(-8) + 99/(-4). Let y = -25 - q. Factor 0 + 3/2*i**4 - y*i**2 - i**3 + 0*i.
i**2*(i - 1)*(3*i + 1)/2
Let s(d) be the second derivative of -5*d**7/42 + 23*d**6/120 - d**5/80 - d**4/24 - 5*d - 3. Determine p, given that s(p) = 0.
-1/4, 0, 2/5, 1
Let m(x) be the third derivative of x**6/360 + x**5/90 + x**4/72 + 4*x**2. Factor m(y).
y*(y + 1)**2/3
Let a(w) be the third derivative of -w**2 - 1/280*w**7 + 0*w + 0*w**3 + 0 + 0*w**4 - 1/160*w**6 + 0*w**5. Factor a(j).
-3*j**3*(j + 1)/4
Let s(y) be the first derivative of -y**2/2 - 10*y + 2. Let n be s(-12). Determine z, given that 0 + 2/7*z**n + 2/7*z = 0.
-1, 0
Factor -3*v**2 - 39 + 39.
-3*v**2
Let p be (-2)/(-7) + (-286)/(-77). Let b(c) be the second derivative of -1/30*c**p - 1/15*c**3 + c + 0 + 0*c**2. Factor b(q).
-2*q*(q + 1)/5
Let z(f) be the second derivative of f**4/8 - 3*f**3/4 + 2*f. Determine u, given that z(u) = 0.
0, 3
Let j be (-26)/(-4) + (-2)/(-4). Suppose -3 = -3*o, -4*v - 3*o + j = -4. Find n, given that 0 + 2/9*n**3 + 2/9*n**4 - 2/9*n**v - 2/9*n = 0.
-1, 0, 1
Let q(h) = -5*h + 7 - 2*h + 5*h + h. Let o be q(6). Let w(g) = -4*g + 2. Let u(c) = c**3 + c - 1. Let i(p) = o*w(p) + 2*u(p). Factor i(r).
2*r*(r - 1)*(r + 1)
Factor 3/4*x**2 + 1/4*x**3 - 3/4 - 1/4*x.
(x - 1)*(x + 1)*(x + 3)/4
Let t be (-4)/(14 - 9/(-3)). Let v = t + 46/51. Factor -2/3*m**2 + 0 + v*m**4 + 0*m**3 - 1/3*m + 1/3*m**5.
m*(m - 1)*(m + 1)**3/3
Let a(u) be the second derivative of u**4/4 - u**3 - 22*u. Factor a(l).
3*l*(l - 2)
Let l = 4 - 2. Factor -2*w**l - 3*w + 0*w + w.
-2*w*(w + 1)
Let n be (-6)/(-5)*(-15)/(-6). Factor 3*f**2 + 7 - 7 - n*f**3.
-3*f**2*(f - 1)
Let f(j) = 9*j**2 + 3. Let u(p) = 9*p**2 + p + 4. Let b(g) = 4*f(g) - 3*u(g). Solve b(s) = 0 for s.
0, 1/3
Let p be (0 - -1) + 6/2. Let a(u) be the third derivative of -2/15*u**3 + 0*u + 0 - 1/300*u**5 - 2*u**2 + 1/30*u**p. Let a(r) = 0. What is r?
2
Let u(a) = -2*a**3 + 2*a - 4. Let z = 0 - -1. Let i(v) = -z - 2*v**3 - 2 + 2*v + 0*v. Let m(c) = 4*i(c) - 3*u(c). Determine y so that m(y) = 0.
-1, 0, 1
Let z = -5 + 12. Let r(f) be the second derivative of 2*f + 1/75*f**6 + 1/105*f**z + 0 + 0*f**2 + 0*f**3 - 1/50*f**5 - 1/30*f**4. Factor r(v).
2*v**2*(v - 1)*(v + 1)**2/5
Let q(b) = 2*b + 3 + 14 - 3. Let y be q(-6). What is v in 2/9*v**3 + 0 + 4/9*v**y + 2/9*v = 0?
-1, 0
Let k(w) = 5*w**3 + 2*w**2 + 12*w - 4. Let g(u) = -14*u**3 - 7*u**2 - 35*u + 11. Let v(s) = 4*g(s) + 11*k(s). Factor v(n).
-n*(n + 2)*(n + 4)
Let s be 10/(-15) - (-22)/6. Solve -2*k - k**3 + 0*k**3 - 3*k**2 + s*k - 3*k = 0.
-2, -1, 0
Let s = 1 + 1. Let c = s + 2. Factor 5*t**4 + 4*t**3 + 0*t**2 + 2*t**2 - 3*t**c.
2*t**2*(t + 1)**2
Suppose k = 8 - 8. Suppose -2/11*u**2 + k + 2/11*u = 0. What is u?
0, 1
Let m(r) be the first derivative of r**5/5 + r**4/3 - 2*r**3/9 - 2*r**2/3 - r/3 - 2. Factor m(s).
(s - 1)*(s + 1)**2*(3*s + 1)/3
Suppose -53 - 62 = -5*i. Let b = 25 - i. Factor -5/4*x**b + x + 1/4.
-(x - 1)*(5*x + 1)/4
Let x(c) = c**2 - 23*c + 45. Let m be x(21). Let v(r) be the first derivative of 0*r - 2/9*r**m + 2/15*r**5 + 2 + 1/3*r**2 - 1/6*r**4. Solve v(w) = 0.
-1, 0, 1
Let z(t) = 3*t**2 + t + 1. Let x be z(-1). Let s = 9/11 + -5/33. Factor 4/9*u**x - s*u**4 + 2/9 + 2/9*u**5 + 4/9*u**2 - 2/3*u.
2*(u - 1)**4*(u + 1)/9
Let t(l) be the third derivative of l**8/20160 - l**7/5040 + l**5/20 + 5*l**2. Let j(i) be the third derivative of t(i). Suppose j(k) = 0. Calculate k.
0, 1
Let j be (4/(-6))/(2/(-6)). Suppose 6*i - 5*i - 3 = 0. Factor i*y + 2*y**j + y + 0*y.
2*y*(y + 2)
Factor 5*v**5 - 25*v**3 + 11*v**4 - 6*v**4 + 15*v**2 - 4 + 4.
5*v**2*(v - 1)**2*(v + 3)
Factor 1/6*t + 0 + 0*t**2 - 1/6*t**3.
-t*(t - 1)*(t + 1)/6
Let b = 3 + 5. Let i(c) be the third derivative of 0*c**4 + 0*c**3 + 2*c**2 - 1/60*c**5 - 1/120*c**6 + 0*c + 1/210*c**7 + 1/336*c**b + 0. What is s in i(s) = 0?
-1, 0, 1
Let i(x) be the second derivative of -x**6/195 + x**5/65 - x**4/78 - 3*x. Factor i(t).
-2*t**2*(t - 1)**2/13
Let y(o) = 3*o**2 - 15*o. Let n(v) be the second derivative of -v**4/12 + v**3/6 - v**2/2 + 2*v. Let d(z) = -6*n(z) - y(z). Factor d(w).
3*(w + 1)*(w + 2)
Let f(d) = -11*d - 55. Let r be f(-5). Let c(a) be the second derivative of r - 1/2*a**3 + 4*a + 1/4*a**4 + 3/20*a**5 - 3/2*a**2. Suppose c(y) = 0. What is y?
-1, 1
Let g be (-7 - -4) + 48/15. Let a = 20 + -20. Factor a - g*h**2 - 2/5*h.
-h*(h + 2)/5
Let z(s) be the third derivative of -2*s**7/945 + s**6/108 - s**5/90 - s**4/108 + s**3/27 - s**2. Factor z(q).
-2*(q - 1)**3*(2*q + 1)/9
Let f be (-210)/(-63)*((-2)/(-4) + 0). Factor f*l**2 + 0 + 1/3*l**4 + 2/3*l + 4/3*l**3.
l*(l + 1)**2*(l + 2)/3
Let q(n) be the second derivative of 0*n**4 - 1/210*n**5 - 3/2*n**2 + 1/21*n**3 + 3*n + 0. Let x(r) be the first derivative of q(r). Factor x(m).
-2*(m - 1)*(m + 1)/7
Let c(t) = t**2 - 5*t + 4. Let f(p) = 3*p - 7. Let n be f(4). Let x be c(n). What is h in -1/2*h**5 + 1/2*h**3 + 0*h - 1/2*h**2 + 0 + 1/2*h**x = 0?
-1, 0, 1
Let r be -4 - ((-6)/(-2) + -3). Let v = 22/5 + r. Factor 0 - v*f + 2/5*f**2.
2*f*(f - 1)/5
Let a(p) be the third derivative of 2*p**2 - 1/18*p**3 + 1/180*p**5 + 0*p + 0 + 1/360*p**6 - 1/72*p**4. Factor a(r).
(r - 1)*(r + 1)**2/3
Factor -u**2 + 0 + 0*u + 1/2*u**4 + 1/2*u**3.
u**2*(u - 1)*(u + 2)/2
Let t(s) = s**3 - 9*s**2 + 8*s. Let r(g) = -g**3 + 8*g**2 - 7*g. Let l(y) = 6*r(y) + 5*t(y). Factor l(p).
-p*(p - 2)*(p - 1)
Let v(f) = -2*f**2 + 22*f - 10. Let n(k) = -2*k. Let o(g) = 10*n(g) + 2*v(g). Factor o(y).
-4*(y - 5)*(y - 1)
Let l = 8 + -4. Find h, given that -l*h + 5*h + 0*h**2 + 1 + h**3 - 2*h - h**2 = 0.
-1, 1
Let v(i) be the second derivative of i**7/14 - 3*i**6/10 + 9*i**5/20 - i**4/4 + 13*i. Suppose v(q) = 0. What is q?
0, 1
Solve 2*g**2 + 1 + 4*g**2 - 5 - 3*g**4 + 1 = 0.
-1, 1
Let k(j) be the first derivative of 0*j**3 + 6/7*j - 3 + 9/14*j**2 - 3/28*j**4. Factor k(m).
-3*(m - 2)*(m + 1)**2/7
Determine y so that 0 + 8/3*y - 4/3*y**4 - 20/3*y**2 + 16/3*y**3 = 0.
0, 1, 2
Let s(f) be the third derivative of f**8/40320 - f**6/1440 + f**5/20 - f**2. Let j(i) be the third derivative of s(i). Factor j(r).
(r - 1)*(r + 1)/2
Let o(v) be the second derivative of -2*v + 0*v**3 - 2/3*v**4 - 2/5*v**5 + 0*v**2 + 0 - 1/15*v**6. Suppose o(h) = 0. What is h?
-2, 0
Solve -2*v - 4 - 1/2*v**4 + 3*v**2 + 1/2*v**3 = 0.
-2, -1, 2
Let b(k) be the second derivative of -k**4/108 - k**3/27 + k**2/6 - 3*k. Factor b(c).
-(c - 1)*(c + 3)/9
Let u = -421/5 - -8842/105. Let a(n) be the third derivative of 1/735*n**7 - n**2 + 0 + 1/21*n**3 + 0*n + u*n**6 + 1/35*n**5 + 1/21*n**4. Factor a(k).
2*(k + 1)**4/7
Let y(b) be the first derivative of -b**4/4 + 3*b**2/2 + 2*b + 2. Suppose y(h) = 0. What is h?
-1, 2
Let d(r) = r**3 + r**2 + 4*r + 3. Let h be (-18)/12*8/(-6). Let v(k) = 0*k**2 + 0 - h*k**2 - k - 1 + k**2. Let c(t) = d(t) + 3*v(t). Factor c(i).
i*(i - 1)**2
Factor 30*l**3 + 144*l - 2*l**3 - 46*l**2 - 15 - 74*l**2 - 17.
4*(l - 2)**2*(7*l - 2)
Let x = -1 - -1. Let p be ((-4)/3)/(6 + (-1 - 15)). Factor x + 2/15*f**2 - p*f.
2*f*(f - 1)/15
Let d(y) = 5*y - 6*y**2 - y**2 + y + 5 + 9*y**2. Let j be d(-3). Determine s, given that -2/5*s**j - 12/5*s**3 - 8/5*s**4 - 2/5*s + 0 - 8/5*s**2 = 0.
-1, 0
Suppose 0*q + 4/11*q**3 + 0 + 2/11*q**5 + 0*q**2 - 6/11*q**4 = 0. Calculate q.
0, 1, 2
Factor -14*v**5 + 4*v**5 - 1 - 2*v**2 - 2*v**3 + 3*v + 3*v**4 + 0 + 9*v**5.
-(v - 1)**4*(v + 1)
Let b(c) = -c**3 + 4*c**2 + 5*c - 16. Let k be b(4). Let x(m) be the second derivative of 0 + 0*m**2 + 0*m**3 - 1/6*m**k - 3*m. Factor x(i).
-2*i**2
Let f be 2/48*9 + (-2)/6. Let k(g) be the t