y) be the first derivative of -1/30*y**4 - y + 4/15*y**3 + 1 - 4/5*y**2. Let d(b) be the first derivative of h(b). Factor d(l).
-2*(l - 2)**2/5
Factor -36/7*k - 12/7 + 3*k**2.
3*(k - 2)*(7*k + 2)/7
Let q(w) = 14*w**3 - 28*w**2 + 16*w. Let t(o) = o**4. Let p(g) = q(g) - 2*t(g). Factor p(z).
-2*z*(z - 4)*(z - 2)*(z - 1)
Let 0 + 4/9*k + 2/9*k**2 = 0. Calculate k.
-2, 0
Let h = 10 + -8. Let a(k) be the first derivative of -k + 5/2*k**h - k**3 - 1 + 4/5*k**5 - 5/4*k**4. Find c such that a(c) = 0.
-1, 1/4, 1
Suppose -7/3*p**5 - 4*p**4 + 0 - 4/3*p + 4*p**2 + 11/3*p**3 = 0. What is p?
-2, -1, 0, 2/7, 1
Suppose -7 = 4*y - 15. Let m(c) be the first derivative of -8/3*c - 8/3*c**2 - 3 - 2/3*c**5 + 4/3*c**4 + y*c**3. Let m(v) = 0. Calculate v.
-1, -2/5, 1, 2
Suppose 0 = -4*m + 16. Let x(r) be the second derivative of -1/18*r**m + 1/45*r**6 + 0*r**2 + r + 0*r**3 + 0 + 0*r**5. Factor x(p).
2*p**2*(p - 1)*(p + 1)/3
Factor 36*n**3 - 2*n**2 + 2*n**5 - 38*n**3 + 6*n**4 - 4*n**4.
2*n**2*(n - 1)*(n + 1)**2
Let c(j) be the third derivative of j**7/14 - j**6/24 - 3*j**2. Find l such that c(l) = 0.
0, 1/3
Let j(l) be the second derivative of 1/3*l**3 + l**2 - 1/6*l**4 - 1/10*l**5 + 0 - 3*l. Factor j(w).
-2*(w - 1)*(w + 1)**2
Let b(t) be the third derivative of t**5/30 + t**4/3 + 4*t**3/3 + 10*t**2. Factor b(i).
2*(i + 2)**2
Let t be (-63)/(-60) - (-7)/(-112)*4. Find i such that 8/5*i**2 + 0*i**3 - t*i**5 + 0 - 8/5*i**4 + 4/5*i = 0.
-1, 0, 1
Let z(j) be the first derivative of 5*j**6/6 - 3*j**5 + 15*j**4/4 - 5*j**3/3 + 7. Let z(v) = 0. Calculate v.
0, 1
Let t(g) be the first derivative of 3*g**5/40 - g**4/3 - g**3/3 - 7*g**2/2 - 1. Let h(z) be the second derivative of t(z). Factor h(x).
(x - 2)*(9*x + 2)/2
Let x = -41 - -46. Let u(r) be the third derivative of -1/150*r**6 + 1/30*r**4 + 1/150*r**x + 0*r - r**2 + 0 - 1/15*r**3. Let u(h) = 0. Calculate h.
-1, 1/2, 1
Let t(q) = -q**3 - 7*q**2 - 8*q - 3. Let o be t(-6). Let j be (o/(-12))/((-6)/4). Factor j*h**4 - h**3 + 0*h**2 - 1/2 + h.
(h - 1)**3*(h + 1)/2
Solve 8/15 + 2/15*z**2 + 8/15*z = 0.
-2
Solve 139*t**2 - t**4 - 6*t**3 - 136*t**2 - 2*t**4 + 6*t = 0 for t.
-2, -1, 0, 1
Let r(w) = w**2 - 2*w. Let z(p) = p. Let d(u) = -r(u) + 5*z(u). Suppose d(a) = 0. Calculate a.
0, 7
Factor 3/4*q**3 + 3/4*q**4 - 3/4*q**2 - 3/4*q**5 + 0 + 0*q.
-3*q**2*(q - 1)**2*(q + 1)/4
Let a(w) be the third derivative of 0 + 1/315*w**7 + 0*w + 0*w**4 + 1/90*w**6 + 0*w**3 + w**2 + 1/90*w**5. Find n, given that a(n) = 0.
-1, 0
Let b(c) = 5*c**2 + 2*c. Let o(k) = 5*k**2 + k. Let y(v) = -2*b(v) + 3*o(v). Factor y(r).
r*(5*r - 1)
Let q = -7 - -27. Let v be ((-12)/(-15))/(56/q). Let 6/7*h**4 + 0*h + 0 - v*h**5 + 2/7*h**2 - 6/7*h**3 = 0. What is h?
0, 1
Let x(i) be the first derivative of -i**4/42 - 4*i**3/21 - 4*i**2/7 + i + 1. Let j(c) be the first derivative of x(c). Factor j(a).
-2*(a + 2)**2/7
Let x(p) = -p**2 + 10*p + 5. Let b be x(10). Suppose -21 = -5*h + 3*c - 0*c, -4*c = h + b. Factor -1/5*k**4 + 0*k - 1/5 + 0*k**h + 2/5*k**2.
-(k - 1)**2*(k + 1)**2/5
Let d(p) be the third derivative of p**6/1140 - p**4/76 - 2*p**3/57 - 2*p**2. Find x such that d(x) = 0.
-1, 2
Let i be -1*(-6 + 51/9). Factor -1/3*v**3 - 2/3 + i*v + 2/3*v**2.
-(v - 2)*(v - 1)*(v + 1)/3
Let u be 0/((-1)/(2/(-6))). Let f(c) be the first derivative of -2/55*c**5 - 3 + 0*c**3 + 0*c**2 + 0*c**4 + u*c. Factor f(j).
-2*j**4/11
Let z(i) be the second derivative of i**7/14 - 3*i**6/10 + 9*i**5/20 - i**4/4 - 12*i. Factor z(s).
3*s**2*(s - 1)**3
Let z(b) be the second derivative of -2*b**7/21 + b**6/3 - 9*b**5/20 + 7*b**4/24 - b**3/12 - 8*b. Find d such that z(d) = 0.
0, 1/2, 1
Let t(m) be the first derivative of 0*m - 2/3*m**2 + 2/15*m**5 - 2/9*m**3 + 1/3*m**4 - 1. Solve t(l) = 0.
-2, -1, 0, 1
Let n(x) be the second derivative of x**6/90 + x**5/15 - 4*x + 2. Determine h so that n(h) = 0.
-4, 0
Let m(a) = 4*a**2 + 10*a - 8. Let l(k) = 7*k**2 + 19*k - 16. Let w(o) = 6*l(o) - 10*m(o). Factor w(j).
2*(j - 1)*(j + 8)
Let i(s) be the third derivative of -s**5/180 - s**4/4 - 9*s**3/2 + 21*s**2 + 2. Determine r, given that i(r) = 0.
-9
Find l, given that 45/7*l**3 + 375/7*l + 225/7*l**2 + 3/7*l**4 + 0 = 0.
-5, 0
Factor 0 - 2/9*w**2 - 2/9*w.
-2*w*(w + 1)/9
Let w(i) be the second derivative of 1/39*i**3 + 0 - i - 1/78*i**4 + 0*i**2. Suppose w(t) = 0. Calculate t.
0, 1
Let w = 95/3 - 31. What is q in -2/3*q**2 + 2/3 - 2/3*q**3 + w*q = 0?
-1, 1
Let h(s) be the first derivative of -s**2/2 + 11*s + 8. Let u be h(9). Factor 2/5*y**3 + 2/5*y**u + 0 - 2/5*y - 2/5*y**4.
-2*y*(y - 1)**2*(y + 1)/5
Let u(v) be the third derivative of v**9/7560 + v**8/1120 + v**7/420 + v**6/360 - v**4/8 + 4*v**2. Let g(h) be the second derivative of u(h). Factor g(k).
2*k*(k + 1)**3
Let s(p) be the first derivative of 2*p**5/65 - 2*p**3/13 - 2*p**2/13 - 3. Find a such that s(a) = 0.
-1, 0, 2
Suppose 2*l - 3 = -2*d + 7, 2*l - 3*d = 0. Factor 24/7*b**2 + 2*b**l + 6/7*b - 4/7.
2*(b + 1)**2*(7*b - 2)/7
Factor 3/4*y**3 + y**2 + 0 - y.
y*(y + 2)*(3*y - 2)/4
Let n(k) be the third derivative of k**7/120 - k**6/16 + 43*k**5/240 - k**4/4 + k**3/6 - 2*k**2. Determine g, given that n(g) = 0.
2/7, 1, 2
Let o(d) be the second derivative of 0 + 3/130*d**5 + 1/78*d**4 - 1/195*d**6 + 0*d**2 - 1/91*d**7 + 0*d**3 + 9*d. Determine r, given that o(r) = 0.
-1, -1/3, 0, 1
Let g(a) be the third derivative of a**6/120 + 3*a**5/20 + 3*a**2. Let r(j) = -2*j**3 - 22*j**2. Let n(w) = 12*g(w) + 5*r(w). Factor n(i).
2*i**2*(i - 1)
Factor 4*n + 4*n - 5 - 5*n**2 + 2*n.
-5*(n - 1)**2
Let v(s) = s**2 - 3. Let l = -7 - -2. Let i be 47/l - 4/(-10). Let r(o) = 5*o**2 - o - 13. Let p(f) = i*v(f) + 2*r(f). Find w such that p(w) = 0.
1
Let g(w) = -w**2 + 6*w + 4. Let p be g(6). Let u = -3 - -5. Factor x**3 + u*x + 0*x**3 + 2*x**2 - 2*x**p - 3*x**3.
-2*x*(x - 1)*(x + 1)**2
Solve 47*s**5 + 21*s - 765*s**3 - 62*s**5 + 140*s**4 + 325*s**3 - 320 + 59*s + 480*s**2 = 0 for s.
-2/3, 2, 4
Let y(l) = -2*l**3 + 7*l**2 + 5*l - 2. Let s be y(-1). Factor -1/5*v**3 + 1/5*v**5 + 0 + 0*v**s + 0*v**4 + 0*v.
v**3*(v - 1)*(v + 1)/5
Let j(g) = g - 1. Let o be j(2). Determine d, given that 3*d**2 + o + d**3 + 2*d**3 - 1 = 0.
-1, 0
Factor -4*d**5 - 6*d + 146*d**4 - 134*d**4 + 12*d**5 - 2*d**3 - 11*d**2 - 1.
(d - 1)*(d + 1)*(2*d + 1)**3
Let g(l) be the second derivative of l**7/70 - l**6/20 + l**4/4 - l**3/2 - 7*l**2/2 - 7*l. Let v(b) be the first derivative of g(b). Factor v(d).
3*(d - 1)**3*(d + 1)
Let c(i) be the second derivative of 2*i + 3/2*i**2 - 4/3*i**3 + 0 - 1/6*i**5 - i**4. Let q(z) be the first derivative of c(z). Find f such that q(f) = 0.
-2, -2/5
Let n = 15 - 11. Let t(z) be the first derivative of 0*z - 2/5*z**5 + 2/3*z**3 - 1/2*z**n - 1 + z**2. Factor t(j).
-2*j*(j - 1)*(j + 1)**2
Factor -5/4*h**4 + 0 - 5/4*h**5 + 0*h**2 + 5/2*h**3 + 0*h.
-5*h**3*(h - 1)*(h + 2)/4
Suppose 0 = -5*r - 3*o - 5, r - o + 5 = 6*r. Let p(q) be the first derivative of 1/2*q**2 + 1/20*q**4 + 2/5*q + 4/15*q**3 + r. Factor p(g).
(g + 1)**2*(g + 2)/5
Suppose r = -0*r + 2. Suppose -5*p = -4*o - 12, -5*p - 5 + 35 = 5*o. Factor -2*q + p*q + 5*q**2 + 0*q**r + q**2.
2*q*(3*q + 1)
Factor 1/4*m**2 + 1 - 5/4*m.
(m - 4)*(m - 1)/4
Let s(n) be the first derivative of -3*n**4/28 - n**3 - 33*n**2/14 - 15*n/7 - 9. Let s(q) = 0. What is q?
-5, -1
Suppose 15*o - 2*o - 26 = 0. Let y(k) be the first derivative of 15*k**3 - 15/4*k**4 - 12*k + 0*k**o - 9*k**5 + 9/2*k**6 - 3. Factor y(p).
3*(p - 1)**3*(3*p + 2)**2
Suppose 0*b + 72 = -4*b. Let o be -4*((-69)/b + -4). Factor 2/3*h**2 - o*h + 0.
2*h*(h - 1)/3
Factor -25/3*b + 0 - 11/3*b**3 + 1/3*b**4 + 35/3*b**2.
b*(b - 5)**2*(b - 1)/3
Let r(o) be the third derivative of -1/3*o**3 - 4*o**2 + 0 - 1/18*o**4 + 1/90*o**5 + 0*o. Find b, given that r(b) = 0.
-1, 3
Let s = -6 - -10. Determine t, given that -4/7*t + 4/7*t**3 + 2/7*t**s + 0*t**2 - 2/7 = 0.
-1, 1
Let k be (-2)/(-8) - (7 + (-27)/4). Factor k + 10/13*i**2 - 4/13*i.
2*i*(5*i - 2)/13
Let l(m) be the third derivative of m**11/997920 - m**10/453600 + m**5/15 + 7*m**2. Let y(t) be the third derivative of l(t). Solve y(x) = 0 for x.
0, 1
Let m(b) be the second derivative of 1/5*b**2 + 0 + 4*b - 1/50*b**5 - 1/30*b**4 + 1/15*b**3. Factor m(w).
-2*(w - 1)*(w + 1)**2/5
Let u(c) be the first derivative of 10 - c**2 + 0*c - 