 1)**2
Let z(f) be the second derivative of -f**5/30 + f**4/12 + 4*f**2 + 6*f. Let g(r) be the first derivative of z(r). Factor g(p).
-2*p*(p - 1)
Let c(y) be the third derivative of -5*y**2 - 1/336*y**8 + 0 + 0*y + 1/42*y**7 - 5/24*y**4 - 1/12*y**6 + 1/6*y**5 + 1/6*y**3. Factor c(p).
-(p - 1)**5
Factor -9/7*q**2 + 6/7 - 3/7*q.
-3*(q + 1)*(3*q - 2)/7
Let s be 8/44 + (-42)/(-11). Factor -2*p**s + p + 2*p - 3*p.
-2*p**4
Let i(a) be the third derivative of -a**9/6048 + a**8/1680 - a**7/1680 - 2*a**3/3 + a**2. Let o(k) be the first derivative of i(k). Factor o(l).
-l**3*(l - 1)**2/2
Let t(m) be the third derivative of -m**5/20 - m**4/8 - 8*m**2. Factor t(c).
-3*c*(c + 1)
Let a(t) be the third derivative of 1/48*t**4 - 1/120*t**5 + 0*t + 0 - 2*t**2 + 0*t**3. Factor a(c).
-c*(c - 1)/2
Factor 4*g**4 - 7*g**5 - 31*g + 5*g**5 + 6*g**3 + 31*g.
-2*g**3*(g - 3)*(g + 1)
Let o be 10 - 1/(-3 - -2). Let x(s) = -s + 13. Let a be x(o). Suppose 1/3*r**a + 1/3 + 2/3*r = 0. What is r?
-1
Let a be ((-99)/30)/(6/(-152)). Let u = 84 - a. Find t, given that 6/5*t - 4/5*t**2 - 2/5*t**5 - u - 4/5*t**3 + 6/5*t**4 = 0.
-1, 1
Suppose 3*f - 2*f = -2. Let u be -2*(-4)/(-48)*f. Find a, given that a**2 + 0*a - u*a**3 - 4/3 = 0.
-1, 2
Let x be ((-4)/14)/((-1)/7). Let i = -3/74 + 175/666. Suppose 0 - i*t**x + 0*t = 0. What is t?
0
Suppose 21*h = 22*h - 2. Factor -1/4*o**5 - 1/4*o**3 + 0*o**h + 0*o + 1/2*o**4 + 0.
-o**3*(o - 1)**2/4
Let n(b) be the second derivative of 2*b**6/15 - 4*b**5/5 + 4*b**4/3 + 15*b. Find f such that n(f) = 0.
0, 2
Let u(x) be the third derivative of x**8/16800 + x**7/3150 + x**6/1800 + x**4/12 - 2*x**2. Let h(t) be the second derivative of u(t). Let h(s) = 0. What is s?
-1, 0
Let u(p) be the first derivative of 3*p**5/20 + p**4/2 - p**3/2 - 3*p**2 - 4*p - 2. Let s(y) be the first derivative of u(y). Find w such that s(w) = 0.
-2, -1, 1
Suppose m - 2*m - 4 = 0. Let w(q) = 2*q**3 - 6*q**2 - 12*q - 4. Let o(b) = -b**3 + 7*b**2 + 13*b + 5. Let t(y) = m*o(y) - 3*w(y). Factor t(r).
-2*(r + 1)*(r + 2)**2
Let v(k) be the first derivative of 6*k**5/65 + 5*k**4/13 + 8*k**3/13 + 6*k**2/13 + 2*k/13 - 11. Factor v(l).
2*(l + 1)**3*(3*l + 1)/13
Let z(h) be the second derivative of -h**5/60 - 5*h**4/36 - h**3/6 + 3*h**2/2 - h. Determine r, given that z(r) = 0.
-3, 1
Suppose -6 = -3*z - 4*i, -2*z = -0*z - 4*i - 4. Factor -4*b**2 - 9*b**4 - 2*b**5 + 8*b**4 + z*b + 5*b**4.
-2*b*(b - 1)**3*(b + 1)
Find d, given that 6 - 4*d + 4*d - 3*d**2 - 3*d = 0.
-2, 1
Let q(n) be the first derivative of 0*n - 2/5*n**5 + 2 + 1/3*n**6 + 0*n**2 - 1/2*n**4 + 2/3*n**3. Suppose q(b) = 0. What is b?
-1, 0, 1
Let h(o) = 12*o**3 + 2*o**2 - 6*o - 6. Let u(n) = 6*n**3 + 2*n**2 - 5 + 5*n**3 - 8*n**3 + 8*n**3 - 5*n. Let c(d) = -5*h(d) + 6*u(d). Solve c(v) = 0.
-1/3, 0
Let c be -1*(-2)/(-8)*(-16)/10. Factor c*n**4 - 4/5*n + 2*n**2 - 8/5*n**3 + 0.
2*n*(n - 2)*(n - 1)**2/5
Let h be 4/(-14) + (-22)/(-28). Let p be (-6)/45 + (-36)/(-270). Suppose -1/2*o**2 + h + p*o = 0. Calculate o.
-1, 1
Let y(t) be the second derivative of -t**4/60 + t**3/30 - 10*t. Suppose y(u) = 0. What is u?
0, 1
Let t(j) be the first derivative of -j**6/30 - 2*j**5/25 - j**4/20 - 7. Factor t(s).
-s**3*(s + 1)**2/5
Suppose 0 = -0*i + 3*i. Determine t so that 0*t**3 + 2/5*t**4 + 1/5*t**5 - 2/5*t**2 + i - 1/5*t = 0.
-1, 0, 1
Factor -6/7*j**3 - 4/7*j + 0 + 10/7*j**2 - 2/7*j**4 + 2/7*j**5.
2*j*(j - 1)**3*(j + 2)/7
Let d = -2 + -8. Let f be 84/20 + 2/d. Factor -2/7*u + 4/7*u**2 + 2/7*u**5 + 0*u**3 - 4/7*u**f + 0.
2*u*(u - 1)**3*(u + 1)/7
Factor -28/3*s - 4/3*s**2 + 0.
-4*s*(s + 7)/3
Determine l, given that 4*l + 3 - l**2 + 0 + 3 - l**2 = 0.
-1, 3
Let u(z) = -z**2 - z. Let k(p) = p**2 + p. Let s(q) = q**2 + 5*q + 2. Let f be s(-4). Let m(r) = f*u(r) - k(r). Factor m(n).
n*(n + 1)
Let i(a) = -3*a**3 - 21*a**2 + 9*a + 15. Let c(p) = -p**3 - 5*p**2 + 2*p + 4. Let f(b) = 15*c(b) - 4*i(b). Factor f(g).
-3*g*(g - 2)*(g - 1)
Let n(y) = -y**2 + 4*y - 1. Let t be n(3). Factor -3*k**t + 10*k + 6*k - 4*k + 6*k**2 + 12.
3*(k + 2)**2
Let m(v) = -10*v**3 + 14*v**2 + 12*v. Let k(r) = r**3 - r**2 - r. Let o(w) = 12*k(w) + m(w). Suppose o(t) = 0. Calculate t.
-1, 0
Factor -2*s - 1/3*s**2 - 3.
-(s + 3)**2/3
Let i be (-4)/9*(-6)/48. Let d(u) be the third derivative of 0*u**5 - u**2 - 1/630*u**7 + i*u**3 + 1/180*u**6 - 1/36*u**4 + 0*u + 0. Factor d(z).
-(z - 1)**3*(z + 1)/3
Let i(v) be the first derivative of v**6/30 + 2*v**5/25 - v**4/10 - 4*v**3/15 + v**2/10 + 2*v/5 - 12. Let i(t) = 0. Calculate t.
-2, -1, 1
Let j(o) be the first derivative of o**5 - 15*o**4/4 + 10*o**2 - 3. Suppose j(p) = 0. Calculate p.
-1, 0, 2
Let v(b) = b**3 + 15*b**2 - 16*b + 2. Let c be v(-16). Let d(w) be the second derivative of 1/3*w**3 - c*w**2 - 3*w + 1/6*w**4 + 0. Factor d(q).
2*(q - 1)*(q + 2)
Let d(u) be the first derivative of 1/3*u**3 + 0*u**2 - 3 - u. Solve d(r) = 0 for r.
-1, 1
Find c, given that -8/15*c**4 - 16/5*c**2 + 2/5*c**5 - 52/15*c**3 - 2/15*c + 8/15 = 0.
-1, 1/3, 4
Let d(p) be the second derivative of p**7/1365 - p**6/780 - p**5/390 + p**4/156 - 5*p**2/2 - 3*p. Let a(r) be the first derivative of d(r). Factor a(w).
2*w*(w - 1)**2*(w + 1)/13
Suppose -20 = 5*q, 7 = 3*k + 2*q - 0. Factor 26*m**4 + 36*m**4 - 14*m**4 + 8*m**2 + 20*m**k + 36*m**3.
4*m**2*(m + 1)**2*(5*m + 2)
Let o(u) be the first derivative of -u**5/90 - u**4/54 + 3*u + 2. Let x(q) be the first derivative of o(q). Suppose x(i) = 0. What is i?
-1, 0
Let d be -1 - (-14)/6 - 12/(-18). Solve 0 - 1/4*v + 1/4*v**d = 0 for v.
0, 1
Let h(i) be the first derivative of i**4 + 16*i**3/3 + 8*i**2 - 3. Factor h(d).
4*d*(d + 2)**2
Let h = -3 - -6. Suppose -2 - 2*n + 3 + 3*n - h*n**2 - n**3 + 2*n**2 = 0. Calculate n.
-1, 1
Let r = -10 - -14. Suppose 2*z - r*p = -8 - 8, p + 5 = 5*z. Factor -1 - 2*g**5 + 3*g - 2*g + z*g**2 - g**4 - 2*g**3 + 3*g**5.
(g - 1)**3*(g + 1)**2
Factor 262*s + 30*s**2 + 9*s**2 - 118*s + 3*s**3 + 108.
3*(s + 1)*(s + 6)**2
Let u(a) be the first derivative of -a**5/10 - 3*a**4/8 - a**3/6 + 3*a**2/4 + a + 5. Factor u(t).
-(t - 1)*(t + 1)**2*(t + 2)/2
Let n be (-6)/33 + 251/1320. Let v(g) be the third derivative of 0 - 1/24*g**3 - 2*g**2 + 0*g + n*g**5 - 1/96*g**4. Factor v(h).
(h - 1)*(2*h + 1)/4
Suppose 2*y - 2*t + 1 + 9 = 0, 0 = -4*y - 4*t + 20. Factor y - 3/4*o**3 + 0*o**2 + 3/4*o**4 + 0*o + 3/2*o**5.
3*o**3*(o + 1)*(2*o - 1)/4
Let w(n) be the third derivative of n**5/20 - 3*n**4/8 - 4*n**3/3 + 10*n**2. Let c(k) = 3*k**2 - 8*k - 7. Let u(t) = 7*c(t) - 6*w(t). Factor u(d).
(d - 1)*(3*d + 1)
Suppose 0*m = -2*m + 6. Factor 8*q**5 - 2*q - 7*q**5 - 4*q**2 + m*q - 4*q**4 + 6*q**3.
q*(q - 1)**4
Let b(u) = u**3 - u**2 - u + 1. Let w(a) = 10*a**2 + a + 5 - a**3 - 25*a**2 - 6 + 16*a**2. Let g(q) = 4*b(q) + 3*w(q). Factor g(c).
(c - 1)**2*(c + 1)
Let f(j) be the second derivative of -j**8/1008 - j**7/630 - j**2/2 - j. Let n(t) be the first derivative of f(t). Suppose n(a) = 0. Calculate a.
-1, 0
Let m = -448/5 - -90. Suppose -6*b = -2*b - 8. Factor 18/5*h**2 + b*h + 4/5*h**4 + m + 14/5*h**3.
2*(h + 1)**3*(2*h + 1)/5
Factor 15/2*t**3 + 49/2*t - 63/2*t**2 - 1/2*t**4 + 0.
-t*(t - 7)**2*(t - 1)/2
Factor -24/5 - 18/5*p - 3/5*p**2.
-3*(p + 2)*(p + 4)/5
Let 605/3 + 5/3*i**2 + 110/3*i = 0. Calculate i.
-11
Let u(o) be the first derivative of o**8/2940 + o**7/1470 - o**6/210 - o**5/210 + o**4/21 - 8*o**3/3 - 3. Let n(s) be the third derivative of u(s). Factor n(v).
4*(v - 1)**2*(v + 1)*(v + 2)/7
Suppose -6/7*i**2 + 0 + 3/7*i**3 + 3/7*i = 0. Calculate i.
0, 1
Let n = 2/53 - -49/106. Factor 1/2*c - n*c**2 + 1.
-(c - 2)*(c + 1)/2
Let n = -9448873/44418609 + -140/11779. Let j = -1/419 - n. Factor 2/9*y**4 - 2/9*y**3 + 2/9*y + 0 - j*y**2.
2*y*(y - 1)**2*(y + 1)/9
Let p(n) be the second derivative of n**5/180 + n**4/18 + 2*n**3/9 - 3*n**2 + 5*n. Let a(c) be the first derivative of p(c). Suppose a(s) = 0. Calculate s.
-2
Let -58/3*v - 243/2*v**4 - 405/2*v**3 - 99*v**2 - 4/3 = 0. What is v?
-1, -2/9
Let r(g) = -4 - 10*g + 2*g**2 - 1 - 2*g**2 - g**2. Let z be r(-9). Solve -4*s - 3*s + s**2 + s - 3*s**2 - z = 0 for s.
-2, -1
Let s(l) be the first derivative of -2*l**3 + 4*l**2 - 2*l + 1. Factor s(i).
-2*(i - 1)*(3*i - 1)
Let g(b) = -b**2. Let d(w) = -6*w**2 + 6*w - 3. Let y(j) = -j + 1. Let v be y(4). Let u(c) = v*g(