first derivative of 3*g**5/25 - 9*g**4/20 + 3*g**3/5 - 3*g**2/10 + 31. Factor b(k).
3*k*(k - 1)**3/5
Let c(y) be the third derivative of -y**6/480 + y**5/240 + 5*y**4/96 + y**3/8 - 11*y**2. Factor c(w).
-(w - 3)*(w + 1)**2/4
Let n(b) = 20*b**4 + 5*b**3 + 5*b**2 + 20*b - 25. Let h(o) = -o**4 - o + 1. Let j(i) = -25*h(i) - n(i). Factor j(d).
5*d*(d - 1)**2*(d + 1)
Let p(u) be the first derivative of -u**4/22 + 4*u**3/33 + 11. Factor p(y).
-2*y**2*(y - 2)/11
Suppose 2*l = -4*x + 10, l + 30 = 5*x - 0*x. Suppose -6*t - 2*m + 6 = -2*t, 5 = -x*m. Factor 0*g + 1/2*g**t - 1/2.
(g - 1)*(g + 1)/2
Let i(c) be the second derivative of -1/24*c**4 - 1/6*c**3 + 4*c - 1/4*c**2 + 0. Suppose i(a) = 0. Calculate a.
-1
Let r(l) = -l - 1. Let j be r(-5). Let d(h) be the second derivative of 0 + 2*h + 0*h**3 + 0*h**2 - 1/42*h**j. Let d(f) = 0. Calculate f.
0
Let q be 2*((-27)/12)/(-3) + -1. Let x(m) be the first derivative of 1 - 1/3*m - q*m**2 - 1/12*m**4 - 1/3*m**3. Determine k, given that x(k) = 0.
-1
Let k be 72/42 + 4/14. Let m(l) be the third derivative of -1/240*l**5 + 0*l + 0 + 1/24*l**3 + 0*l**4 - 2*l**k. Find o such that m(o) = 0.
-1, 1
Let m(f) be the third derivative of -1/630*f**7 + 1/180*f**5 + 0*f**4 + 0*f + 0 - 8*f**2 + 0*f**3 + 1/360*f**6 - 1/1008*f**8. Factor m(s).
-s**2*(s - 1)*(s + 1)**2/3
Find m, given that 1/4*m**2 - 2*m + 4 = 0.
4
Let m(d) be the second derivative of -d**8/26880 + d**7/10080 - d**4/4 - 2*d. Let u(y) be the third derivative of m(y). Factor u(o).
-o**2*(o - 1)/4
Let g be ((-2)/(-21) - 0)*6. Find o, given that -16/7*o**3 + 0 - g*o + 6/7*o**4 + 2*o**2 = 0.
0, 2/3, 1
Factor 0 + 3/5*z**3 + 3/5*z - 6/5*z**2.
3*z*(z - 1)**2/5
Determine l, given that 1/4 - 1/8*l**2 - 1/8*l = 0.
-2, 1
Suppose v + g - 3 = 0, -2*v = -v + 4*g - 3. Suppose -8*m**4 - 6*m**v + 18*m**3 + 6*m - 15*m**2 + 5*m**4 = 0. Calculate m.
0, 1, 2
Let a(i) be the second derivative of 5*i**7/147 - i**6/15 - 3*i**5/70 + i**4/6 - 2*i**3/21 + 6*i. Determine u so that a(u) = 0.
-1, 0, 2/5, 1
Let a be (-22)/(-33) - 2*8/(-21). Determine i so that 18/7*i**2 - 4/7 - a*i**3 - 2*i**4 + 10/7*i = 0.
-1, 2/7, 1
Let c(f) be the second derivative of -1/10*f**6 + 1/6*f**4 + 0*f**2 + 0*f**3 - f - 1/20*f**5 + 0. Suppose c(z) = 0. Calculate z.
-1, 0, 2/3
Let u = -4 + 7. Suppose v - 4 + 11 = u*z, 0 = -z + 3*v - 3. Factor -6*r**3 + 0*r**3 + 5*r**2 - 2*r**5 + 6*r**4 - z*r**2.
-2*r**2*(r - 1)**3
Let 1/7*s**3 - 5/7*s + 4/7*s**2 + 0 = 0. What is s?
-5, 0, 1
Let o be -2 + 52/32*-98. Let c = 162 + o. Factor c*d**3 + 0 + 3/4*d**2 + 0*d.
3*d**2*(d + 1)/4
Let a(w) be the first derivative of -2/7*w**3 + 1/7*w**2 + 0*w - 3. Determine l, given that a(l) = 0.
0, 1/3
Factor -351*h**4 - 297*h**2 + 341*h**4 - 37*h**3 + 100*h + 87*h**2 - 59*h**3.
-2*h*(h + 5)**2*(5*h - 2)
Let q(t) be the first derivative of 0*t - 2/21*t**3 - 2/35*t**5 - 1/7*t**4 + 0*t**2 + 3. Suppose q(v) = 0. What is v?
-1, 0
Let m(t) be the third derivative of -5*t**8/1344 - t**7/105 - t**6/480 + t**5/120 - 2*t**2. Factor m(x).
-x**2*(x + 1)**2*(5*x - 2)/4
Let r(y) = -y**2 + y. Let v(b) be the second derivative of -b**4/4 + b**3 - 3*b**2/2 + 3*b. Let g(i) = -6*r(i) + v(i). Let g(s) = 0. Calculate s.
-1, 1
Let c(s) be the second derivative of 0*s**4 + 0 - 1/9*s**3 - 1/6*s**2 + 1/30*s**5 + 1/90*s**6 + 3*s. Determine q so that c(q) = 0.
-1, 1
Let c(w) = -w**2 - 5*w - 2. Let p be c(-4). Let j(g) be the first derivative of 2*g**3 + 2*g + 3 + 3*g**p + 1/2*g**4. What is r in j(r) = 0?
-1
Let u(v) be the first derivative of v**6/1260 + v**5/420 - v**3 + 2. Let k(o) be the third derivative of u(o). Determine y so that k(y) = 0.
-1, 0
Factor 8/7 + 578/7*y**2 + 136/7*y.
2*(17*y + 2)**2/7
Suppose 8*x**2 + 34*x - 43*x - 4*x**3 + 21*x = 0. What is x?
-1, 0, 3
Suppose 6*o = o + 10. Let t(s) be the first derivative of 6/5*s**5 - 4/3*s**6 + 0*s**3 + 1/2*s**4 + 0*s - o + 0*s**2. Solve t(d) = 0 for d.
-1/4, 0, 1
Let j(k) be the first derivative of k**6/300 - k**4/60 + k**2/2 - 2. Let u(i) be the second derivative of j(i). Factor u(r).
2*r*(r - 1)*(r + 1)/5
Let v(c) be the third derivative of -1/8*c**4 + 0*c + 0*c**3 - 1/70*c**7 - c**2 - 3/40*c**6 + 0 - 3/20*c**5. Factor v(x).
-3*x*(x + 1)**3
Factor -1/4*m**2 + 0 - 1/4*m.
-m*(m + 1)/4
Let q(g) be the third derivative of -g**5/180 + g**3/18 + 2*g**2. Factor q(u).
-(u - 1)*(u + 1)/3
Let n(d) be the third derivative of -d**8/70560 - d**7/8820 - d**6/2520 - d**5/20 - 4*d**2. Let f(g) be the third derivative of n(g). Solve f(h) = 0 for h.
-1
Factor 9*q**4 + 2*q**3 + 5*q**4 - 2*q - 2*q**2 - 12*q**4.
2*q*(q - 1)*(q + 1)**2
Let h(c) be the first derivative of -c**3 + 3*c**2/2 + 21. Factor h(o).
-3*o*(o - 1)
Suppose 12 = 5*v + a, -v - 3*a = -7 - 1. Factor 2*i**3 + i**2 + 0*i**3 + v*i - 5*i**2.
2*i*(i - 1)**2
Let b(g) = -g**3 - 35*g**2 - 42*g - 18. Let m(x) = -3*x**3 - 123*x**2 - 147*x - 63. Let f(j) = -18*b(j) + 5*m(j). Factor f(d).
3*(d + 1)**2*(d + 3)
Let b be 1*0/(0 - 1). Let o(v) be the third derivative of 0 + 2*v**2 + 1/12*v**3 - 1/24*v**4 + 1/120*v**5 + b*v. Solve o(u) = 0 for u.
1
Let j = -2173/3 - -735. Factor -2/3*u**5 - 6*u - 28/3*u**3 - j*u**2 - 4*u**4 - 4/3.
-2*(u + 1)**4*(u + 2)/3
Factor 8/5 - 8/5*x - 2/5*x**2 + 2/5*x**3.
2*(x - 2)*(x - 1)*(x + 2)/5
Factor 0*q - 25/4*q**3 + 0 + 45/4*q**5 - 5/4*q**2 - 15/4*q**4.
5*q**2*(q - 1)*(3*q + 1)**2/4
Find g such that 1/6*g**3 + 1/6 + 1/2*g + 1/2*g**2 = 0.
-1
Factor -59*z**2 + 24*z**2 - 3*z**3 - z**4 + 30*z**2 + 2*z + 7*z**3.
-z*(z - 2)*(z - 1)**2
Let g(u) be the first derivative of 4*u**6/9 - 22*u**5/15 + 5*u**4/6 + 4*u**3/9 - 3. Determine c so that g(c) = 0.
-1/4, 0, 1, 2
Let l be (-9)/(-6) - 5/(-10). Factor 0 + 2/7*v**l + 4/7*v.
2*v*(v + 2)/7
Let l(b) be the first derivative of 4*b**5/15 - 8*b**4/3 + 28*b**3/3 - 44*b**2/3 + 32*b/3 - 35. Let l(z) = 0. What is z?
1, 2, 4
Let b be (5/30)/(5/20). Determine c so that -b*c**2 + 2*c**3 - 2/3*c**5 - 4/3*c + 2/3*c**4 + 0 = 0.
-1, 0, 1, 2
Let m(o) be the third derivative of 2*o**7/105 + 2*o**6/15 + 4*o**5/15 + 9*o**2. What is j in m(j) = 0?
-2, 0
Let v = -817/7 - -117. Factor 0*o**2 + 0 + v*o - 2/7*o**3.
-2*o*(o - 1)*(o + 1)/7
Let n(k) be the second derivative of 1/9*k**3 + 1/10*k**5 - k + 1/6*k**4 + 0 + 1/45*k**6 + 0*k**2. Factor n(x).
2*x*(x + 1)**3/3
Suppose 0 = 2*n + 2*n - 12. Suppose -2*z = -0*z. Factor j**3 + 3*j**n + j**2 + z*j**2 + 0*j**3.
j**2*(4*j + 1)
Let u(p) = 2*p - 7. Let s be u(5). Factor -y + 3 - 3 - y + 2*y**s.
2*y*(y - 1)*(y + 1)
Let r(z) be the first derivative of 3*z**4/5 + 20*z**3/3 + 112*z**2/5 + 64*z/5 - 1. Factor r(w).
4*(w + 4)**2*(3*w + 1)/5
Suppose a = 5*j + 2*a - 15, 3*j + a = 11. Suppose -d + 4*n - 12 = 0, -3*d + 2*d = -n + 3. Factor d - 2/5*t**j + 0*t.
-2*t**2/5
Let q(w) be the third derivative of 1/240*w**5 + 0*w + 0 + 10*w**2 + 1/6*w**3 - 5/96*w**4. Determine l, given that q(l) = 0.
1, 4
Let b be (-5)/1 - 153/(-27). Suppose 0 + 4/3*h - b*h**2 = 0. What is h?
0, 2
Suppose 2*y + 5 = 21. Let p be (-4)/y*(-4)/1. Factor -1/4*s**p + 0 + 0*s.
-s**2/4
Let z = 4015/4 - 1003. Solve z*v**2 + 0 + 3/4*v = 0.
-1, 0
Let 0*h**2 - 2/5*h**4 + 0*h + 2/5*h**3 + 0 = 0. What is h?
0, 1
Suppose -2 = 5*k + 4*c - 0, 5*k = 3*c + 19. Let o(d) be the first derivative of k + 0*d + 0*d**2 - 2/21*d**3. Suppose o(b) = 0. What is b?
0
Let f(m) = -m**2 + 1. Let j(l) = 12*l**2 - 4*l - 5. Let w(a) = 8*a**2 - 3*a - 3. Let k(s) = -5*j(s) + 8*w(s). Let o(t) = 3*f(t) + k(t). Factor o(d).
(d - 2)**2
Let d(s) be the first derivative of s**4/4 + 2*s**3 + 6*s**2 + s + 3. Let l(i) be the first derivative of d(i). What is k in l(k) = 0?
-2
Let b(t) be the second derivative of t**4/8 + 5*t**3/4 - 9*t**2/2 - 8*t. Factor b(h).
3*(h - 1)*(h + 6)/2
Let b be ((2/(-28))/1)/(360/(-28)). Let r(f) be the third derivative of f**2 + 0 - 1/72*f**4 + b*f**5 + 0*f**3 + 0*f. Factor r(n).
n*(n - 1)/3
Let u = 5 + -5. Suppose 3*c = -u*c. Determine d, given that c*d - 9/5*d**3 + 3*d**4 + 0 - 6/5*d**2 = 0.
-2/5, 0, 1
Let z(q) be the third derivative of 1/6*q**4 + 1/9*q**3 + 0*q + 1/720*q**6 + 0 - 1/105*q**7 + 3*q**2 + 11/120*q**5. Determine g so that z(g) = 0.
-1, -2/3, -1/4, 2
Let v(y) be the first derivative of -y**3/5 + 3*y**2/5 - 1. Factor v(x).
-3*x*(x - 2)/5
Factor -2*n**3 + 0 + 2/3*n**4 + 2*n**2 - 2/3*n.
2*n*(n - 1)**3/3
Suppose -2 - 8/3*j**2 + 26