35 + d**6/420 - 8*d**2. Factor l(g).
2*g**3*(g + 1)**2/7
Let q = -10 + 15. Suppose -2*z = -q*z. Factor -1/2*d**4 - 1/4*d**3 + 0*d + 0*d**2 - 1/4*d**5 + z.
-d**3*(d + 1)**2/4
Suppose -11 = 4*w - 11. Let t(j) be the second derivative of w*j**2 + 0 + j - 1/48*j**4 + 1/12*j**3. Factor t(l).
-l*(l - 2)/4
Let d(b) = -5*b**2 + 5*b + 28. Let m(p) = -20*p**2 + 20*p + 111. Let w(q) = 9*d(q) - 2*m(q). Factor w(g).
-5*(g - 3)*(g + 2)
Find u, given that 1/3*u**2 + 2/3 - u = 0.
1, 2
Let p(t) be the second derivative of -t + 0 - 1/6*t**2 + 1/18*t**4 - 1/126*t**7 + 1/30*t**5 - 1/90*t**6 - 1/18*t**3. Let p(f) = 0. What is f?
-1, 1
Let a(z) = z + 7. Let m be a(0). Suppose 2*b = 3*x - 6, -5*b = -x - x - m. Factor 3*q + 8*q**2 + 4*q + 2 + 4*q**b - q**3.
(q + 1)**2*(3*q + 2)
Let q(z) be the second derivative of z**4/18 - z**3/9 - 2*z**2/3 + 3*z. Factor q(m).
2*(m - 2)*(m + 1)/3
Let f(v) be the third derivative of -v**6/900 + v**5/150 + v**4/180 - v**3/15 - 19*v**2. Solve f(s) = 0.
-1, 1, 3
Let r = -15 - -17. Find s, given that 2/3*s + 4/3 - 2/3*s**r = 0.
-1, 2
Let o(l) = 3*l**3 + 28*l**2 + 39*l - 42. Let k(q) = -q**3 - 9*q**2 - 13*q + 14. Let u(n) = -17*k(n) - 6*o(n). Let j be u(-14). Factor j + 6/7*y + 4/7*y**2.
2*y*(2*y + 3)/7
Suppose -2*n - 59 - 7 = 0. Let k be (n/(-27) - 1)*9. Solve -9/2*g**2 + k*g + 0*g**3 - 1/4 + 27/4*g**4 = 0.
-1, 1/3
Let i(p) = 2*p + 7. Let k be i(6). Factor 4*s**2 - k + 19 - 4*s.
4*s*(s - 1)
Let x = 10 + -2. Suppose -2*h = -0 - x. Let -2*t**4 + 3*t**4 + t**h + 3*t**5 - 11*t**5 = 0. What is t?
0, 1/4
Let g(o) be the first derivative of -3*o**5/20 + 3*o**4/16 + o**3/2 + 45. What is b in g(b) = 0?
-1, 0, 2
Let w(l) be the first derivative of -5*l**4/4 - 10*l**3/3 - 5*l**2/2 + 8. Solve w(k) = 0 for k.
-1, 0
Suppose 2*f - 14 = -14. Suppose -4/3*a**3 + 0 + f*a**4 + 0*a**2 + 2/3*a + 2/3*a**5 = 0. Calculate a.
-1, 0, 1
Let z(p) = 6*p**3 - 26*p**2 + 50*p - 14. Let d(t) = -t**3 + 5*t**2 - 10*t + 3. Let h(c) = 16*d(c) + 3*z(c). Factor h(b).
2*(b - 1)**2*(b + 3)
Factor -l + l - 5*l + 4 + 2*l**2 - l.
2*(l - 2)*(l - 1)
What is v in 50/11*v**4 + 4/11*v - 12/11*v**3 + 0 - 28/11*v**5 - 14/11*v**2 = 0?
-1/2, 0, 2/7, 1
Let j be (-813)/(-672) - (0 - 0). Let h = j - -7/32. Factor h*w**2 + 2*w + 4/7.
2*(w + 1)*(5*w + 2)/7
Factor -4*u + 0*u + 9*u - 5*u**2 + 0*u**2.
-5*u*(u - 1)
Let u(t) be the third derivative of -3*t**2 + 0*t**5 + 0 + 0*t - 1/120*t**6 + 0*t**3 + 0*t**4. Factor u(o).
-o**3
Let q = -102 + 308/3. Factor 2/3*h**2 - q*h**4 + 0 + 2/3*h - 2/3*h**3.
-2*h*(h - 1)*(h + 1)**2/3
Factor -5*r**2 + 2*r**2 + 10*r**2 + 2*r.
r*(7*r + 2)
Let g(w) be the second derivative of -2/15*w**5 - 1/18*w**4 + w + 1/15*w**6 + 0 + 0*w**2 + 2/9*w**3. Suppose g(o) = 0. What is o?
-2/3, 0, 1
Let b(d) be the second derivative of -d**5/20 + d**4/3 - 2*d**3/3 + 2*d. Suppose b(p) = 0. Calculate p.
0, 2
Let p(k) be the second derivative of k + 3/20*k**5 - 1/2*k**3 + 1/12*k**4 - 1/2*k**2 + 0. Determine t, given that p(t) = 0.
-1, -1/3, 1
Suppose -3*r = -0*r - 2*o - 13, -2*r + 8 = -o. Let i = -3 + r. Factor -3*j**3 + 2*j**4 + 0*j**4 + i*j**4 + 5*j**3.
2*j**3*(j + 1)
Let f(z) be the third derivative of -z**5/240 - 6*z**2 - 4. Factor f(s).
-s**2/4
Solve 4*d**2 + 40*d - 35*d - 19*d**2 = 0 for d.
0, 1/3
Let q be ((-20)/(-30))/(10/(-66)). Let a = q - -23/5. Factor -1/5 + a*j**2 - 1/5*j + 1/5*j**3.
(j - 1)*(j + 1)**2/5
Let a(g) = g - 3. Let o be a(5). Suppose 3*y - 3*y - y**2 + 0*y**o = 0. Calculate y.
0
Let o = -27 - 1. Let c be ((-2)/6)/(o/48). Factor 0*q**3 + 0 + c*q**2 + 2/7*q**5 - 4/7*q**4 - 2/7*q.
2*q*(q - 1)**3*(q + 1)/7
Let p(y) = -y**3 + 32*y**2 - 61*y - 3. Let b(w) = w**3 + w - 1. Let c(z) = -3*b(z) + p(z). Factor c(g).
-4*g*(g - 4)**2
Let d(c) = -c**3 - 3*c**2 + 10*c + 2. Let v be d(-5). Let s be v*((-15)/(-21))/5. Suppose s*f + 2/7*f**2 - 4/7 = 0. Calculate f.
-2, 1
Let r(t) be the first derivative of -t**4/2 + 2*t**3 + t**2 - 6*t - 6. Suppose r(i) = 0. What is i?
-1, 1, 3
Let x = 13 + -11. Factor i**2 - 2*i**x + 0*i + 2*i + 3*i**2.
2*i*(i + 1)
Let y be (-1)/(2 + (-11)/5). Factor -y + 5 + 6*f**4 - 3*f**5.
-3*f**4*(f - 2)
Let i(k) = -k**3 - 3*k**2 + 2*k + 2. Let p be i(-4). Let x = p - 8. Factor 0 - 4/7*v**3 + 0*v**x + 2/7*v**5 + 0*v**4 + 2/7*v.
2*v*(v - 1)**2*(v + 1)**2/7
Let o(v) be the second derivative of 0*v**3 + 1/30*v**6 + 0*v**2 + 0 + 1/10*v**5 + 1/12*v**4 - 2*v. Factor o(a).
a**2*(a + 1)**2
Suppose 0 = 2*s + 5*c - 20, -4 = -3*s + s - c. Suppose -2*i - 3 + 11 = s. Factor 2*j**4 + 4 - 2*j**5 - 2*j + 4 - 4*j**2 + i*j**3 - 6.
-2*(j - 1)**3*(j + 1)**2
Let o(x) = 13*x**2 + 4*x + 10. Let f(g) = -28*g**2 - 7*g - 19. Let w(r) = 6*f(r) + 13*o(r). Let w(l) = 0. What is l?
-8, -2
Let f(m) be the third derivative of -m**5/30 + m**4/4 - 23*m**2. Let f(u) = 0. What is u?
0, 3
Let g(l) = -l**3 + 5*l**2 + 3. Let s be g(5). Suppose -3*r + 22 - 2 = 5*c, -r + 3*c = 12. Factor 1/3*v**4 + 1/3 + 0*v**s - 2/3*v**2 + r*v.
(v - 1)**2*(v + 1)**2/3
Let r(a) be the third derivative of a**7/105 - a**5/30 - 8*a**2. Let r(c) = 0. Calculate c.
-1, 0, 1
Let f = -4 - -8. Let i(w) be the third derivative of 1/180*w**6 + 0*w**5 + 0*w**3 - 1/36*w**f + 0 + 0*w - w**2. Factor i(d).
2*d*(d - 1)*(d + 1)/3
Let x = -32 + 1345/42. Let s(j) be the second derivative of 0*j**2 + j + 1/21*j**3 + x*j**4 + 0. Solve s(h) = 0.
-1, 0
Let b(g) be the second derivative of -g**6/60 + g**5/10 - g**4/4 + g**3/3 + 3*g**2/2 + 2*g. Let v(c) be the first derivative of b(c). Factor v(a).
-2*(a - 1)**3
Let m = 0 + 2. Suppose i - 4 = -0*i. Factor -3 + 5 - v - 5*v**m + i*v**2.
-(v - 1)*(v + 2)
Let a = 28 + -22. Let j(s) be the second derivative of 1/15*s**a + 0*s**2 + 0*s**3 + 2*s + 0*s**5 - 1/6*s**4 + 0. Factor j(i).
2*i**2*(i - 1)*(i + 1)
Let v be 32/(-112) - (-2)/7. Let d(a) be the first derivative of 1/15*a**5 - 1/12*a**4 + v*a + 0*a**2 - 1/9*a**3 + 1/18*a**6 + 1. Let d(g) = 0. Calculate g.
-1, 0, 1
Let c be 20/75*5/(-58). Let a = c - -95/348. Suppose -5/4*p**2 + 9/4 - a*p**3 - 3/4*p = 0. Calculate p.
-3, 1
Let 27/8*h**2 - 75/8 + 45/8*h + 3/8*h**3 = 0. What is h?
-5, 1
Let k(n) be the first derivative of -n**6/1980 - n**5/220 - n**4/66 - n**3 - 2. Let g(c) be the third derivative of k(c). Factor g(o).
-2*(o + 1)*(o + 2)/11
Let i(a) be the third derivative of a**7/2100 + a**6/900 - a**5/300 - a**4/60 - 5*a**3/6 - 8*a**2. Let p(v) be the first derivative of i(v). Solve p(u) = 0.
-1, 1
Let k(g) be the first derivative of g**6/24 + 3*g**5/5 + 23*g**4/8 + 5*g**3 + 25*g**2/8 - 39. Factor k(p).
p*(p + 1)**2*(p + 5)**2/4
Let t(d) be the second derivative of d**4/12 + d**3/6 + 2*d. Factor t(o).
o*(o + 1)
Let y(o) be the third derivative of o**8/896 - o**7/112 + 9*o**6/320 - 7*o**5/160 + o**4/32 - 2*o**2 - 1. Let y(r) = 0. What is r?
0, 1, 2
Let u = 1007/2 + -499. What is c in -9/2*c**3 + 3 - u*c - 12*c**2 = 0?
-2, -1, 1/3
Factor -3/2*b**3 + 6*b + 0 + 3/4*b**4 - 3*b**2.
3*b*(b - 2)**2*(b + 2)/4
Let j be ((-2)/6*0)/(-2). Suppose 3*a - 5 - 1 = j. Factor -3*n**4 - 2*n**5 + 2*n**3 - n**4 + 2*n**4 + 2*n**a.
-2*n**2*(n - 1)*(n + 1)**2
Let a(g) be the third derivative of -g**6/24 - g**5/4 - 5*g**4/12 + 14*g**2. Solve a(v) = 0 for v.
-2, -1, 0
Factor -7 + 25*f + 3*f**2 - 17 - 8*f**2 + 4.
-5*(f - 4)*(f - 1)
Let t(z) be the first derivative of -z**4/12 - z**3/9 - 1. Factor t(r).
-r**2*(r + 1)/3
Let a be (4/(-6))/((-6)/27). Find s such that s**3 - 2*s**a - 1 + 1 - s**4 = 0.
-1, 0
Let l = 7004/5845 + 2/1169. Let x(a) = a**2 - 4*a + 2. Let r be x(4). Factor 4/5*q**r + l*q + 2/5.
2*(q + 1)*(2*q + 1)/5
Suppose 4*r + 5 = 17. Determine s so that 0*s + 0 - 2/5*s**2 + 2/5*s**r = 0.
0, 1
Let a = -7 - -9. Suppose s**2 + 4 + 0*s + 3*s - s + a*s = 0. Calculate s.
-2
Suppose -8/15*b**2 - 2/5*b - 2/15*b**3 + 0 = 0. Calculate b.
-3, -1, 0
Let -52 + 3*q**2 - 60 + 20*q + 12 - 4*q**2 = 0. Calculate q.
10
Let l(y) be the first derivative of y**7/210 + y**6/24 + 3*y**5/20 + 7*y**4/24 + y**3/3 + y**2/2 - 1. Let j(s) be the second derivative of l(s). Factor j(d).
(d + 1)**3*(d + 2)
Suppose -4*i - 26 = -2. Let q(a) = -a**4 + a**3 - 5*a**2 - 7*a. Let p(r) = r**4 - r**3 + 4*r**2 + 6*r. Let t(c) = i*p(c) - 5*q(c). Factor t(u).
-u*(u - 1)**2*(u + 1)
Let k(y) be the third derivative of -1/54*y**4 + 0*y + 0*y**3 - 8*y**2 + 1/270*y**6 + 0 - 7/270*y**5 + 1/135*y**7. Suppose k(i)