*3 - 16*a**4 = 0.
-1, -1/4, 1
Let b(y) be the second derivative of 0*y**2 - 1/9*y**4 - 1/90*y**5 - 1/3*y**3 + 0 + 3*y. Factor b(j).
-2*j*(j + 3)**2/9
Let h(j) be the first derivative of 2*j**3/21 - 3*j**2/7 + 4*j/7 - 39. Factor h(u).
2*(u - 2)*(u - 1)/7
Let j be (-2)/1 + (30 - -2). Suppose -j = -5*z + 4*c, 4*z - c - 7 = 6. Factor -3/2*o**2 - z + 3*o + 1/4*o**3.
(o - 2)**3/4
Suppose 0 = -m + 3*m + 2*f + 96, -3*m - f = 142. Let p = -140/3 - m. Factor -p*u**5 + 2/3*u**3 - 1/3*u**4 + 2/3*u**2 - 1/3*u - 1/3.
-(u - 1)**2*(u + 1)**3/3
Let i = -1 + 4. Let w = -251/4 - -63. Factor -1/4*v**2 - w*v**i + 1/4 + 1/4*v.
-(v - 1)*(v + 1)**2/4
Let j(y) be the second derivative of y**5/70 - 2*y**4/21 + 4*y**3/21 - 3*y. Let j(b) = 0. What is b?
0, 2
Let d(o) be the first derivative of o**7/420 + o**6/240 - o**5/120 - o**4/48 + 7*o**2/2 + 7. Let h(l) be the second derivative of d(l). Factor h(k).
k*(k - 1)*(k + 1)**2/2
Let b(r) = r**3 + r**2 + r - 2. Let s be b(0). Let i be 2/(-6)*18/s. Determine u, given that -2/7*u + 2/7*u**4 + 0 + 6/7*u**2 - 6/7*u**i = 0.
0, 1
Let c(w) = w**2 - 10*w + 4. Let p be c(10). Suppose 0 = -5*h - 5*j, p*h - 2*j + 3 = 15. Factor -5*s**2 + s**2 + h*s**2.
-2*s**2
Factor 0 - 4*r - 7*r**2 - 3/2*r**3.
-r*(r + 4)*(3*r + 2)/2
Suppose 4*a + 4*x - 4 = 0, -a + 2*x + 11 = x. Suppose 0 = -k + a - 2. Find g, given that 0 + 1/3*g**3 + 0*g + 1/3*g**k + 0*g**2 = 0.
-1, 0
Let x = 147 - 145. Let f(n) be the first derivative of -1/6*n**4 + 1/3*n**2 - 2/3*n - x + 2/9*n**3. Factor f(k).
-2*(k - 1)**2*(k + 1)/3
Let i be ((-24)/48)/(2/(-8)). Let -8/3*g**i + 0 - 2/3*g**5 - 2/3*g - 8/3*g**4 - 4*g**3 = 0. What is g?
-1, 0
Let m = -4 + 1. Let s(x) = 2*x**5 - 6*x**3 + 7*x**2 + 3*x. Let k(w) = w**2 + w. Let p(t) = m*k(t) + s(t). Suppose p(b) = 0. What is b?
-2, 0, 1
Let w = -1/114 + -25/38. Let l = w - -1. Let -l*v**2 + 0*v + 1/3 = 0. What is v?
-1, 1
Determine c, given that -14*c**4 + 9*c**4 - 4*c**5 - c**5 = 0.
-1, 0
Suppose -2*u - u**2 + 0*u**2 + 2*u + 2*u = 0. Calculate u.
0, 2
Let l(x) be the first derivative of -2*x**3/33 - 4*x**2/11 + 10*x/11 + 6. Solve l(g) = 0 for g.
-5, 1
What is d in -10*d**2 - 5*d**2 + 3*d**2 - d - 3*d = 0?
-1/3, 0
Let q be 1 - ((-3 - -1) + 0). Factor 8*z**4 - 11*z - 3*z**q - z - 17*z**4 + 24*z**2 + 0*z**3.
-3*z*(z - 1)*(z + 2)*(3*z - 2)
Let -5 + 62*z**2 + 65*z**2 - 132*z**2 + 10*z = 0. What is z?
1
Let a(w) be the second derivative of w**5/4 - 5*w**4/6 + 5*w**3/6 - 4*w. Find c such that a(c) = 0.
0, 1
Let d be 4/(-28) - 2/(-2). Let w be 2/(-6) - 14/(-6). Factor d*a + 4/7 + 2/7*a**w.
2*(a + 1)*(a + 2)/7
Let m be 3/(-2) - (-55)/10. Let q be (-40)/12 + m + 0. Factor -1/3*v + 0 - 1/3*v**3 - q*v**2.
-v*(v + 1)**2/3
Let i(j) be the third derivative of -j**7/840 - j**6/60 - 3*j**5/40 + j**4/24 - 3*j**2. Let r(m) be the second derivative of i(m). Factor r(l).
-3*(l + 1)*(l + 3)
Let z = 71/40 - 11/8. Factor -z*o + 0 - 1/5*o**2.
-o*(o + 2)/5
Let u(z) = -z**3 - 3*z**2 + 3*z + 3. Let b be u(-4). Suppose -3*w = -b - 5. Factor -4*a + 0*a**4 + 8*a**2 + 30*a**3 + 8*a**w + 10*a - 4 + 24*a**2.
2*(a + 1)**2*(a + 2)*(4*a - 1)
Let p(s) be the first derivative of -3/8*s**4 + 0*s - 4 - 1/2*s**3 - 1/4*s**2 - 1/10*s**5. Factor p(h).
-h*(h + 1)**3/2
Let b(s) = -4*s**5 + 8*s**3 - 12*s - 4. Let h(u) = u**4 + u**3 - u**2 + u + 1. Let k(r) = b(r) + 4*h(r). Find y, given that k(y) = 0.
-1, 0, 1, 2
Factor 0*u**2 + 3*u**3 - 2*u**3 - 3*u**2 + 2*u**2.
u**2*(u - 1)
Suppose 0*i = i - 4. Solve -47*o**i + 2*o - 58*o**3 + 2*o + 2*o**2 - 9*o**4 = 0 for o.
-1, -2/7, 0, 1/4
Let s be (2/(-4))/(3/(-18)). Let 8*n**2 + 6*n**s - 10*n**3 - 3*n - n = 0. Calculate n.
0, 1
Let v(u) be the second derivative of 0 - 1/12*u**2 + 2*u + 1/18*u**3 + 7/72*u**4 + 1/30*u**5. Factor v(g).
(g + 1)**2*(4*g - 1)/6
Let y(a) = a**3 - 8*a**2 + a - 5. Let u be y(8). Let m = u + -1. Suppose -2*g**m - 4*g**3 - g**5 + 0*g**3 + 5*g**3 - g**4 + 3*g**2 = 0. Calculate g.
-1, 0, 1
Suppose -8/5*v**3 + 64/5*v - 12*v**2 - 16/5 + 4*v**4 = 0. Calculate v.
-2, 2/5, 1
Let g(v) be the first derivative of -v**6/300 - v**5/75 - v**4/60 + 5*v**2/2 - 2. Let m(l) be the second derivative of g(l). Suppose m(r) = 0. Calculate r.
-1, 0
Let k(d) = -8*d**4 - 29*d**3 - 16*d**2 - 5*d. Let x(i) = 12*i**4 + 44*i**3 + 24*i**2 + 8*i. Let g(j) = 8*k(j) + 5*x(j). Factor g(p).
-4*p**2*(p + 1)*(p + 2)
Let w(b) be the first derivative of 3*b**7/280 - b**6/24 - b**5/10 + b**4/2 - 4*b**3/3 + 2. Let o(x) be the third derivative of w(x). Factor o(z).
3*(z - 2)*(z + 1)*(3*z - 2)
Let v(r) be the first derivative of -1/11*r**2 - 6 + 0*r + 1/22*r**4 + 0*r**3. Solve v(l) = 0 for l.
-1, 0, 1
Let j = -1828/9 + 204. Let u(p) = 12*p + 3. Let d be u(0). Factor j*c**2 - 10/9*c - 2/9*c**d + 4/9.
-2*(c - 2)*(c - 1)**2/9
Suppose -2*h + 2 = 2*c, 4 = 2*h + c + 1. Let y be -1 - 4/(-8)*h. Solve 0*f + 2/7*f**4 + 0*f**2 + y + 6*f**5 - 4/7*f**3 = 0 for f.
-1/3, 0, 2/7
Factor -4/5*z**3 + 4/5*z - 2/5*z**2 + 0 + 2/5*z**4.
2*z*(z - 2)*(z - 1)*(z + 1)/5
Let k(n) = -n + 1. Let f be k(1). Let u(a) = -a**2 + 7*a + 1. Let i be u(4). What is c in f - 3*c**2 - i*c**2 - 1 + 8*c = 0?
1/4
What is h in -8*h**2 + 6*h**4 + 2 + 20/3*h - 28/3*h**3 + 8/3*h**5 = 0?
-3, -1, -1/4, 1
Let v(h) be the second derivative of h**7/105 - h**6/30 + h**5/30 + h**2 + 2*h. Let d(z) be the first derivative of v(z). Factor d(g).
2*g**2*(g - 1)**2
Let k(n) be the second derivative of -n**4/3 + 2*n**2 + 5*n. Factor k(g).
-4*(g - 1)*(g + 1)
Suppose j + 3*j = 20, -3*s + 17 = j. Suppose 20 = s*u - 2*t - 2, -4*u = 3*t + 3. What is i in -2*i**3 - i**5 - 2*i**u + 3*i**3 + 2*i**5 = 0?
-1, 0, 1
Let r(t) = -5*t + 18. Let i be r(-8). Solve -12 + i - 24*c + 2 + 3*c**2 = 0 for c.
4
Let k(l) be the third derivative of 1/540*l**6 - 1/27*l**3 + 1/36*l**4 - 1/90*l**5 + 0*l + 0 - 4*l**2. Factor k(p).
2*(p - 1)**3/9
Let s(h) = -7*h**2 + 7*h - 5. Let a be (30/(-4))/(7/(-14)). Let z(d) = 3*d**2 - 3*d + 2. Let l(j) = a*z(j) + 6*s(j). Factor l(b).
3*b*(b - 1)
Let a(g) be the second derivative of -g**5/5 + g**4 - 2*g**3 + 2*g**2 + 11*g. Factor a(b).
-4*(b - 1)**3
Suppose -6*c + c = -30. Let i(n) be the third derivative of 0*n + 1/60*n**5 + 0 + 1/60*n**c + 0*n**4 - 2*n**2 + 1/210*n**7 + 0*n**3. Factor i(h).
h**2*(h + 1)**2
Suppose -5*v = 10, -v - v - 4 = -a. Let q = 2 + a. Factor -2*w + 0*w + q*w**2 + 4*w.
2*w*(w + 1)
Let g be ((-1)/(-4))/(-1 + 2). Let j be -2 + 9/2 - 2. Factor 0 + g*o**3 + 1/4*o - j*o**2.
o*(o - 1)**2/4
Suppose 3*c + 2*c = 0. Let h(f) be the second derivative of 1/42*f**4 + f - 1/7*f**2 + c - 1/21*f**3 + 1/70*f**5. Factor h(y).
2*(y - 1)*(y + 1)**2/7
Suppose 2*m + 12 = 5*n - 0*n, -m + 3*n = 8. Suppose -3 - 4*w - 4*w + 2*w**2 + 5*w + m = 0. What is w?
1/2, 1
Find a, given that 3 + 3*a**3 - 3 + a**3 - 4*a = 0.
-1, 0, 1
Let o be (-2)/(-8)*4 + 2. Suppose 0 = -r - w - o*w + 18, -4*r + 4*w - 8 = 0. Determine c, given that 8*c + 6*c**r + 8/3 = 0.
-2/3
Let m(k) be the second derivative of k**7/70 + 3*k**6/50 + 3*k**5/50 - k**4/10 - 3*k**3/10 - 3*k**2/10 + k. Factor m(l).
3*(l - 1)*(l + 1)**4/5
Factor 1/2*f**2 + 0*f + 1/4*f**3 - 3/4*f**4 + 0.
-f**2*(f - 1)*(3*f + 2)/4
Let i(j) be the second derivative of -j**4/18 - 2*j**3/9 - j**2/3 - 8*j. Suppose i(o) = 0. Calculate o.
-1
Let r(j) be the first derivative of -4*j**5/5 - 4*j**4 - 8*j**3/3 + 8*j**2 + 12*j + 22. Factor r(t).
-4*(t - 1)*(t + 1)**2*(t + 3)
Let c be (-3)/(81/(-24))*2/8. Determine s, given that -2/3*s**5 + 4/3*s**3 + 4/9*s**2 - 2/3*s - 2/9 - c*s**4 = 0.
-1, -1/3, 1
Let w(z) be the third derivative of 2*z**2 + 0*z - 1/75*z**5 + 0 + 0*z**3 + 1/60*z**4. Determine s, given that w(s) = 0.
0, 1/2
Let u(c) be the third derivative of -c**9/20160 - c**4/4 - 5*c**2. Let f(m) be the second derivative of u(m). Find q, given that f(q) = 0.
0
Let d(f) be the third derivative of -f**5/120 - f**4/8 - 3*f**3/4 + 7*f**2. Factor d(v).
-(v + 3)**2/2
Let y(l) be the first derivative of -32*l**6/3 + 16*l**5 + 5*l**4 - 25*l**3/3 - 5*l**2 - l - 11. Factor y(v).
-(v - 1)**2*(4*v + 1)**3
Let u(z) be the first derivative of -2*z**5/25 + 2*z**4/5 - 2*z**3/3 + 2*z**2/5 + 6. Factor u(q).
-2*q*(q - 2)*(q - 1)**2/5
Factor 0*h - 1/8*h**5 - 3/8*h**4 + 0 - 3/8*h**3 - 1/8*h**2.
-h**2*(h + 1)**3/8
Let m(w) = -w**3 - 35*w**2 - 18*w + 8. Let n(q) = q**3 + 23*q**2 + 12*q - 5. Let l(g) = -5*m