Suppose 5*c = -3*w - 25, -2*w + 4 + 1 = -c. Factor w*n - 4/13*n**3 + 2/13*n**4 + 2/13*n**2 + 0.
2*n**2*(n - 1)**2/13
What is p in 1/2*p**2 + 1/2*p + 0 = 0?
-1, 0
Let n be (-4)/8*6 + (1 - -4). Let 6/7*i**4 + 0 + 2/7*i**n + 6/7*i**3 + 0*i + 2/7*i**5 = 0. Calculate i.
-1, 0
Let n(m) be the third derivative of 1/180*m**6 + 0 - 1/90*m**5 - 6*m**2 + 0*m**4 + 0*m - 1/504*m**8 + 1/315*m**7 + 0*m**3. Factor n(z).
-2*z**2*(z - 1)**2*(z + 1)/3
Let m(b) = -3*b + 10. Let x(i) = i - 1. Let v(k) = -m(k) - 6*x(k). Let r be v(-3). Solve 0 + 1/5*l + 2/5*l**4 - 2/5*l**2 + 0*l**3 - 1/5*l**r = 0 for l.
-1, 0, 1
Let f(c) be the third derivative of c**6/1440 - c**4/96 + c**3/6 - c**2. Let m(k) be the first derivative of f(k). Factor m(a).
(a - 1)*(a + 1)/4
Suppose 0 - 2/3*m**3 - 10/3*m + 4*m**2 = 0. What is m?
0, 1, 5
Let r = -4 - 2. Let c(g) = 7*g**3 - 19*g**2 + 6*g - 7. Let w(t) = t**3 - 3*t**2 + t - 1. Let z(i) = r*c(i) + 39*w(i). Factor z(b).
-3*(b - 1)*(b + 1)**2
Let y(m) be the second derivative of -m**4/32 + 3*m**3/8 - 15*m**2/16 + 14*m - 2. Determine t, given that y(t) = 0.
1, 5
Factor -10/7*v - 2/7*v**2 + 2/7*v**3 - 6/7.
2*(v - 3)*(v + 1)**2/7
Let h(o) be the first derivative of 0*o - 2/9*o**3 + 1 + 1/18*o**6 - 1/6*o**2 + 2/15*o**5 + 0*o**4. Let h(t) = 0. Calculate t.
-1, 0, 1
Suppose 5*d + 0*b + 2*b - 16 = 0, -4*d + b = -18. Let z(l) be the second derivative of 4*l + 0 + 1/4*l**3 + 1/24*l**d + 0*l**2. Factor z(j).
j*(j + 3)/2
Suppose -3 = -2*z + 33. Let f = z - 13. Find q, given that -f*q**4 + q**3 + q**4 + 3*q**4 = 0.
0, 1
Let i(k) be the first derivative of -2*k**7/315 + k**6/120 + k**5/180 + k**2/2 + 1. Let z(t) be the second derivative of i(t). Factor z(n).
-n**2*(n - 1)*(4*n + 1)/3
Let j(f) be the second derivative of 1/3*f**3 - 2*f**2 - 3*f + 1/6*f**4 + 0. Find u such that j(u) = 0.
-2, 1
Let k = 133/345 + -6/115. Suppose 40/3*m**4 + 16/3*m**5 - 5/3*m**2 + 25/3*m**3 + k - 5/3*m = 0. What is m?
-1, 1/4
Let x(y) be the third derivative of y**2 + 1/6*y**4 + 0 + 1/10*y**5 + 1/210*y**7 + 1/30*y**6 + 0*y + 1/6*y**3. Factor x(j).
(j + 1)**4
Let f(a) be the first derivative of -3*a**4/8 + 9*a**2/4 - 3*a - 14. Factor f(n).
-3*(n - 1)**2*(n + 2)/2
Determine a, given that 5/2*a - 3/4*a**4 + 0*a**2 + 3/4 - 5/2*a**3 = 0.
-3, -1, -1/3, 1
Suppose -11*p - 6*p + 34 = 0. Let x(u) be the second derivative of -5*u + 0*u**p + 1/6*u**4 + 0 + 1/3*u**3. Factor x(v).
2*v*(v + 1)
Let a(z) = z**3 + 3*z**2 + 2. Let m be a(-3). Suppose m*g = -g. Suppose 4*q**3 + 2*q**2 - 2*q + 2 + g*q**3 + 15*q**5 - 14*q**5 - 3*q - 4*q**4 = 0. What is q?
-1, 1, 2
Find p, given that 34*p**2 - 8/3 - 175/3*p**4 + 4/3*p - 85/3*p**3 = 0.
-1, -2/7, 2/5
Let m(v) = -v + 4*v**3 - 5*v**3 - v**3 + 4*v**2 + 0*v**3 + 2. Let a(h) = h**3 - h**2 - 1. Let r(o) = -3*a(o) - m(o). Solve r(c) = 0 for c.
-1, 1
Suppose 2*m = 3 + 5. Find t such that t**2 + 6*t**2 + t**3 - 2*t - 6*t**3 + 3*t**m - 3*t**3 = 0.
0, 2/3, 1
Let k(v) be the third derivative of -5*v**8/336 + 2*v**7/21 - v**6/24 - 5*v**5/6 + 5*v**4/6 + 20*v**3/3 + 24*v**2. Suppose k(q) = 0. Calculate q.
-1, 2
Let w = -1 + 3. Let p = 6 - w. Find s such that 5 - 8*s**4 + 6*s**3 - 2*s + p*s**2 - 8*s**5 - 5 = 0.
-1, 0, 1/2
Let d(b) be the second derivative of b**6/720 + b**5/120 + 2*b**3/3 - 3*b. Let k(a) be the second derivative of d(a). Factor k(w).
w*(w + 2)/2
Let b(y) be the second derivative of y**5/5 - 5*y**4/3 - 26*y**3/3 - 14*y**2 - 16*y. Solve b(z) = 0.
-1, 7
Let q(o) be the second derivative of -4*o + 0*o**2 - 1/30*o**5 + 1/360*o**6 + 1/2*o**3 + 1/6*o**4 + 0. Let s(n) be the second derivative of q(n). Factor s(y).
(y - 2)**2
Factor 4*v**2 + 8 - 16*v**3 + 4*v**2 - v + 7*v + 14*v - 4*v**5 - 16*v**4.
-4*(v - 1)*(v + 1)**3*(v + 2)
Let c(m) be the first derivative of 3*m**4/16 + 33*m**3/4 + 1089*m**2/8 + 3993*m/4 + 20. Factor c(k).
3*(k + 11)**3/4
Let d = 19 + -15. Factor 5*f**3 - 13*f**3 + d*f + 5*f**5 - f**5.
4*f*(f - 1)**2*(f + 1)**2
Let g(y) be the third derivative of -y**9/30240 - y**8/3360 - y**7/840 - y**6/360 + y**5/20 - 5*y**2. Let n(z) be the third derivative of g(z). Factor n(t).
-2*(t + 1)**3
Let b = -39 - -39. Let x(a) be the second derivative of b + 2*a + 1/2*a**3 + a**2 + 1/12*a**4. Factor x(r).
(r + 1)*(r + 2)
Suppose 4*f + 0*f + 15 = -5*v, -f = -2*v - 6. Solve -9/5*j**2 + 3/5*j**3 + 12/5 + f*j = 0.
-1, 2
Suppose 0 = -3*b + 2*b + 1. Let d be (-4)/2 - (b - 5). Let 0*u**2 + u + u**2 - 1 + 0*u**d - u**3 = 0. What is u?
-1, 1
Let h(w) be the third derivative of w**5/75 + w**4/30 + 8*w**2. Factor h(y).
4*y*(y + 1)/5
Suppose n + 2*x + 22 = 5*n, -4*x = n - 1. Find r, given that 21*r**4 - 2*r**3 - 23*r**4 + r**n + 3*r**3 = 0.
0, 1
Factor -2/11*h**2 + 0 + 18/11*h.
-2*h*(h - 9)/11
Let h be -2 + 1 + -8 + 0. Let v be (-4)/(-6)*h/(-24). Let 1/2 - 1/4*g - v*g**2 = 0. Calculate g.
-2, 1
Suppose -4*h = -30 + 10. Let u be (-2)/h - (-36)/15. Factor -3*k**2 + 2*k**2 - k**u.
-2*k**2
Factor w - 14*w**2 - 4*w - 12*w**3 + 10*w**2 - 11*w**2.
-3*w*(w + 1)*(4*w + 1)
Let q be (-3 + 63/15)*5. Factor 2*z + 0 - q - 3*z**2 + 6*z + z**2.
-2*(z - 3)*(z - 1)
Let b(h) be the first derivative of -h**4/16 + h**3/12 + h**2/4 - 10. Solve b(g) = 0 for g.
-1, 0, 2
Let y(j) = 2*j**2 - 10*j - 3. Let r be y(5). Let s be 0/((r - -1) + 0). Let 0 + 0*q**2 + s*q - 2/3*q**5 + 0*q**4 + 2/3*q**3 = 0. Calculate q.
-1, 0, 1
Let a be 3 - ((-1 - -2)*1)/1. Let v(i) be the second derivative of i + 1/70*i**5 - 1/7*i**a + 0 + 1/42*i**4 - 1/21*i**3. Find x, given that v(x) = 0.
-1, 1
Find g such that 9*g**3 + 10*g**4 - 12*g - 32*g**4 + 9*g**4 + 10*g**4 = 0.
-1, 0, 2
Let i(t) = -9*t**2 - 12*t - 3. Let r(m) = -8*m**2 - 12*m - 4. Let a(l) = 4*i(l) - 5*r(l). Suppose a(y) = 0. Calculate y.
-2, -1
Let y = 245/3 + -81. Suppose 0*v - 1/3*v**5 + 1/3*v**4 + y*v**3 + 0 + 0*v**2 = 0. Calculate v.
-1, 0, 2
Let v = -26 + 6. Let h be (v/(-15))/((-42)/(-9)). Factor -2/7 - 4/7*w - h*w**2.
-2*(w + 1)**2/7
Determine h, given that 6*h**2 + 4*h**2 + 0*h**2 + 3*h**3 - h**2 = 0.
-3, 0
Suppose j = -4*m + 1, -5 = -2*m + j - 6*j. Factor 3/5*n**2 + 1/5*n**4 + 1/5*n + m + 3/5*n**3.
n*(n + 1)**3/5
Solve -2/17 - 2/17*d**2 + 4/17*d = 0.
1
Let r(t) be the third derivative of -1/60*t**6 + 1/6*t**4 + 0*t + 2*t**2 + 0 - 2/3*t**3 - 1/210*t**7 + 1/20*t**5. Factor r(u).
-(u - 1)**2*(u + 2)**2
Let p be 147/27 + -3 - 2. Let b(s) be the second derivative of 0 - 1/3*s**2 + 2/15*s**5 - 1/3*s**4 + p*s**3 + s - 1/45*s**6. Find i, given that b(i) = 0.
1
Let p = -29 - -33. Let k be (-34)/(-8) + 1/(-4). Suppose -q**5 - q**2 + 4*q**3 + q**4 - 3*q**3 + 4*q**k - 4*q**p = 0. What is q?
-1, 0, 1
Let p(o) be the third derivative of 8/3*o**3 + 0*o - 2*o**2 - 2/3*o**4 + 1/15*o**5 + 0. Let p(d) = 0. What is d?
2
Let p(j) be the third derivative of -j**6/600 + j**4/120 + 36*j**2. Solve p(x) = 0 for x.
-1, 0, 1
Let s = 2835 - 1899. Let l be 90/s + (-4)/(-26). Factor 0 - 1/4*k**5 + l*k**2 - 1/4*k**4 + 0*k + 1/4*k**3.
-k**2*(k - 1)*(k + 1)**2/4
Let q(l) be the first derivative of l**4 - 8*l**3/3 + 2*l**2 - 54. Factor q(u).
4*u*(u - 1)**2
Let c = -17/30 + 9/10. Suppose c*h + 1/6 + 1/6*h**2 = 0. What is h?
-1
Let d = -123/2 + 62. Solve 0*x**2 - 1/2*x + d*x**3 + 0 = 0 for x.
-1, 0, 1
Let w = 0 + 2. Find m, given that 1 + 2*m - 2*m**w + 4*m**2 - m**2 = 0.
-1
Let i(k) be the third derivative of k**8/112 - 3*k**7/35 + 13*k**6/40 - 3*k**5/5 + k**4/2 - 14*k**2. Suppose i(v) = 0. Calculate v.
0, 1, 2
Let w(t) be the first derivative of -t**5/25 - 3*t**4/20 - 2*t**3/15 - 6. Factor w(q).
-q**2*(q + 1)*(q + 2)/5
Let q(s) be the first derivative of 4*s**5/5 - 5*s**4 + 12*s**3 - 14*s**2 + 8*s - 5. Determine z, given that q(z) = 0.
1, 2
Find z such that -32/9*z**3 + 0 - 14/9*z**4 - 4/9*z - 22/9*z**2 = 0.
-1, -2/7, 0
Let x(v) be the second derivative of -v**5/70 - v**4/7 - 4*v**3/7 - 8*v**2/7 + 18*v. Factor x(n).
-2*(n + 2)**3/7
Solve 10/11 - 12/11*b - 2/11*b**4 - 8/11*b**2 + 12/11*b**3 = 0 for b.
-1, 1, 5
Let f(i) be the first derivative of 1/3*i**6 - 5 + 0*i**4 - 4/5*i**5 - i**2 + 0*i + 4/3*i**3. Let f(d) = 0. What is d?
-1, 0, 1
Let p(j) be the third derivative of 0*j + 8*j**2 - 1/780*j**6 + 0 + 0*j**4 + 0*j**3 - 1/1365*j**7 + 0*j**5. Factor p(c).
-2*c**3*(c + 1)/13
Let m(t) be the first derivative of -t**5/20 - t**4/16 + 21. Factor m(g).
-g**3*(g + 1)/4
Factor -a + 10*a 