l*(l - 1)*(l + 1)*(l + 2)/3
Let l = 14 - 12. Let r(d) be the first derivative of -1/4*d**2 - 1/10*d**5 + 0*d + 1/8*d**4 + l + 1/6*d**3. What is m in r(m) = 0?
-1, 0, 1
Determine s so that -4*s**3 + 181*s + 0*s**3 + 2*s**3 - 179*s = 0.
-1, 0, 1
Suppose h - 1 = m + 1, -m - 11 = -4*h. Factor 0 - 1/2*j**h + j**4 - 1/2*j**5 + 0*j + 0*j**2.
-j**3*(j - 1)**2/2
Suppose 0 = -4*s - 3*s + s. Let r(x) be the second derivative of -1/60*x**6 - 3/40*x**5 + 1/2*x**2 + 1/4*x**3 + s - 1/24*x**4 - x. Factor r(f).
-(f - 1)*(f + 1)**2*(f + 2)/2
Find v such that -21*v**2 + 4*v**2 - 8*v - 11*v**2 = 0.
-2/7, 0
Let g = 10 + -10. Suppose -2*k - 2*k = g. Factor 0 - 2/5*t**4 + k*t**2 + 2/5*t**3 + 0*t.
-2*t**3*(t - 1)/5
Factor -8/7 - w + 1/7*w**2.
(w - 8)*(w + 1)/7
Let r(f) be the first derivative of 2*f**5/15 - f**4/3 - 2*f**3/9 + 2*f**2/3 + 11. Factor r(c).
2*c*(c - 2)*(c - 1)*(c + 1)/3
Let c be -2 + 0 - (2 - -2). Let m(g) = g**2 + g. Let t(f) = 8*f**2 + 4*f - 4. Let w(u) = c*m(u) + t(u). Let w(a) = 0. What is a?
-1, 2
Let x(v) = 20*v**4 + 12*v**3 - 8*v**2 - 24. Let j(c) = c**4 + c**3 - 1. Let m(i) = 24*j(i) - x(i). Factor m(d).
4*d**2*(d + 1)*(d + 2)
Let l(j) = 7*j**2 + 3*j - 6. Let y(c) = -5*c**2 + 6*c - 6. Let f(z) = 9*z**2 - 11*z + 11. Let q(k) = -6*f(k) - 11*y(k). Let t(x) = -l(x) + 4*q(x). Factor t(o).
-3*(o - 1)*(o + 2)
Let d(f) = -40*f**2 - 64*f - 10. Let i(s) be the first derivative of 8*s**3/3 + 13*s**2/2 + 2*s - 1. Let c(q) = 3*d(q) + 14*i(q). Solve c(b) = 0.
-1, -1/4
Let g(m) be the third derivative of 0*m**6 + 1/30*m**3 + 0*m - 1/150*m**5 + 4*m**2 + 0 + 1/1050*m**7 + 0*m**4. Solve g(n) = 0 for n.
-1, 1
Let n(g) be the third derivative of g**2 + 1/60*g**5 + 1/2*g**3 + 0*g - 1/120*g**6 + 0 + 5/24*g**4. Determine l, given that n(l) = 0.
-1, 3
Let v = 4 + 1. Suppose v*s - 21 = -6. Factor -2/9 + 2/9*x**s + 2/3*x - 2/3*x**2.
2*(x - 1)**3/9
Suppose 2*a + 10 = 2*x, -3*a - 15 = 2*x - 7*x. Find b, given that x*b**2 - 6/7*b + 2/7*b**3 - 4/7 = 0.
-1, 2
Let x = -6/79 - -176/237. Let 4/3*y - 2 + x*y**2 = 0. Calculate y.
-3, 1
Suppose 95 + 19 = 38*r. Determine n so that 0 + 1/2*n**2 + 3/2*n**r + 1/2*n**5 + 0*n + 3/2*n**4 = 0.
-1, 0
Let d(r) be the second derivative of r**5/160 - r**4/12 - 19*r**3/48 - 5*r**2/8 + 5*r. Suppose d(n) = 0. What is n?
-1, 10
Suppose 23*v = 25*v - 4. Let u(c) be the third derivative of 0*c + 2/15*c**5 + 0*c**3 + 0 - c**v + 1/3*c**4 + 1/60*c**6. Suppose u(s) = 0. Calculate s.
-2, 0
Let y(c) be the first derivative of c**7/14 - 9*c**5/20 - c**4/2 - 6*c - 4. Let n(j) be the first derivative of y(j). Solve n(p) = 0.
-1, 0, 2
Let p be (124/8)/((-63)/(-6)). Let w = p + -8/7. Determine y so that 0 + w*y**3 + 2/3*y**2 + 0*y = 0.
-2, 0
Let i(a) be the second derivative of -a**6/6 + 9*a**5/4 - 35*a**4/4 + 95*a**3/6 - 15*a**2 + 24*a. Suppose i(j) = 0. Calculate j.
1, 6
Let m(y) be the third derivative of y**5/8 - 9*y**4/16 - y**3/2 - 15*y**2. Factor m(c).
3*(c - 2)*(5*c + 1)/2
Let u(a) be the second derivative of -a**7/18 + a**6/10 - a**5/30 - 9*a. Factor u(k).
-k**3*(k - 1)*(7*k - 2)/3
Let t = -10 - -17. Let k = -3 + t. Suppose -k*i**2 + i**2 + 3*i**2 - 2*i**2 = 0. Calculate i.
0
Let j(y) = 9*y**2 + 42*y - 12. Let s be j(-5). Suppose 5*o = -5, u + 0*o = -2*o - 2. Solve 0*f + u + 2/7*f**s + 2/7*f**2 = 0.
-1, 0
Let g(y) be the first derivative of -1/96*y**4 + 1/3*y**3 - 1 + 0*y + 1/1440*y**6 + 0*y**2 + 0*y**5. Let j(v) be the third derivative of g(v). Factor j(x).
(x - 1)*(x + 1)/4
Factor -83*o**4 + 28*o**5 + 128*o**3 - 91*o - 49*o**4 - 101*o - 64 + 160*o**2.
4*(o - 2)**3*(o + 1)*(7*o + 2)
Suppose 2*z**5 - 17 + z - z**4 + 16 - 2*z**3 - z**5 + 2*z**2 = 0. Calculate z.
-1, 1
Let w(j) be the third derivative of -j**6/120 - j**5/30 + 34*j**2. Find k, given that w(k) = 0.
-2, 0
Let f be 2*((-4)/(-10))/((-18)/(-15)). Let o(b) be the first derivative of -1 + 1/4*b + f*b**3 - 3/4*b**2. Solve o(g) = 0 for g.
1/4, 1/2
Suppose 4*w + 9 - 9 = 0. Let s(l) be the second derivative of w + 0*l**3 + 0*l**2 - 7/20*l**5 + 1/6*l**4 + 2*l + 1/10*l**6. Factor s(j).
j**2*(j - 2)*(3*j - 1)
Let p(m) be the first derivative of m**2/2 - 2*m - 1. Let f be p(4). Let -16 - 2*n**3 + 0*n - 7*n - 9*n - 8*n - 12*n**f = 0. What is n?
-2
Let k be 0/(4*4/16). Let v(u) be the third derivative of -1/630*u**7 + 2*u**2 + 0*u**4 - 1/180*u**6 + 0 + k*u**3 - 1/180*u**5 + 0*u. Factor v(s).
-s**2*(s + 1)**2/3
Factor 49*q - 80 - 11*q - 5*q**2 + 2*q.
-5*(q - 4)**2
Suppose -k + 5*k = 5*m + 5, m - 13 = -2*k. Solve -1/3 - h**2 + h + 1/3*h**m = 0 for h.
1
Let x be ((-2)/(-40))/(28/16). Let l = x - -67/105. Determine w, given that l*w + 0 + 1/3*w**2 = 0.
-2, 0
Let s(u) be the second derivative of -2*u**6/15 - 3*u**5/5 - u**4/3 + 2*u**3 + 4*u**2 + 3*u. Determine x, given that s(x) = 0.
-2, -1, 1
Factor 1/2*h**3 - 1/2*h + 1/2 - 1/2*h**2.
(h - 1)**2*(h + 1)/2
Let m(r) be the second derivative of -r**6/2700 + r**5/225 - r**4/60 - r**3/3 - 3*r. Let u(n) be the second derivative of m(n). Let u(p) = 0. Calculate p.
1, 3
Let r(f) be the second derivative of f**6/540 - f**5/180 - f**4/18 - f**3/3 - 2*f. Let y(t) be the second derivative of r(t). Suppose y(s) = 0. What is s?
-1, 2
Suppose -4*p = -3*q - 6, -q - 3*q + 4*p = 4. Let b = -1247/4 + 312. Factor 1/2*i - b*i**3 + 0 - 1/4*i**q.
-i*(i - 1)*(i + 2)/4
Let g(t) = 17*t**2 - 21*t + 6. Let m(s) = 222*s**2 - 273*s + 78. Let n(v) = 27*g(v) - 2*m(v). Factor n(k).
3*(k - 1)*(5*k - 2)
Let t(n) be the first derivative of -2*n + 0*n**2 + 3 + 1/60*n**4 + 1/30*n**3. Let o(b) be the first derivative of t(b). Let o(d) = 0. Calculate d.
-1, 0
Let v(c) = -c**3 + 3*c**2. Let w be v(2). Factor -5*p**2 + w*p**2 + 8*p**3 - p**4 - 6*p**3.
-p**2*(p - 1)**2
Let d(u) = -u**4 + u - 1. Let y(j) = -3*j**5 + 12*j**4 - 2*j**3 - 6*j**2 + 4. Let m(w) = -5*d(w) - y(w). Factor m(k).
(k - 1)**3*(k + 1)*(3*k - 1)
Let t(w) be the second derivative of -w**9/16632 + w**8/4620 - w**7/4620 + w**3/2 - 3*w. Let l(u) be the second derivative of t(u). What is y in l(y) = 0?
0, 1
Suppose -5*h - 36 = -11. Let a(l) = l**2 + 7*l + 10. Let m be a(h). Determine b so that -1/4*b + 1/2*b**3 + 0*b**4 + 0 - 1/4*b**5 + m*b**2 = 0.
-1, 0, 1
Let a be (-1)/3*(4 - 13). Let l be 21/28*25/a. Find s such that -4 - 24*s - l*s**4 - 46*s**2 - 30*s**3 = 0.
-2, -2/5
Let t(z) = -z**5 + z**3 + z**2 - z - 1. Let m(n) = n**5 - 2*n**4 - n**3 - n**2 + 3*n + 3. Let w(i) = -2*m(i) - 6*t(i). Suppose w(r) = 0. Calculate r.
-1, 0, 1
Suppose u + 10 = -u. Let h(w) = 4*w**2 - 3*w - 2. Let f(v) = 4*v**2 - 2*v - 2. Let q(a) = u*f(a) + 4*h(a). Factor q(o).
-2*(o + 1)*(2*o - 1)
Let b(k) = 25*k**3 - 9*k**2 + 3*k + 4. Let o be b(4). Let a = -2887/2 + o. Factor -12*d - a*d**2 - 9/2*d**5 - 39/2*d**4 - 2 - 67/2*d**3.
-(d + 1)**3*(3*d + 2)**2/2
Let d(i) = -i**2 - 2*i + 4. Let k be d(0). Let v(y) be the second derivative of 4/7*y**2 - 4/21*y**3 + 1/42*y**k + 2*y + 0. Suppose v(p) = 0. Calculate p.
2
Suppose -20/9*f + 2/9*f**2 + 16/9 + 2/9*f**3 = 0. What is f?
-4, 1, 2
Let y(l) = l**4 + l**3 + l**2 + l + 1. Let t(m) = -5*m**4 + 10*m**3 + 2*m**2 - 17*m - 5. Let b(k) = 5*t(k) + 5*y(k). Determine z, given that b(z) = 0.
-1, -1/4, 2
Let w(r) be the third derivative of r**7/840 - r**6/120 + r**5/40 - r**4/24 + r**3/24 + 2*r**2 - 12. Factor w(g).
(g - 1)**4/4
Let q(x) be the first derivative of x**6/1620 - x**5/270 + x**4/108 + x**3 + 3. Let z(p) be the third derivative of q(p). Find t, given that z(t) = 0.
1
Let a be 1 - (6/(-2) + 1). Suppose 6 = a*w, 3*f - f - w = 6. Let f + 8*h**2 - h**3 + 10*h + 6*h**3 - 3*h**3 = 0. What is h?
-2, -1
Factor 10/7*x**2 + 2*x**3 + 0 + 6/7*x**4 + 2/7*x.
2*x*(x + 1)**2*(3*x + 1)/7
Solve 2/7*y + 2/7*y**4 - 6/7*y**2 - 2/7*y**3 + 4/7 = 0.
-1, 1, 2
Let x(m) = m**3 + 4*m**2 - 7*m - 6. Let s be x(-6). Let l = 110/3 + s. Determine r, given that l - 2/3*r**2 + 2/3*r**3 - 2/3*r = 0.
-1, 1
Let d(a) = a**2 + a + 1. Let c(r) = 6*r + 9. Let p(l) = c(l) - 3*d(l). Factor p(t).
-3*(t - 2)*(t + 1)
Let v(d) = -d**2. Let s(r) = 6*r**2 + 10*r + 6. Let x(i) = -s(i) - 2*v(i). Factor x(f).
-2*(f + 1)*(2*f + 3)
Let b(s) = -8*s**2 + 58*s + 56. Let n(v) = 12*v**2 - 88*v - 84. Let a(y) = 8*b(y) + 5*n(y). Factor a(w).
-4*(w - 7)*(w + 1)
Let l(f) = -f**3 + 6*f**2 - 3*f - 2. Let p(c) = -2*c**3 + 11*c**2 - 5*c - 4. Let s(j) = -7*l(j) + 4*p(j). Find n, given