 + 60/7*n + 92/7*n**2 + 4/7*n**4.
4*n*(n + 1)*(n + 3)*(n + 5)/7
Let f(w) be the second derivative of -w**6/180 + w**5/120 + w**4/36 + 2*w + 144. Factor f(y).
-y**2*(y - 2)*(y + 1)/6
Suppose 0 = -33*c + 40*c. Factor c + 3/4*k + 3/4*k**2.
3*k*(k + 1)/4
Let t be (-1)/8*6/(-15). Let f(o) be the second derivative of 0*o**3 + o + t*o**5 + 0*o**2 + 0 - 1/12*o**4. Solve f(n) = 0.
0, 1
Let u(d) be the first derivative of -d**6/660 + d**5/330 + 5*d**2/2 + 2. Let i(o) be the second derivative of u(o). Suppose i(y) = 0. Calculate y.
0, 1
Let d = 104 + -207/2. Let g(t) be the second derivative of 5*t - 1/12*t**4 + 1/6*t**3 + d*t**2 - 1/20*t**5 + 0. Find q, given that g(q) = 0.
-1, 1
Let o(a) be the first derivative of -4/7*a**2 + 0*a - 1/14*a**4 + 8/21*a**3 - 4. Factor o(s).
-2*s*(s - 2)**2/7
Let k(v) = 2*v**2 + 103*v + 200. Let n be k(-2). Factor 1/3*x**n - 1/3*x + 0.
x*(x - 1)/3
Let u(b) = -b**3 + 4. Let r be u(0). Let v be r/(-6)*108/(-24). Let -v*p**2 - 6*p + 6*p + 0*p**2 = 0. What is p?
0
Let f(k) be the first derivative of -5/8*k**4 - 1/3*k**3 - 2/5*k**5 + 0*k**2 + 14 + 0*k - 1/12*k**6. Factor f(m).
-m**2*(m + 1)**2*(m + 2)/2
Suppose -4*l - 1 = -5*h - 7, -2*l + 6 = -h. Suppose 3*k - 15 = -i, -5*k + 5*i + 4 = -41. Factor x - 6 - 5*x - h*x**2 + k.
-2*x*(x + 2)
Let d = 35 - 31. Let 16*g**3 + g**4 + 16*g**2 - 5*g**d + 8*g**4 = 0. What is g?
-2, 0
Let w be (30/45)/(-1 + 22/(-18)*-1). Determine j so that -10/3*j - 2 - 2/3*j**2 + 2/3*j**w = 0.
-1, 3
Let r(h) be the first derivative of -h**5/80 + h**3/24 - 6*h - 14. Let n(o) be the first derivative of r(o). Factor n(a).
-a*(a - 1)*(a + 1)/4
Suppose 0 = -2*w + 4*i + 18, -4*i + 12 = 4*w - 0*i. Suppose w*u - 4*d - 105 = 41, -4*u = -d - 119. Solve 5*h**2 - 1 - 2*h**2 - 6*h + 49 + u*h = 0 for h.
-4
Factor -41*p + 117*p**2 - 990*p**3 + 75*p**2 + 54*p**2 + 405*p**4 + 134*p**2 + p.
5*p*(p - 2)*(9*p - 2)**2
Let w(r) = -24*r + 14. Let z be w(-14). Let q be -4 + 13/(1105/z). Factor -q*v**2 + 4/17 - 2/17*v.
-2*(v - 1)*(v + 2)/17
Factor 0*l**2 + 47 + 5*l**2 - 155 - 2*l**2 + 57 - 48*l.
3*(l - 17)*(l + 1)
Let j(n) = -5*n**4 + 5*n**2 - 20*n + 5. Let z(s) = 5*s**4 - s**3 - 7*s**2 + 21*s - 6. Let t(k) = 4*j(k) + 5*z(k). Solve t(x) = 0.
-2, 1
Find r such that 461*r + 12*r**2 - 409*r - 2*r**3 + 69 - r**3 - r**4 - 21 = 0.
-3, -2, 4
Let o(g) be the second derivative of 0 + 0*g**3 + 12*g - 1/6*g**4 - 1/45*g**6 - 2/15*g**5 + 0*g**2. Find w such that o(w) = 0.
-3, -1, 0
Suppose 9*p**2 - 5*p**2 - 34*p**3 - 2*p**2 + 36*p**3 = 0. What is p?
-1, 0
Let r(t) be the third derivative of -t**6/40 - 2*t**5/5 - 5*t**4/8 + 7*t**3 - 82*t**2. Factor r(n).
-3*(n - 1)*(n + 2)*(n + 7)
Let m(z) be the second derivative of -7*z**5/120 - 4*z**4/3 - 35*z**3/4 + 49*z**2/6 + 24*z. What is x in m(x) = 0?
-7, 2/7
Factor -30/7*z**2 + 156/7*z - 30/7.
-6*(z - 5)*(5*z - 1)/7
Let o = 160 - 144. Suppose -8*p**2 - p + 4*p**5 + 16*p**3 - 8 - 4*p + o*p**4 - 15*p = 0. Calculate p.
-2, -1, 1
Solve -48*w**2 - 58*w**4 + 59*w**3 + 4*w + 82*w**4 + 18*w**4 = 0.
-2, 0, 2/21, 1/2
Let j(m) be the first derivative of m**4/4 - m**3/3 - 2*m**2 + 4*m - 45. Determine b, given that j(b) = 0.
-2, 1, 2
Suppose 5/6*v**2 - 2/3 + 1/2*v**3 - 2/3*v = 0. Calculate v.
-2, -2/3, 1
Suppose 0*w = -4*w + 2*h + 16, 9 = 3*w - 3*h. Factor -1 + w - 25*j - 21*j**2 - 11*j + 8.
-3*(j + 2)*(7*j - 2)
Let d(w) = w**3 + 7*w**2 + 3. Let p be d(-7). Factor -44*i**2 - 3*i**3 - 8*i**3 - 24*i - 5*i**p + 4*i**3.
-4*i*(i + 3)*(3*i + 2)
Let r be 410/(-123)*6/(-10). Factor 10*y**r - 7/4*y**3 - 9/2 - 51/4*y.
-(y - 3)**2*(7*y + 2)/4
Let a be ((-5)/(-3))/(119/(-102) - -2). Solve -6/7*q - 4/7 - 2/7*q**a = 0 for q.
-2, -1
Let s(y) be the first derivative of 5*y**4/4 + 5*y**3/3 - 5*y**2/2 - 5*y + 279. Factor s(u).
5*(u - 1)*(u + 1)**2
Let y = -7 + 11. Let o(l) = -24*l**3 - 39*l**2 + 70*l - 11. Let s(f) = 95*f**3 + 155*f**2 - 280*f + 45. Let x(v) = y*s(v) + 15*o(v). Factor x(b).
5*(b - 1)*(b + 3)*(4*b - 1)
Let r(j) be the third derivative of -j**7/455 + j**6/156 + j**5/195 + 7*j**2 + 2. Find d such that r(d) = 0.
-1/3, 0, 2
Let c(q) be the second derivative of -q**7/245 - q**6/35 - 3*q**5/70 - 25*q**2/2 + 27*q. Let o(l) be the first derivative of c(l). Solve o(u) = 0 for u.
-3, -1, 0
Factor 204*f + 828*f - 112801 + 112961 - 52*f**2.
-4*(f - 20)*(13*f + 2)
Let a = -21906 - -43845/2. Determine f, given that -6 - 21/4*f**3 + 69/4*f**2 + a*f = 0.
-1, 2/7, 4
Let x(d) be the third derivative of -1/30*d**4 + 1/1050*d**7 - 26*d**2 - 1/50*d**5 + 4/15*d**3 + 1/600*d**6 + 0*d + 0. Factor x(t).
(t - 2)*(t - 1)*(t + 2)**2/5
Let k(b) = -5*b**3 - 27*b**2 + 16*b + 32. Let v(n) = -2*n**3 - 9*n**2 + 5*n + 12. Let r(c) = -3*k(c) + 8*v(c). Suppose r(t) = 0. What is t?
0, 1, 8
Let s(m) be the second derivative of -m**6/60 - m**5/30 + m**4/6 - 3*m**2 - 13*m. Let f(h) be the first derivative of s(h). Find i such that f(i) = 0.
-2, 0, 1
Let a(g) be the third derivative of g**6/75 - g**5/30 - 23*g**4/60 + 2*g**3/5 - g**2 - 47. Factor a(t).
2*(t - 3)*(t + 2)*(4*t - 1)/5
Let v = -163/30 + 89/15. Let w(b) be the second derivative of 0 - v*b**4 + 3/20*b**5 - 6*b + 1/2*b**3 + 0*b**2. Suppose w(x) = 0. What is x?
0, 1
Let u(l) be the first derivative of -1 - 1/10*l**5 + 1/6*l**4 + 0*l**3 - 6*l + 0*l**2. Let y(w) be the first derivative of u(w). Factor y(h).
-2*h**2*(h - 1)
Factor 2/3*a**4 + 1/3*a**2 + 1/6*a + 0 - 7/6*a**3.
a*(a - 1)**2*(4*a + 1)/6
Factor 3/5*d**2 + 0 - 132/5*d.
3*d*(d - 44)/5
Let k(r) be the third derivative of r**5/100 + r**4/40 - 6*r**3/5 + 160*r**2. Factor k(l).
3*(l - 3)*(l + 4)/5
Let p(r) = -19*r**3 + 89*r**2 + 108*r - 13. Let j(b) = 3*b**3 - 15*b**2 - 18*b + 2. Let m(o) = 39*j(o) + 6*p(o). Find w such that m(w) = 0.
-1, 0, 18
Let x = -197 - -200. Let w(g) be the third derivative of g**4 + 0*g + 1/60*g**6 + 0 - 1/5*g**5 - 8/3*g**x + g**2. Let w(b) = 0. Calculate b.
2
Factor 100/9 + 28/9*l**3 + 740/9*l + 284/9*l**2.
4*(l + 5)**2*(7*l + 1)/9
Let i(l) be the second derivative of 0 - 1/18*l**4 - 1/3*l**3 - 22*l - 2/3*l**2. Suppose i(u) = 0. Calculate u.
-2, -1
Let q(k) be the first derivative of -k**4/10 + 56*k**3/15 - 256*k**2/5 + 1536*k/5 + 41. Let q(o) = 0. Calculate o.
8, 12
Let r(x) be the first derivative of -x**7/420 + 19*x**6/720 - 19*x**5/240 - x**4/8 + 34*x**3/3 + 39. Let c(i) be the third derivative of r(i). Factor c(y).
-(y - 3)*(y - 2)*(4*y + 1)/2
Let r = -2659 - -7979/3. Suppose 2/3*l**2 + 8/3*l + r*l**4 - 20/9*l**3 - 8/9 = 0. What is l?
-1, 1/3, 2
Suppose 5 = 2*r + 5*a - 15, -2*r - 3*a + 16 = 0. Suppose 2*t + 2*t = -r*o + 14, 2*t - 8 = -3*o. Factor i + o*i + 4*i**2 + i.
4*i*(i + 1)
Suppose -o - 8 = -5*i, -4*i = 2*o + 47 - 59. Determine s so that 3/2*s - 1/2*s**o + 0 = 0.
0, 3
Let q(i) = -5*i**3 + 11*i + 3*i**2 - 5 + 0*i**3 - 6*i. Let f(c) = -6*c**3 + 3*c**2 + 6*c - 6. Let n(a) = 2*f(a) - 3*q(a). Solve n(z) = 0 for z.
-1, 1
Suppose -3*o + 5*o = -3*b + 8, -4*b = 2*o - 8. Factor -3*x - o*x**3 + 7*x + 2 - 2.
-4*x*(x - 1)*(x + 1)
Let l = 34 - 2. Let t(g) = 84*g**3 - 240*g**2 + 240*g - 32. Let f(h) = 13*h**3 - 37*h**2 + 37*h - 5. Let j(x) = l*f(x) - 5*t(x). Let j(m) = 0. What is m?
0, 2
Let i(c) be the third derivative of c**8/50400 + c**7/6300 - c**6/600 + 7*c**5/30 + 32*c**2. Let p(d) be the third derivative of i(d). Solve p(y) = 0.
-3, 1
Let z(t) be the first derivative of t**3/12 - 3*t**2/8 - t + 390. Find g, given that z(g) = 0.
-1, 4
Solve -2*c**3 + 21*c - 18*c + 5*c**3 - 6*c**3 - 3*c**2 + 3 = 0.
-1, 1
Let n(a) be the third derivative of 0*a**3 - 9*a**2 - 1/270*a**5 + 0 + 0*a - 1/27*a**4. Solve n(j) = 0.
-4, 0
Let c(r) be the first derivative of -r**4/14 - 44*r**3/21 + 100*r**2/7 - 208*r/7 + 25. Factor c(q).
-2*(q - 2)**2*(q + 26)/7
Let z = 3039 - 6077/2. Factor 0 + g + z*g**2.
g*(g + 2)/2
Let -12 + 3*q**2 + 3/7*q**3 - 12/7*q = 0. Calculate q.
-7, -2, 2
Let c(j) be the third derivative of -j**7/2100 + j**5/300 - j**3/6 - 4*j**2. Let w(p) be the first derivative of c(p). Factor w(o).
-2*o*(o - 1)*(o + 1)/5
Let r(q) be the first derivative of q**5/180 - q**3/2 - 21*q**2/2 - 1. Let a(o) be the second derivative of r(o). Suppose a(p) = 0. What is p?
-3, 3
Let r(k) be the first derivative of -15/4*k**4 - 1 - 12*k + 3/5*k**5 - k**3 + 1/2*k**6 + 12*k**2. Find s such that r(s) = 0.
-2, 1
Let 7 - 22 + 18*t - 21*t**2 - 66*t