 - 3*n**4.
-(n - 1)**2*(n + 1)**2*(n + 3)
Let i(f) be the second derivative of 11*f**5/38 - 13*f**4/19 - 20*f**3/19 - 8*f**2/19 + 2*f - 75. Solve i(q) = 0.
-2/5, -2/11, 2
Let n(j) be the second derivative of j**6/90 - 3*j**5/20 - j**4/36 + j**3/2 - 60*j. Factor n(r).
r*(r - 9)*(r - 1)*(r + 1)/3
Let k(r) be the first derivative of -2/3*r**3 + 1/4*r**4 + 8*r + 16 - 2*r**2. Factor k(p).
(p - 2)**2*(p + 2)
Suppose -79*p = -15*p. Factor 18/13*r**3 + 10/13*r**4 + 4/13*r + 2/13*r**5 + p + 14/13*r**2.
2*r*(r + 1)**3*(r + 2)/13
Factor -2/5*m**3 - 576/5*m - 66/5*m**2 - 512/5.
-2*(m + 1)*(m + 16)**2/5
Let x(p) = 10*p**3 + 175*p**2 - 77*p - 9. Let l(s) = 5*s**3 + 87*s**2 - 38*s - 4. Let w(d) = -9*l(d) + 4*x(d). Factor w(k).
-k*(k + 17)*(5*k - 2)
Let r(b) be the second derivative of b**6/255 - 61*b**5/170 - 63*b**4/34 - 191*b**3/51 - 64*b**2/17 + 95*b - 2. Factor r(h).
2*(h - 64)*(h + 1)**3/17
Let y(p) be the third derivative of 0 + 4*p**2 + 0*p - 1/12*p**5 + 2/3*p**3 - 1/40*p**6 + 1/6*p**4. Factor y(s).
-(s - 1)*(s + 2)*(3*s + 2)
Let n = -2599 + 2601. Find g such that -4/7*g**n - 4/7 + 8/7*g = 0.
1
Factor 15*u**2 - 3*u + 33265 - 33265.
3*u*(5*u - 1)
Let q(v) = -v**3 + 25*v**2 + 25*v + 28. Suppose 16*h - 156 = 10*h. Let x be q(h). Factor -4/7*l + 0*l**3 - 2/7*l**4 + 6/7*l**x + 0.
-2*l*(l - 1)**2*(l + 2)/7
Let j be -10 + 15 - (4 - 1). Suppose -32*y**2 - 4 + 40*y**j + 4 - 8*y**4 + 4*y - 4*y**5 = 0. Calculate y.
-1, 0, 1
Suppose 0 = 4*o - 4 - 72. Let b = o - 25. Let k(v) = -v**2 + 7*v + 6. Let q(a) = a**2 - 6*a - 5. Let p(i) = b*q(i) - 5*k(i). Factor p(u).
-u*(u - 1)
Suppose -2*d + 3*z = 13, 4*d - 4 + 5 = z. Let o be d*(5 - (-27)/(-6)). What is i in 1/2*i**2 + i + o = 0?
-1
Solve -18*t - 371 - 45*t**2 - 6*t + 5*t**3 + 361 - 21*t + 15*t**4 = 0 for t.
-1, -1/3, 2
Let b = -14028 - -42086/3. Factor 1/6*a**5 - b*a - 1/3*a**4 + 0 - 1/2*a**3 + 4/3*a**2.
a*(a - 2)*(a - 1)**2*(a + 2)/6
Let p(w) = w**3 - 6*w**2 + 13*w - 10. Let a be p(3). Solve 0*j**a + 3/2*j**3 + 0*j + 0 = 0 for j.
0
Let u = 57 + -169/3. Suppose -6*b = 22*b - 56. Factor 0 + 0*m - u*m**b.
-2*m**2/3
Suppose -3*q - 20 = -4*x, -4*q - 3*x + 3 = -12. Let v(i) be the second derivative of -5/6*i**3 + 1/4*i**5 + 0 + 12*i + q*i**4 + 0*i**2. Factor v(o).
5*o*(o - 1)*(o + 1)
Suppose -2*c**3 - 3 + 2277*c**4 - 2278*c**4 + 3 = 0. Calculate c.
-2, 0
Let z(p) be the first derivative of 1/2*p**4 + 0*p - 7/2*p**2 - 1/15*p**5 - 4/3*p**3 - 4. Let w(c) be the second derivative of z(c). Let w(k) = 0. Calculate k.
1, 2
Factor -3*m**4 + 0*m**3 + 83 - 80 - 6*m**3 + 6*m.
-3*(m - 1)*(m + 1)**3
Let r be 360/864*-4*3/(-30). Let z(c) be the third derivative of -1/45*c**5 + 0*c - 9*c**2 - 4/9*c**3 + 0 + r*c**4. Factor z(n).
-4*(n - 2)*(n - 1)/3
Let x(v) be the second derivative of 13/10*v**3 + 12*v - 3/4*v**4 + 2 + 3/5*v**2. Factor x(m).
-3*(m - 1)*(15*m + 2)/5
Let w(x) be the first derivative of -1/2*x**4 - 2/3*x**3 + 2*x + x**2 - 2. Let w(h) = 0. What is h?
-1, 1
Let z = 54346/3135 + -2/1045. Let d = z + -38/3. Factor -4/3 + 6*k - d*k**2.
-2*(k - 1)*(7*k - 2)/3
Let v(d) be the first derivative of -3*d**5/5 - 201*d**4/4 - 1575*d**3 - 43659*d**2/2 - 111132*d + 61. Factor v(w).
-3*(w + 4)*(w + 21)**3
Let b = 13373/3 + -4456. What is x in 4/3*x**2 - 1/3*x**5 + b*x**4 + 0*x + 0 - 8/3*x**3 = 0?
0, 1, 2
Let b = -522 - -3655/7. Let n(z) be the first derivative of -3/7*z**2 - 3 - 3/7*z - b*z**3. Determine j, given that n(j) = 0.
-1
Factor 4*l + 5*l**3 - 7*l**3 + 2*l**2 - 16193 + 16193.
-2*l*(l - 2)*(l + 1)
Let q(a) be the third derivative of 1/12*a**4 + 0*a**3 + 1/30*a**5 + 0*a + 0 + 17*a**2. Factor q(j).
2*j*(j + 1)
Let k be 80/25 - (-1)/(-5). Suppose -3*y = -k*f - 13 + 1, -2*y + 8 = 4*f. Factor 2*m**2 - 9*m**3 + 2*m**y - 4 + 13*m**3 + 4.
2*m**2*(m + 1)**2
Factor -5/4*x**2 + 475/4 - 35/2*x.
-5*(x - 5)*(x + 19)/4
Let l(b) be the third derivative of b**5/12 - 445*b**4/4 + 118815*b**3/2 - 1071*b**2. Factor l(z).
5*(z - 267)**2
Let y = -6014 + 24155/4. Solve y*r + 69/2*r**2 + 27/4*r**4 + 27/4 + 45/2*r**3 + 3/4*r**5 = 0 for r.
-3, -1
Determine y so that 40/9*y**2 + 44/9*y - 4/9*y**3 + 0 = 0.
-1, 0, 11
Let j(r) be the second derivative of -r**7/21 - 4*r**6/35 + 53*r**5/70 + r**4 - 100*r**3/21 + 24*r**2/7 + 16*r. Solve j(z) = 0.
-3, -2, 2/7, 1, 2
Let z = 36 + -34. What is y in -2*y - z*y + 3*y**3 + 3*y - 2*y = 0?
-1, 0, 1
Suppose -4*a = 5*y - 71, -5*a + 107 = -y - 18. Let p be a/4 + -4 - -1. Factor 6*c**3 + 12*c - 16*c - 4*c**5 + 2*c**p.
-4*c*(c - 1)**2*(c + 1)**2
Let w = 15 - 12. Suppose 3*v = 4*v - w. Factor -4*s**2 + v - s**3 + 6*s**2 - 2 - 3*s + s**2.
-(s - 1)**3
Suppose -139 - 171 = -62*j. Let h(t) be the second derivative of -5/18*t**3 - 8*t + 0*t**4 + 1/12*t**j + 0*t**2 + 0. Factor h(o).
5*o*(o - 1)*(o + 1)/3
Suppose 5494 = -11*g + 5516. Factor -1/3*w**4 - 3*w - 7/3*w**3 + 0 - 5*w**g.
-w*(w + 1)*(w + 3)**2/3
Suppose m + 4 = 2*v - 4, 3*v - 3 = -3*m. Determine n, given that 8/5*n**2 + 16/5*n**v + 2/5*n**5 + 0*n + 0 + 2*n**4 = 0.
-2, -1, 0
Let a(l) be the second derivative of 0 - 1/14*l**7 - 4*l + 0*l**2 + 3/20*l**5 + 1/4*l**4 - 1/10*l**6 + 0*l**3. Factor a(o).
-3*o**2*(o - 1)*(o + 1)**2
Suppose -142*z = 227*z - 1107. Factor -3/5*l**5 + 21/5*l**4 - 39/5*l + 66/5*l**2 - 54/5*l**z + 9/5.
-3*(l - 3)*(l - 1)**4/5
Let f = 2020/3021 + -2/1007. Factor -f*b + 1/6*b**2 + 1/2.
(b - 3)*(b - 1)/6
Let o(k) be the second derivative of -3*k**5/40 - 7*k**4/2 + 29*k**3/4 + 451*k. Suppose o(v) = 0. Calculate v.
-29, 0, 1
Let u(q) be the third derivative of q**5/180 - 5*q**4/18 + q**2 + 24*q. Let u(l) = 0. Calculate l.
0, 20
Let k(y) be the third derivative of 17*y**5/240 + 31*y**4/96 - y**3/4 + 4*y**2 - 12. Factor k(t).
(t + 2)*(17*t - 3)/4
Let r = -7040 - -7044. Factor -9/4*k**2 - 3/2*k + 3 - 3/8*k**r + 15/8*k**3.
-3*(k - 2)**3*(k + 1)/8
Suppose 5*t + 0*t = j - 9, 0 = -3*j + t + 13. Suppose -2*m + m + j = 0. Let -2*d**2 - 2*d**3 + 2*d**4 + 0*d**2 + 2*d**5 + 0*d**m = 0. What is d?
-1, 0, 1
Let n(c) be the second derivative of -c**8/168 + 2*c**7/105 - c**6/60 - 13*c**2 + 5*c. Let o(p) be the first derivative of n(p). What is f in o(f) = 0?
0, 1
Solve 4/5*b**3 + 0 - 4/5*b + 2/5*b**4 - 2/5*b**2 = 0 for b.
-2, -1, 0, 1
Suppose m + 4 = 2*m. Factor -16*h**3 - 8*h**2 + m*h**3 - 3*h**4 - 5*h**4 + 4*h**4.
-4*h**2*(h + 1)*(h + 2)
Factor 10*h**2 - 7 + 3/2*h**3 - 9/2*h.
(h - 1)*(h + 7)*(3*h + 2)/2
Let j = 15 + 68. Suppose 3*z = j - 29. Factor 0 + b - z*b**3 + 1/2*b**2.
-b*(4*b - 1)*(9*b + 2)/2
Let m = -60 - -54. Let o be (m + (-3 - -1))/(-3 + 1). Factor 2/5*k**2 + 1/5*k - 1/5*k**o - 2/5*k**3 - 1/5 + 1/5*k**5.
(k - 1)**3*(k + 1)**2/5
Let f(l) be the second derivative of l**4/24 + 15*l**3/2 + 2025*l**2/4 - 128*l. Suppose f(t) = 0. Calculate t.
-45
Let p(r) be the second derivative of r**5/10 - 5*r**4/3 + 17*r**3/3 - 8*r**2 + r + 11. Solve p(y) = 0.
1, 8
Let p(r) be the second derivative of r**6/30 - r**5/2 + 13*r**4/12 + 10*r**3 + 18*r**2 - 540*r. Let p(u) = 0. Calculate u.
-1, 6
Let a(v) = v**3 + v**2 + v + 8. Let k(m) = 3*m**3 - 80*m**2 + 757*m + 1331. Let n(h) = 4*a(h) - 4*k(h). What is c in n(c) = 0?
-3/2, 21
Let b be 12/8 - 1/(-2). Suppose 5*j - 4*x - 20 = x, x - 12 = -j. Find a, given that -a**b + 4*a + 0 + 4 - j = 0.
2
Let d(m) = m**2 - 8*m - 1. Let o be d(9). Suppose -4*u + 4*l = -o, 5*u + 0*l - 4*l = 11. Solve 1/6*r**4 - 1/3*r + 0 + 0*r**u - 1/2*r**2 = 0 for r.
-1, 0, 2
Find b, given that -10*b**3 + 20*b**3 + 40 + b**3 - 6*b**3 - 10*b**2 - 15*b**2 + 10*b = 0.
-1, 2, 4
Factor 36*n**2 - 9*n**2 + n**4 - 36*n**3 + 6*n + 2*n**4 + 26*n + 34*n.
3*n*(n - 11)*(n - 2)*(n + 1)
Let x(q) be the second derivative of -2*q**6/15 + 31*q**5/10 - 121*q**4/48 + 5*q**3/8 + 7*q + 21. Let x(k) = 0. What is k?
0, 1/4, 15
Determine n so that 12 - 34/3*n**4 - 2*n + 98/3*n**3 - 98/3*n**2 + 4/3*n**5 = 0.
-1/2, 1, 2, 3
Let u(j) be the third derivative of j**7/70 - 3*j**6/20 - 6*j**5/5 - 13*j**4/4 - 9*j**3/2 + j**2 + 2*j. Factor u(m).
3*(m - 9)*(m + 1)**3
Suppose 20/9*k**2 + 16/9 + 34/9*k + 2/9*k**3 = 0. Calculate k.
-8, -1
Let r = -2666 + 2669. Let i(p) be the second derivative of 0*p**6 + 0*p**2 - 1/3*p**4 - 3/10*p**5 - 9*p + 0*p**r + 1/21*p**7 + 0. Factor i(y).
2*y**2*(y - 2)*(y + 1)**2
Let v be ((-2)/(-3) + -1)*0. Suppose v = 5*h - 30 + 10. Find m, given that 0*m**h + 4*m**2 - 4*m**3 