504 - 2*s**7/45 - 73*s**6/180 - 86*s**5/45 - 44*s**4/9 - 64*s**3/9 - 453*s**2. Factor n(k).
-2*(k + 1)**2*(k + 4)**3/3
Suppose -319 = -32*b + 1. Let x(y) be the second derivative of 1/20*y**5 + 0 - b*y + 0*y**2 + 0*y**4 - 1/20*y**6 + 1/84*y**7 + 0*y**3. Factor x(a).
a**3*(a - 2)*(a - 1)/2
Let q(y) = -y**2 + 8*y - 25. Suppose -g = -2*z + g - 30, -4*z - g - 35 = 0. Let o(l) = l. Let d(h) = z*o(h) - 5*q(h). Factor d(p).
5*(p - 5)**2
Suppose -7*h = 4*h - 2*h. Let p(w) be the third derivative of 1/180*w**6 + 0*w + 0*w**5 + 0 - 1/36*w**4 + h*w**3 + 4*w**2. Find r such that p(r) = 0.
-1, 0, 1
Let p(v) be the third derivative of 1/60*v**5 + 1/24*v**4 + v**2 + 1/360*v**6 + 0 + 0*v + 1/18*v**3. Factor p(r).
(r + 1)**3/3
Let x = 12034/3 - 3976. Let d = -34 + x. Determine z, given that 2/3*z**5 - d*z**3 + 0 + 0*z**4 + 0*z**2 + 2/3*z = 0.
-1, 0, 1
Let o(d) be the first derivative of -d**6/75 - d**5/100 + d**4/30 + d**3/30 + 3*d + 7. Let z(s) be the first derivative of o(s). Factor z(i).
-i*(i - 1)*(i + 1)*(2*i + 1)/5
Factor 52*g**2 - 8*g - 5*g + 21*g - 53*g**2.
-g*(g - 8)
Let w = 1 + -4. Let i be (-1)/(4/16) - w. Let p(n) = -7*n**2 - n + 3. Let g(k) = -k**2 + k - 1. Let a(c) = i*p(c) - 3*g(c). Let a(x) = 0. Calculate x.
0, 1/5
Let r be (12/(-720)*-9)/((-51)/(-85)). Factor -1/8*c**2 - r*c - 1/8.
-(c + 1)**2/8
Let k(u) be the third derivative of -8/3*u**3 - 10/3*u**4 + 0 + 0*u + 15*u**2 - 5/3*u**5. Factor k(i).
-4*(5*i + 2)**2
Suppose 5*g = 3*u - u + 45, -4*g = 4*u - 8. Let -2*o - 10 - 4*o**3 + g*o**2 - 10 + 19 = 0. What is o?
-1/4, 1
Let f be (189 - 189)/(0 + 0 - -1). Let i(b) be the third derivative of 0*b + 0 + f*b**4 + 0*b**3 - 7*b**2 - 1/210*b**6 - 1/735*b**7 + 0*b**5. Factor i(u).
-2*u**3*(u + 2)/7
Let u(m) be the second derivative of 1/15*m**4 - 1/25*m**5 + 0*m**3 + 21*m + 0 + 2/105*m**7 - 2/75*m**6 + 0*m**2. Suppose u(o) = 0. Calculate o.
-1, 0, 1
Let k be 98/88 - 30/40. Let j be (-9)/33*(-4)/3. Find u such that j - 2/11*u**3 - k*u**2 + 2/11*u = 0.
-2, -1, 1
Let k(l) be the third derivative of -7*l**6/480 + 19*l**5/240 + 17*l**4/48 + l**3/3 - 5*l**2 + 30. Let k(i) = 0. Calculate i.
-1, -2/7, 4
Let o(n) = 4 + n - 9*n - 2*n**2 - 2*n. Let w be o(-5). Solve 10*a**3 - 16*a + w*a**4 + 6*a**3 - 16 + 21*a**2 - 9*a**2 = 0 for a.
-2, -1, 1
Let r = 66 + -62. Solve -2*s**4 - 7*s**5 - 2*s**r + 11*s**5 - 8*s**3 = 0 for s.
-1, 0, 2
Suppose -4*f + 4*k = -k - 19, 20 = 3*f + 2*k. Suppose -23*c + g = -28*c + 26, -26 = -c + 5*g. Factor c + 3/2*l**2 - f*l.
3*(l - 2)**2/2
Suppose -4*w = w + 3*v - 8, -w - 5*v = -6. What is j in -3 - 2*j + 5*j**2 + 0*j**2 + w - 7*j = 0?
-1/5, 2
Factor -15/4*b - 31/8 + 1/8*b**2.
(b - 31)*(b + 1)/8
Let b(o) be the third derivative of -1/240*o**4 - 1/600*o**5 + 0*o + 1/60*o**3 + o**2 + 0 + 1/1200*o**6. Factor b(i).
(i - 1)**2*(i + 1)/10
Let h(p) be the second derivative of -13/6*p**3 + 0 - 2/3*p**4 - 1/20*p**5 + 10*p - 3*p**2. Let h(v) = 0. Calculate v.
-6, -1
Let y(x) be the first derivative of x**4/16 + 17*x**3/12 + 7*x**2/4 - 8*x - 53. Factor y(p).
(p - 1)*(p + 2)*(p + 16)/4
Let p(m) = m**2 - 2*m + 1. Let d(w) = 0 - 8 + 5 + w + 2. Suppose 7 = 2*s + 3. Let c(f) = s*d(f) + p(f). Factor c(g).
(g - 1)*(g + 1)
Factor -w**5 - 40*w - 18*w**3 - 62*w**4 + 54*w**4 + 35*w - 16*w**2.
-w*(w + 1)**3*(w + 5)
Let z(v) = -2*v**3 + 5*v**2 + 48*v - 48. Let g(a) = -25*a**3 + 60*a**2 + 575*a - 575. Let i(n) = 3*g(n) - 35*z(n). Solve i(m) = 0 for m.
-3, 1, 3
Let w(y) be the second derivative of -9/2*y**2 + y**3 + 1/4*y**4 - 40*y + 0. Solve w(x) = 0.
-3, 1
Suppose -5*b + 26 = 6. Find j, given that 935*j**b - 8*j**3 - 6*j**5 - 2 - 919*j**4 + 2 = 0.
0, 2/3, 2
Factor 0 - 4*d**2 - 7/2*d - 1/2*d**3.
-d*(d + 1)*(d + 7)/2
Let k(w) be the second derivative of -w**6/360 - w**5/60 - w**4/24 + 5*w**3/2 - 20*w. Let g(z) be the second derivative of k(z). Solve g(f) = 0.
-1
Factor -4/11*f**2 - 8/11*f + 16/11 + 2/11*f**3.
2*(f - 2)**2*(f + 2)/11
What is t in 1/4*t + 1/4*t**4 - 1/4*t**3 - 3/4*t**2 + 1/2 = 0?
-1, 1, 2
Factor 385*s - 30*s**3 - 55*s**2 - 5*s**4 + 443*s - 858*s.
-5*s*(s + 1)*(s + 2)*(s + 3)
Let s = 45985 - 45982. Solve 2/9*p**s - 1/9*p**4 + 7/9*p**2 + 4/9*p + 0 = 0.
-1, 0, 4
Let c be 4/16*(2 - -18). Suppose -2*k - 4*g + 3 = -c, -2*g + 6 = 2*k. Let -17*a**3 - a**5 - a**4 + 18*a**3 + 0*a**k + a**2 = 0. Calculate a.
-1, 0, 1
Let d(l) = -l + 2. Suppose 0 = -4*v - 0*v. Let s be d(v). Factor -1/2*b**s + 1/2*b + 0.
-b*(b - 1)/2
Suppose -2/7*a**2 + 8/7*a + 24/7 = 0. Calculate a.
-2, 6
Let b = -8 - -26. Let r = b - 15. Factor -2*g**3 - 3*g**3 + 5*g**3 - g**r - g**2.
-g**2*(g + 1)
Let z(b) be the first derivative of -5*b**4/4 + 55*b**3/3 - 95*b**2 + 200*b - 473. Factor z(j).
-5*(j - 5)*(j - 4)*(j - 2)
Let l(s) be the first derivative of -29*s**3 - 3/5*s**5 - 33 - 117/2*s**2 - 54*s - 27/4*s**4. Solve l(h) = 0.
-3, -2, -1
Let x(u) be the first derivative of -64/5*u + 12 + 16/5*u**2 - 4/15*u**3. Factor x(s).
-4*(s - 4)**2/5
Let j be 12 - 0/(-3) - 3. Suppose -5*g + j + 1 = 0. Solve v**3 + v**2 + g*v**4 - v**2 - v**4 = 0 for v.
-1, 0
Let n be (-1)/(-3*(-4)/72). Let q be ((-8)/n)/(12/27). Factor 10*k + 6 + k - q*k**2 - 18 + k.
-3*(k - 2)**2
Let t(x) be the first derivative of -29*x**3/12 - 59*x**2/4 - 2*x - 616. Factor t(w).
-(w + 4)*(29*w + 2)/4
Let j = -37 + 33. Let y(c) = -3*c**4 + 2*c**3 - 7*c**2 + 4*c + 4. Let f(b) = -2*b**4 + 2*b**3 - 6*b**2 + 3*b + 3. Let z(r) = j*f(r) + 3*y(r). Solve z(q) = 0.
-3, 0, 1
Let w = -1/299 + 359/17940. Let h(m) be the third derivative of 1/72*m**4 + 2*m**2 + 0 + 0*m**3 + 1/120*m**6 + 0*m - 1/630*m**7 - w*m**5. Factor h(l).
-l*(l - 1)**3/3
Suppose -11 = -2*i + c, -5*i - c = -4*i + 2. Suppose -i + 1 = u. Let y(n) = n**2 - 57*n - 72. Let v(g) = -14*g - 18. Let m(p) = u*y(p) + 9*v(p). Factor m(f).
-2*(f + 3)**2
Let d(g) be the second derivative of -5*g**7/126 + 7*g**6/45 - g**5/5 + g**4/18 + g**3/18 - 5*g + 2. Factor d(c).
-c*(c - 1)**3*(5*c + 1)/3
Factor -4 + 22*d**2 - 84*d - 67*d**2 + 16.
-3*(d + 2)*(15*d - 2)
Let p(g) = -159*g - 4450. Let d be p(-28). Determine r so that -25/4 + 15/2*r**3 - 15/2*r + 5/4*r**4 + 5*r**d = 0.
-5, -1, 1
Factor 1/2*s**3 + 0 + 5*s + 11/2*s**2.
s*(s + 1)*(s + 10)/2
Let q(u) be the second derivative of -u**5/15 + 11*u**4/18 - 5*u**3/9 - 110*u. Find y such that q(y) = 0.
0, 1/2, 5
Let h(l) be the first derivative of -15/2*l - 2 - 10/3*l**2 + 5/18*l**3. Determine m, given that h(m) = 0.
-1, 9
Suppose 2*a - k + 35 = 0, 0 = -2*a - 0*k + 2*k - 30. Let c = a - -22. Factor -c*b**2 - 1 - 4*b + 2*b + 1.
-2*b*(b + 1)
Let s(z) be the second derivative of 22/9*z**3 + 2*z + 0 - 1/18*z**4 - 121/3*z**2. Suppose s(o) = 0. What is o?
11
Let y(d) be the third derivative of -d**7/455 + d**6/78 - 11*d**5/390 + d**4/39 - 78*d**2. Factor y(a).
-2*a*(a - 1)**2*(3*a - 4)/13
Let u(h) be the second derivative of h**7/2100 + h**6/450 - h**5/100 - h**3/6 + 2*h. Let v(p) be the second derivative of u(p). Factor v(c).
2*c*(c - 1)*(c + 3)/5
Let x be (-43 + 875/25)/(-26). Let z = 252/247 + 4/19. Factor 8/13*q**2 + 0 - 2/13*q**4 + z*q - x*q**3.
-2*q*(q - 2)*(q + 2)**2/13
Let r(q) be the first derivative of -q**6/360 - q**5/75 + q**4/30 - 7*q**3/3 - 1. Let d(z) be the third derivative of r(z). Suppose d(v) = 0. Calculate v.
-2, 2/5
Suppose -22/7*p**3 + 78/7*p**2 - 82/7*p + 4 - 2/7*p**4 = 0. Calculate p.
-14, 1
Factor 253265 - 38007*u**3 - 2763*u - 17772*u + 38002*u**3 + 555*u**2.
-5*(u - 37)**3
Suppose -2/5*s**4 + 2*s + 20 + 22/5*s**3 - 66/5*s**2 = 0. Calculate s.
-1, 2, 5
Suppose -4*c + 8 = 2*u, -4*c + 5*u = u - 8. Let y(d) be the first derivative of 1/4*d**4 + 1/18*d**6 + 4/15*d**5 - 5 + 0*d - 4/9*d**3 - 2/3*d**c. Factor y(x).
x*(x - 1)*(x + 1)*(x + 2)**2/3
Let t be 205/7 - 1/((-7)/(-2)). Let w = t + -29. Let 1/4*n**4 + w*n**3 - 1/4*n**2 + 0 + 0*n = 0. Calculate n.
-1, 0, 1
Let m(u) be the first derivative of -4*u**3/3 - 28*u**2 - 196*u - 221. Factor m(h).
-4*(h + 7)**2
Let t(j) = j**3 + 9*j**2 + j + 9. Suppose -3*f - 26 = -f + 2*v, 5*f - v + 41 = 0. Let i be t(f). Suppose 0*s**2 - 2*s**3 - 4*s**2 + i*s**2 = 0. Calculate s.
-2, 0
Let k be (3 - 5)*(-33 + 1). Let d = k - 44. Determine x, given that 0*x**4 - 48*x**3 + 40*x - 42*x**3 - 5*x**4 - 60*x**2 - d*x**4 = 0.
-2, 0, 2/5
Let h(s) be the third derivative of -5*s**8/336 - s**7/42 + s**6/24 + s**5/12