n(h) be the third derivative of 0*h + 1/12*h**4 + h**3 - h**2 + 26 - 1/540*h**6 - 1/90*h**5. Factor n(c).
-2*(c - 3)*(c + 3)**2/9
Suppose 32 = -6*b - 52. Let r = b + 20. Solve -10*u - 16*u**5 - 5*u**2 + r*u**5 + 15*u**3 + 5*u**5 + 5*u**4 = 0.
-1, 0, 1, 2
Suppose -3*u + 0*u = -15. Suppose 2*f - 24 = -4*t, -3*t - 12 = u*f - 44. Determine h, given that h**5 - h + 475*h**2 - 2*h**t - 3 + 3 - 473*h**2 = 0.
-1, 0, 1
Factor -1/7*j**2 + 48 - 335/7*j.
-(j - 1)*(j + 336)/7
Let s(l) = l**2 - 6*l - 2. Let o(v) be the second derivative of -v**4 + 10*v**3 + 21*v**2/2 - 49*v. Let f(x) = 2*o(x) + 21*s(x). Suppose f(p) = 0. What is p?
-2, 0
Factor -40/3 + 4*w**2 + 38/3*w.
2*(w + 4)*(6*w - 5)/3
Let u = -29072 + 29074. Factor -w**u - 8/3*w + 1.
-(w + 3)*(3*w - 1)/3
Let t(m) be the second derivative of -3*m**5/40 - 9*m**4 - 285*m**3 + 4332*m**2 - 24*m. Factor t(s).
-3*(s - 4)*(s + 38)**2/2
Let o(k) = k**2 + 1. Let t(v) = v + 16. Let u be t(-19). Let c(p) = p**2 - 14*p - 17. Let n(i) = u*o(i) + c(i). Factor n(g).
-2*(g + 2)*(g + 5)
Let q(v) be the third derivative of 1/12*v**4 + 0*v + 2*v**2 + 4/105*v**5 + 0*v**3 + 3 + 1/420*v**6. Solve q(y) = 0.
-7, -1, 0
Suppose 2202 = 24*p - 1566. Factor -20*h**2 + 198*h + p*h - 13*h + 310*h + 264.
-4*(h - 33)*(5*h + 2)
Factor 0 + 12*x**2 - 198*x - 2/11*x**3.
-2*x*(x - 33)**2/11
Let z(b) = -9*b**3 - 55*b**2 + 1912*b + 9800. Let n(x) = -5*x**3 - 24*x**2 + 957*x + 4900. Let w(y) = -11*n(y) + 6*z(y). Factor w(a).
(a - 35)**2*(a + 4)
Suppose 40994*m - 40996*m = 2*b - 8, 3*b - 4 = m. Factor -40/17*y + 2/17*y**b + 38/17.
2*(y - 19)*(y - 1)/17
Let x(i) be the first derivative of 2*i**4 - 4*i**2 + 4/9*i**3 - 4/15*i**5 - 236 + 0*i. Factor x(b).
-4*b*(b - 6)*(b - 1)*(b + 1)/3
Factor 0 - 180/7*c**2 + 2/21*c**3 + 0*c.
2*c**2*(c - 270)/21
Let o(r) be the first derivative of -r**4/28 + 5*r**3/7 - 27*r**2/14 - 246*r - 141. Let s(v) be the first derivative of o(v). Suppose s(n) = 0. Calculate n.
1, 9
Let q(o) be the third derivative of o**5/150 + 9*o**4/10 + 243*o**3/5 + 673*o**2. Suppose q(s) = 0. Calculate s.
-27
Suppose 4*w - 23 = 29. Suppose 0 = -3*s + k + 28 - 18, 0 = -5*s + 3*k + 14. Let g**2 + s*g**3 + w*g**2 - 8 - 8*g**2 - 2*g**4 - 8*g = 0. Calculate g.
-1, 2
Let r(x) be the third derivative of 0 + 83*x**2 - 1/280*x**6 + 1/35*x**5 + 1/14*x**4 - 8/7*x**3 + 0*x. Factor r(h).
-3*(h - 4)*(h - 2)*(h + 2)/7
Let s(d) = -d**3 + 8*d**2 + 4*d - 10. Let b be s(8). Suppose 0 = -5*w + x + 14, -w + b = -x - 4*x. Factor -5*n**w - 7*n**3 + 2*n**2 + 8*n**3 + 2*n.
n*(n - 2)*(n - 1)
Let s(b) be the third derivative of 0*b**3 + 0*b**4 + 90*b**2 - 1/40*b**5 + 1/20*b**6 + 0 + 0*b. Determine m so that s(m) = 0.
0, 1/4
Let o(n) be the third derivative of n**5/240 + 3*n**4/4 - 553*n**3/24 - 2*n**2 - 2*n - 198. Let o(s) = 0. What is s?
-79, 7
Let i(p) be the first derivative of -1/12*p**4 - 35 + 0*p + 5/3*p**2 + p**3. Factor i(o).
-o*(o - 10)*(o + 1)/3
Solve -92*f + 0*f**3 - 14*f + 128*f**2 - 232*f**2 + 2*f**3 = 0.
-1, 0, 53
Let q(v) = -v**2 + 5*v + 5. Let t be q(0). Let m(c) be the third derivative of -1/66*c**t + 1/33*c**3 + 0 + 0*c - 1/33*c**4 + c**2. Factor m(n).
-2*(n + 1)*(5*n - 1)/11
Let s be ((-11224)/(-2440) - -1*(-7)/(-5))*1. Factor 12*b**2 - 8/3*b + 2/3*b**4 + s*b**3 - 16.
2*(b - 1)*(b + 2)**2*(b + 6)/3
Let n(d) = d**2 + 1. Let c(t) be the third derivative of t**5/10 - t**4/24 + t**3/2 + 11*t**2. Let b = -50 - -44. Let f(r) = b*n(r) + 2*c(r). Factor f(q).
2*q*(3*q - 1)
Let k = -10083 + 10087. Let o(n) be the first derivative of 18 + 4/9*n**3 - 4/3*n - 1/6*n**k + 1/3*n**2. Solve o(p) = 0 for p.
-1, 1, 2
Let q = -1109 - -785. Let p = q + 2334/7. Factor p*n - 6/7*n**2 + 0.
-6*n*(n - 11)/7
Let f = -592764 + 1778294/3. Let x = -4 - -6. Factor -4/3 - f*l**2 - x*l.
-2*(l + 1)*(l + 2)/3
Let d = 83112 - 249334/3. Suppose d*m**2 + 1/3*m**3 - m + 0 = 0. What is m?
-3, 0, 1
Let i = -59 - -68. Factor -19*g**3 + 31*g**3 - i*g**3 + 6*g**2.
3*g**2*(g + 2)
Let a(z) be the first derivative of 3*z**5/20 - 123*z**4/16 + 87*z**3/2 + 81*z**2 + 3759. Solve a(f) = 0 for f.
-1, 0, 6, 36
Suppose -268/21*v + 38/3 + 2/21*v**2 = 0. What is v?
1, 133
Factor 577*h**3 - 5755857 - 4065455 + 563*h**3 - 1138*h**3 + 1684951*h + 8145225*h - 8866*h**2.
2*(h - 2216)**2*(h - 1)
Let k(c) = -c**3 + 29*c**2 - c + 33. Let f be k(29). Suppose 4*s - 38 = 6*n - f*n, -n = 3. Factor 47*p + 52*p + 52*p - 2*p**2 + s - 143*p - 2*p**3.
-2*(p - 2)*(p + 1)*(p + 2)
Factor -188/5*j**2 + 0 - 2/5*j**3 + 384/5*j.
-2*j*(j - 2)*(j + 96)/5
Factor 1/3*x**2 - 93 - 30*x.
(x - 93)*(x + 3)/3
Let m(z) = -4*z - 17. Suppose 4*j - 4 = 3*g - 18, 0 = j + 5*g + 15. Let l be m(j). Factor 210 - 210 - 10*r**2 + 5*r**l.
5*r**2*(r - 2)
Suppose -164*k + 5*t - 47 = -171*k, -2*t + 14 = -2*k. Let -k - 1/2*v**2 - 3/2*v = 0. Calculate v.
-2, -1
Let b(d) be the second derivative of -1/150*d**5 + 3/2*d**2 + 0 - 1/15*d**4 + 8*d - 4/15*d**3. Let s(x) be the first derivative of b(x). Solve s(u) = 0 for u.
-2
Let a = -184047/7 - -26295. Find b, given that 0 + 3/7*b**3 - a*b**2 + 0*b = 0.
0, 6
Solve 1040*f**3 + 104*f**4 + 2196 - 35315*f**5 + 4310*f - 35320*f**5 + 70633*f**5 + 412*f + 3460*f**2 = 0 for f.
-3, -2, -1, 61
Suppose 0 = 4*d - 5*o - 41, -2*d + 4*d + 2 = -2*o. Suppose 8*p - 18*p + 30 = 0. Find u, given that u**p - 4*u**4 + 5*u**4 - 2*u**4 + 0*u**d = 0.
0, 1
Let i(h) be the first derivative of -h**4/20 - 44*h**3/5 - 4221*h**2/10 + 8978*h/5 + 276. Solve i(z) = 0 for z.
-67, 2
Solve 474*g + 130*g**4 + 25800*g + 15138 + 24170*g**2 - 10638*g**2 + 2524*g**3 + 2*g**5 = 0 for g.
-29, -3, -1
Let d = 40/33 + -1429/1188. Let i(u) be the third derivative of 1/216*u**4 + 0*u + 26*u**2 - d*u**5 + 0*u**3 - 1/630*u**7 + 0 + 7/1080*u**6. Factor i(o).
-o*(o - 1)**2*(3*o - 1)/9
Suppose -2*n + 4*n - 2 = -2*k, -3*n = -k + 9. Suppose -i + k*z = -6*i + 10, 3*i - 6 = 3*z. Factor -28/5*v - 2/5*v**i - 98/5.
-2*(v + 7)**2/5
Let t(m) = -8*m**2 + 12*m + 12. Suppose 5*k - 21 + 1 = 0. Let v(h) = -9*h**2 + 13*h + 12. Let g(o) = k*v(o) - 5*t(o). Solve g(x) = 0.
-1, 3
Factor 148*p**2 - 140*p**3 + 81*p + 1037 + 1227*p**2 + 177*p - 5*p**4 - 2568*p + 43.
-5*(p - 6)*(p - 1)**2*(p + 36)
Let z(y) be the third derivative of -y**7/105 + 38*y**6/45 + 539*y**5/90 + 5*y**4/3 - 36*y**3 - 22*y**2 - 26*y. Determine j so that z(j) = 0.
-3, -1, 2/3, 54
Let u(w) = 2*w**3 + 15*w**2 + 27*w + 150. Let d be u(-7). Let a(o) be the first derivative of d*o**2 + 24*o - 20 + 4/3*o**3. Factor a(x).
4*(x + 2)*(x + 3)
Let i(n) be the first derivative of -n**5/45 - n**4/3 - 16*n**3/9 - 32*n**2/9 - 166*n + 64. Let v(s) be the first derivative of i(s). Factor v(m).
-4*(m + 1)*(m + 4)**2/9
Let l(z) be the second derivative of z**6/50 - 19*z**5/100 + 3*z**4/5 - 2*z**3/3 - 800*z. Suppose l(u) = 0. What is u?
0, 1, 2, 10/3
Let x be 58/174*(176/(-55) + 8). Find k, given that x*k**2 - 4/5*k**3 - 4/5*k**5 - 2*k**4 + 2/5 + 8/5*k = 0.
-1, -1/2, 1
Determine h, given that 12 + 103/6*h**2 - 35/6*h**4 - 13/2*h**3 + 89/3*h + 1/6*h**5 = 0.
-1, 2, 36
Let a be (4/(-7) + (-13)/(-26))*596/(-149). Factor 4/7*v + 0 + a*v**2.
2*v*(v + 2)/7
Let o(s) be the second derivative of -s**7/280 - s**6/60 + 65*s**3/3 - 42*s. Let v(h) be the second derivative of o(h). Factor v(r).
-3*r**2*(r + 2)
Let w(o) be the first derivative of 5*o**3/6 - 70*o**2 + 275*o/2 - 1858. Factor w(t).
5*(t - 55)*(t - 1)/2
Let o(j) = -24*j + 176. Let x be o(7). Let g(n) = -n**2 + 4*n. Let b(t) = 4*t**2 + 36. Let m(c) = x*g(c) + b(c). Factor m(r).
-4*(r - 9)*(r + 1)
Suppose -131*b - 22848*b**3 - 5*b**4 - 120 + 22928*b**3 - 265*b**2 + 441*b = 0. What is b?
1, 2, 12
Let x(t) be the third derivative of -t**6/180 - 127*t**5/90 - 251*t**4/36 - 125*t**3/9 + 2241*t**2. Solve x(w) = 0.
-125, -1
Let y(c) be the third derivative of -c**7/840 - c**6/120 + 17*c**5/80 - 15*c**4/16 - 982*c**2. Suppose y(k) = 0. Calculate k.
-10, 0, 3
Let b(x) = 24*x**2 + 14293*x + 17007420. Let f(p) = -7*p**2 - 4764*p - 5669143. Let o(q) = 4*b(q) + 14*f(q). Factor o(y).
-2*(y + 2381)**2
Let d be -5 + (2 - 1) - (-9)/(-108)*-88. Factor 2/3*x - d*x**4 + 4/3 - 6*x**2 - 26/3*x**3.
-2*(x + 1)**3*(5*x - 2)/3
Suppose -2*n = 5*m + 2, -37*n - 12 = -14*m - 41*n. Find v, given that -2/5*v**2 - 6/5*v + m = 0.
-5, 2
Let y(h) = h**3 - 223*h**2 - 22*h + 902. Let b(c) = -25*c**3 + 6020*c**2 + 5