*f**6 + 27/4*f**5 + 0 - 9*f**2 + 1/42*f**7 + 0*f**3 + 0*f. Factor g(c).
5*c**2*(c + 9)**2
Let l(o) be the second derivative of o**6/165 - 7*o**5/110 - 75*o**4/22 - 749*o**3/33 + 980*o**2/11 + 310*o - 1. Suppose l(y) = 0. Calculate y.
-7, 1, 20
Let n(b) be the third derivative of -3*b**8/392 + 26*b**7/245 + 29*b**6/105 + 4*b**5/21 + 25*b**2 + 3*b. What is v in n(v) = 0?
-2/3, 0, 10
Let g = -7524/13 - -38764/65. Solve 128/5 + 448/5*d - g*d**2 - 26*d**4 - 344/5*d**3 - 14/5*d**5 = 0 for d.
-4, -2, -2/7, 1
Let x(k) = k**2 - 3*k - 1. Suppose -76*a = -36*a - 1200. Let u(t) = 35*t**2 - 770*t + 23090. Let l(f) = a*x(f) - u(f). Factor l(g).
-5*(g - 68)**2
Let z = 1632358 - 1632355. Determine r, given that -3/2*r**z + 0 + 0*r - 3*r**2 = 0.
-2, 0
Let r(n) be the first derivative of 14*n + 2/3*n**4 + 16/3*n**3 + 1/30*n**5 + 5 + 64/3*n**2. Let x(p) be the first derivative of r(p). Factor x(m).
2*(m + 4)**3/3
Let o(f) be the second derivative of 0*f**2 + 1/15*f**6 + 2/3*f**4 + 0*f**3 + 60*f + 2/5*f**5 + 0. Find h, given that o(h) = 0.
-2, 0
Let n = -1009830 + 6058997/6. Factor -5/3*i**2 + 1/6*i**3 - 4/3 + n*i.
(i - 8)*(i - 1)**2/6
Let r be (-1 - -2)*(-3)/3*-2. Determine x, given that -4*x**3 - 8*x - 12*x**3 - 82*x**2 + 62*x**r - 4*x**4 = 0.
-2, -1, 0
Suppose 5*s + 207 = -5*y + 277, 3*s = -2*y + 30. Factor s + 4/3*j**2 + 14/3*j.
2*(j + 3)*(2*j + 1)/3
Suppose -61220 = 27*l - 61274. Find h such that -2 + 1/2*h**l + 0*h = 0.
-2, 2
Suppose 0 = -w - 2*a + 14 - 3, -2*w - 2*a = -12. Let i(h) = -h**2 - 31*h - 144. Let m(p) = -p**2 + 2*p. Let x(f) = w*i(f) - 4*m(f). Factor x(v).
3*(v - 16)*(v + 3)
Let o(z) = -5*z**3 + 40*z + 5. Suppose 2*n - 5*n + 4*f - 35 = 0, -2*n = -5*f + 35. Let b(y) = -2*y**2 - 1. Let v(i) = n*b(i) - o(i). Factor v(t).
5*t*(t - 2)*(t + 4)
Let y(l) be the first derivative of -1/3*l**5 + 0*l - 1/18*l**6 + 115 + 0*l**2 - 2/3*l**4 - 4/9*l**3. Factor y(v).
-v**2*(v + 1)*(v + 2)**2/3
Suppose 4*d + 9*d = 8*d. Let b be (1 + d)/(5 - (-2 + 6)). Factor 0*u**2 - 2*u**2 + 8*u + 9 + b.
-2*(u - 5)*(u + 1)
Factor 3403*n**3 - 17*n + 24*n**2 + 16 - 19*n - 1698*n**3 - 1709*n**3.
-4*(n - 4)*(n - 1)**2
Let u(m) = -m**3 + 31*m**2 - 54*m. Suppose -5*p - 70 = -45. Let f(b) = -b**3 + 16*b**2 - 27*b. Let r(v) = p*f(v) + 2*u(v). Factor r(d).
3*d*(d - 3)**2
Suppose 3*l + 5*d - 55 = 0, 3*l = d + 19 + 42. Let o(c) be the second derivative of -7/3*c**4 + l*c - 10*c**2 + 0 + 1/5*c**5 + 22/3*c**3. Factor o(s).
4*(s - 5)*(s - 1)**2
Let d(w) = w**3 + 6*w**2 + 10*w + 30. Let o be d(-5). Let l(f) be the third derivative of -1/96*f**4 + 1/240*f**o + 0 + 0*f + 14*f**2 - 1/12*f**3. Factor l(p).
(p - 2)*(p + 1)/4
Let f(g) be the second derivative of g**7/84 - g**6/24 - 11*g**5/80 - g**4/12 + 21*g + 3. Determine b, given that f(b) = 0.
-1, -1/2, 0, 4
Let y(p) = -15*p + 18. Let k = -27 + 22. Let n(u) = -u**2 + 30*u - 36. Suppose 4*h = -4*h - 24. Let s(m) = h*n(m) + k*y(m). Factor s(w).
3*(w - 3)*(w - 2)
Let c = 379/150 + -59/25. Let a(g) be the first derivative of 0*g + 6/5*g**5 + 21 - 9/4*g**4 - c*g**6 + 0*g**2 + 0*g**3. Factor a(s).
-s**3*(s - 3)**2
Suppose -4 = -2*g - 2*c - 3*c, 0 = 10*c - 15*c. Let w(u) be the first derivative of -4/9*u - 1/27*u**3 - 2/9*u**g - 23. Solve w(n) = 0.
-2
Let a = 24325 + -24322. Let y(g) be the first derivative of 8*g + 37 + 4/3*g**a - 6*g**2. What is d in y(d) = 0?
1, 2
Let y(u) be the first derivative of 2/5*u**5 - 23*u**2 - 28*u - 2*u**3 + 7/2*u**4 - 116. Factor y(h).
2*(h - 2)*(h + 1)**2*(h + 7)
Factor -85*t**2 - 675*t**3 + 287*t**3 + 383*t**3 - 310*t + 400.
-5*(t - 1)*(t + 8)*(t + 10)
Solve 2/7*h**2 - 6 + 41/7*h - 1/7*h**3 = 0 for h.
-6, 1, 7
Let s be 1/((-51)/(-210)) - 8/68. Factor -7*h**3 - 2*h**5 + 15*h**3 - 24*h**s + 18*h**3.
-2*h**3*(h - 1)*(h + 13)
Let n(s) be the first derivative of -3*s**5/10 - 159*s**4/8 - 308*s**3 + 1764*s**2 - 2107. Factor n(b).
-3*b*(b - 3)*(b + 28)**2/2
Let 59/2 - 61/4*q + 1/4*q**2 = 0. What is q?
2, 59
Let y(n) be the third derivative of -5*n**8/1008 + n**7/105 + 19*n**6/360 - 2*n**5/15 + n**4/18 - 2392*n**2. Suppose y(v) = 0. What is v?
-2, 0, 1/5, 1, 2
Let w(z) = z**2 - 13*z + 2. Let g be w(13). Let j(q) be the first derivative of 300*q - 17 - 7*q**2 + q**3 + 0*q**3 - 23*q**g. Factor j(y).
3*(y - 10)**2
Let v = -13570 + 488521/36. Let f(q) be the second derivative of -v*q**4 + 0*q**2 - 1/9*q**3 + 0 + 7*q. Find u such that f(u) = 0.
-2, 0
Let k(t) be the third derivative of -t**7/280 - t**6/60 + 19*t**5/40 + 5*t**4/2 + 51*t**3/2 - 156*t**2. Let x(y) be the first derivative of k(y). Factor x(d).
-3*(d - 4)*(d + 1)*(d + 5)
Factor 58*g**2 + 1086*g + 200*g + 352836 - 54*g**2 + 1090*g.
4*(g + 297)**2
Suppose q = d + 280, d = -3*q + 7*q - 1135. Factor 95 + 135*v**2 - 5*v**3 - 175 + 225 + q*v.
-5*(v - 29)*(v + 1)**2
Let o(t) = -155*t**2 - 112915*t - 37476125. Let s(k) = -9*k**2 - 6642*k - 2204478. Let z(m) = -2*o(m) + 35*s(m). Factor z(r).
-5*(r + 664)**2
Let c(i) be the second derivative of -5*i**4/72 + 2075*i**3/18 + 7*i + 91. Factor c(z).
-5*z*(z - 830)/6
What is b in 1242/11*b**2 + 8/11*b - 1656/11 + 2/11*b**4 - 420/11*b**3 = 0?
-1, 2, 207
Let z be (44/66)/(144/30 + -3). Let t(j) be the second derivative of 1/10*j**5 + 19*j - z*j**4 + 0 + 13/27*j**3 - 2/9*j**2. Determine b, given that t(b) = 0.
2/9, 1
Let f(n) be the third derivative of -n**5/20 - 539*n**4/8 + 270*n**3 + 1920*n**2. Factor f(x).
-3*(x - 1)*(x + 540)
Let m = -2 - -4. Let d be m + -2 + (1 - -6 - 0). Factor -3*i**5 + 0*i**5 + 3*i + i**2 - d*i**2 + 86*i**4 - 80*i**4.
-3*i*(i - 1)**3*(i + 1)
Let f(k) be the first derivative of -5*k**6/2 - 11*k**5 + 375*k**4/4 + 385*k**3 + 520*k**2 + 300*k - 1196. Determine g, given that f(g) = 0.
-6, -1, -2/3, 5
Let x(q) be the third derivative of q**6/420 + 3*q**5/70 - 17*q**4/42 + 8*q**3/7 + 2013*q**2. Factor x(h).
2*(h - 2)*(h - 1)*(h + 12)/7
Let y(x) be the second derivative of -x**5/210 - x**4/6 - 7*x**3/3 - 27*x**2/2 + 61*x. Let i(m) be the first derivative of y(m). Find r, given that i(r) = 0.
-7
Let i(z) be the first derivative of -z**7/280 - z**6/20 - z**5/5 + 13*z**3/3 + 2*z + 245. Let m(f) be the third derivative of i(f). Factor m(d).
-3*d*(d + 2)*(d + 4)
Let r(t) = 5*t**2 + 15005*t + 5625015. Let g(n) = -2*n**2 - 7503*n - 2812509. Let p(u) = -5*g(u) - 3*r(u). Determine h so that p(h) = 0.
-750
Suppose z + 4*y + 1 - 12 = 0, -2*y = 2. Let t be ((-12)/z)/(4/(-10)). Factor -7*o**t + 4*o + 3*o**2 + 8 - 8.
-4*o*(o - 1)
Factor 1/4*h**2 + 80089/4 + 283/2*h.
(h + 283)**2/4
Let k = 2007059/21660 + -142/1805. Let n = 280/3 - k. Factor 9/4 - n*w**2 - 3/2*w.
-3*(w - 1)*(w + 3)/4
Let k = -20 - -22. Let r(w) = 9*w + 7. Let f be r(k). Determine s, given that -10*s**5 + 45*s**5 - 8*s**4 - 10*s**3 + 10*s**2 - 2*s**4 - f*s**3 = 0.
-1, 0, 2/7, 1
Let d(r) = -r**2 + 8*r + 8. Suppose 5*f - 28 + 43 = 0. Let p(y) = y**2 - y - 2. Let j(w) = f*p(w) - d(w). Suppose j(z) = 0. What is z?
-2, -1/2
Let n = 782 + -779. Find p such that -6*p**2 - p**4 + 10*p**2 + 2*p**4 - 25*p + 9*p**n + 11*p**2 = 0.
-5, 0, 1
Let d = -3 - -5. Let p = 5753 + -5750. Solve 89*f**3 - 90*f**p - 2*f**2 + 2*f**d + f**5 = 0 for f.
-1, 0, 1
Suppose 11*w - 14 - 6 = -5*p, 0 = -w + 2*w. Determine t so that 2/13*t**p - 2/13*t**5 + 16/13*t**3 - 32/13*t + 32/13 - 16/13*t**2 = 0.
-2, 1, 2
Let a(m) be the first derivative of -m**8/84 + 8*m**7/105 - m**6/10 + 29*m**2 - 4. Let s(b) be the second derivative of a(b). Factor s(i).
-4*i**3*(i - 3)*(i - 1)
Let b(s) = s**3 + 27*s**2 - 10*s - 20. Let x be b(-26). Let p = 921 - x. Determine q so that 153/2*q**4 - 357/2*q**3 + 363/2*q**2 + 12 - 21/2*q**p - 81*q = 0.
2/7, 1, 4
Let q(p) be the second derivative of -25*p + 1/20*p**5 + 1/3*p**4 - 3*p**2 + 0 + 1/6*p**3. Solve q(g) = 0.
-3, -2, 1
Let v be (-3838)/404*(-56)/266. Factor -2*z + 0 - 2*z**v + 3/2*z**3 + z**4 - 1/2*z**5.
-z*(z - 2)**2*(z + 1)**2/2
Let t(w) be the third derivative of 5*w**6/288 + w**5/12 + w**4/6 + 41*w**3/6 + 78*w**2. Let u(k) be the first derivative of t(k). Factor u(c).
(5*c + 4)**2/4
Let b be -7 + 0 + 1 - (6 + -14). Let s(a) be the second derivative of 0 - 1/19*a**b - 14*a + 2/57*a**3 - 1/114*a**4. Let s(f) = 0. What is f?
1
Determine j, given that 21316 - 272/5*j**2 + 2/5*j**3 + 7738/5*j = 0.
-10, 73
Suppose -15 = 7*s + 4*w, -24 + 35 = 3*w + 38. Determine d so tha