 w(o) be the third derivative of -o**5 + r - 1/14*o**7 - 5*o**2 + 0*o + 23/40*o**6 + 0*o**3 - 3/2*o**4. Factor w(u).
-3*u*(u - 3)*(u - 2)*(5*u + 2)
What is i in -9/7*i**3 + 0 + 0*i + 3/7*i**4 + 0*i**2 = 0?
0, 3
Factor z**2 + 450 + 5*z**2 - 95*z + 6*z**2 + 9*z**2 - 16*z**2.
5*(z - 10)*(z - 9)
Suppose -2*q + 2*p + 10424 = 0, 8*q - p + 20873 = 12*q. Factor -16 - 5242*m**2 + q*m**2 - 60*m - 4.
-5*(m + 2)*(5*m + 2)
Let s be (232/(-624) - 9/(-27))/(50/(-325)). Factor 7/4*c - 9/4*c**2 + 5/4*c**3 - s*c**4 - 1/2.
-(c - 2)*(c - 1)**3/4
Let j(f) = 6*f**3 - 4*f**2 - 17. Let a(r) = -7*r**3 + 6*r**2 + r + 18. Let q(h) = -5*a(h) - 6*j(h). Factor q(t).
-(t - 1)*(t + 3)*(t + 4)
Find x, given that 72/17 + 186/17*x - 210/17*x**3 + 2/17*x**2 - 50/17*x**4 = 0.
-4, -3/5, 1
Suppose -368*z + 370*z - 10 = 0. Factor 3 - 2*o**3 - 2*o**2 - 11*o**3 + 52*o + 0*o**3 + z.
-(o - 2)*(o + 2)*(13*o + 2)
Determine q, given that 6 - 3167230*q**2 + 3*q**3 - 9*q + 3167230*q**2 = 0.
-2, 1
Let c(l) = -10*l**2 + 116*l + 3353. Let s(b) = 2*b + 12. Let v be s(-17). Let n(t) = t**2 + 1. Let q(o) = v*n(o) - 2*c(o). Suppose q(i) = 0. Calculate i.
-58
Let w be -1*(-2 - -3) - (-323556)/9140. Factor -2/5*m**2 - w*m - 3698/5.
-2*(m + 43)**2/5
Let y be (-10)/3*297/(-693) - (-10 + 0). Factor -2/7*j**2 - 78/7 - y*j.
-2*(j + 1)*(j + 39)/7
Let w(s) be the first derivative of s**6/120 + s**5/2 + 25*s**4/2 + 101*s**3/3 - 56. Let q(t) be the third derivative of w(t). Find j, given that q(j) = 0.
-10
Suppose -k = 5*h - h - 22, -h + 16 = 2*k. Let z = 13 - k. Let -9*i**2 + 4*i**2 - z*i**3 + 15*i - 8*i**3 + 5*i**4 = 0. Calculate i.
-1, 0, 1, 3
Suppose -27 + 7 = -4*i. Factor -i*y**5 - 7*y**5 + 11*y**5 + 3*y**4 + 6*y**3 - 2*y**5.
-3*y**3*(y - 2)*(y + 1)
Solve 34/19*o**3 + 564/19*o + 2/19*o**5 - 54/19*o**4 + 208/19 + 446/19*o**2 = 0 for o.
-1, 4, 26
Factor 57*c + 0 + 343/3*c**2 + 173/3*c**3 + 1/3*c**4.
c*(c + 1)**2*(c + 171)/3
Suppose -14*n + 12*n = -150. Let v = n + -69. Determine x, given that v*x**4 - 25*x**2 - 876*x**3 + 816*x**3 + 60*x + 39*x**4 - 20 = 0.
-1, 2/3, 1
Let s(w) be the first derivative of w**4/30 - 2*w**3/5 - 72*w**2/5 + 288*w - 957. Factor s(h).
2*(h - 12)**2*(h + 15)/15
Let d(c) be the second derivative of -49*c**7/2 + 30919*c**6/10 - 630*c**5 - 4706*c**4 - 3416*c**3 - 1080*c**2 + 1210*c. Let d(m) = 0. What is m?
-2/7, 1, 90
Let k(t) = 15 - 13 + 36*t**2 + 1 - 33*t**2 - 6*t. Let v(p) = -3*p**2 + 5*p - 4. Let c = -13 + 9. Let o(y) = c*k(y) - 3*v(y). Solve o(u) = 0.
0, 3
Suppose -2*d + 333 = 7*d. Let i = d + -34. Factor 4*o**4 - 2*o**3 + 0*o**3 + 2*o**i - 4*o**2 - 4*o**3 + 4*o**5.
4*o**2*(o - 1)*(o + 1)**2
Let b(u) be the first derivative of 2*u**5/15 - u**4/2 - 50*u**3/9 - 7*u**2 + 7210. Factor b(g).
2*g*(g - 7)*(g + 1)*(g + 3)/3
Let m(t) be the first derivative of t**4/12 - 11*t**3/6 - 6*t**2 - 62*t + 34. Let y(r) be the first derivative of m(r). Suppose y(z) = 0. Calculate z.
-1, 12
Let v = 150344/67347 - 76/7483. Suppose -2/3*l**3 + 46/9*l + v + 20/9*l**2 = 0. What is l?
-1, -2/3, 5
Let y(x) be the first derivative of -1/54*x**4 + 1/135*x**6 - 1/45*x**5 + 17 + 0*x**2 + 11*x + 2/27*x**3. Let d(p) be the first derivative of y(p). Factor d(f).
2*f*(f - 2)*(f - 1)*(f + 1)/9
Factor 4932/11 + 6/11*n**2 - 4938/11*n.
6*(n - 822)*(n - 1)/11
What is b in 2/3*b**2 - 50/3*b - 100 = 0?
-5, 30
Let k(n) be the first derivative of 1/28*n**4 - 16 + 0*n**2 + 1/35*n**6 + 9/140*n**5 - 11*n + 0*n**3. Let c(g) be the first derivative of k(g). Factor c(d).
3*d**2*(d + 1)*(2*d + 1)/7
Suppose 0 = 184*n - 202*n + 90. Suppose -i = -3*f + 10, 0 = -n*i - 3*f - 4 + 26. Factor 4/3*m**4 + 2*m**i + 0*m + 10/3*m**3 + 0.
2*m**2*(m + 1)*(2*m + 3)/3
Let t(g) be the third derivative of -180*g**3 + 0*g + 45/2*g**4 - 3/2*g**5 + 77*g**2 + 0 + 1/24*g**6. Factor t(w).
5*(w - 6)**3
Let m(d) be the second derivative of -d**4/78 + 2464*d**3/39 - 1517824*d**2/13 - 19*d + 157. Suppose m(w) = 0. What is w?
1232
Let d be (-6)/14 - 624/(-84). Let c(o) be the first derivative of d - 4/3*o**3 - 2*o**2 + 8*o. What is i in c(i) = 0?
-2, 1
Factor -224*c**4 + 0*c + 25088*c**3 + 2/3*c**5 - 2809856/3*c**2 + 0.
2*c**2*(c - 112)**3/3
Suppose -479 - 601 - 62*h**3 - 10*h**4 + 3762*h + 2*h**4 + 29*h**4 + 159*h**2 - 280*h**3 = 0. What is h?
-3, 2/7, 4, 15
Let x(f) = -f**2 + 158*f - 601. Let c be x(4). Let s(r) be the first derivative of -5/3*r**3 + c*r + 5*r**2 + 7. Factor s(j).
-5*(j - 3)*(j + 1)
Let b(s) = -19*s**3 - 6*s**2 + 2520*s + 46391. Let l(g) = 2*g**3 + g**2 - 15. Let i(k) = 2*b(k) + 18*l(k). Solve i(h) = 0 for h.
-28, 59
Let g = 4825745/4 - 1206433. What is z in -1/4*z**3 - 7/4*z**2 + 1/4*z**4 + g*z - 3/2 = 0?
-3, 1, 2
Let r be (2/(-4))/(2/(-144)). Let m be r/84 - 50/(-14). Factor 4*a**5 - 152*a**2 + 100*a**3 + 211 + 21*a**m - 53*a**4 + 112*a - 243.
4*(a - 2)**3*(a - 1)**2
Let c(m) be the first derivative of m**6/15 + 38*m**5/25 + 117*m**4/10 + 198*m**3/5 + 54*m**2 - 2260. Factor c(o).
2*o*(o + 3)**3*(o + 10)/5
Factor -2/13*t**2 - 42/13 - 20/13*t.
-2*(t + 3)*(t + 7)/13
Let q(s) be the second derivative of s**4/4 - 819*s**3 + 2012283*s**2/2 + 781*s. Find n, given that q(n) = 0.
819
Let d(q) be the second derivative of q**6/120 + q**5/10 + q**4/3 - 25*q**2/2 + 74*q. Let s(g) be the first derivative of d(g). Find m, given that s(m) = 0.
-4, -2, 0
Suppose 3*n + 5*u - 20 = 0, -31 = 5*n - 5*u - 11. Let h(s) = 423*s - 2961. Let k be h(7). Factor 0*v + 2/3*v**4 + n - 2/3*v**2 + k*v**3.
2*v**2*(v - 1)*(v + 1)/3
Let k = -9148 - -9154. Let u(t) be the third derivative of -1/90*t**4 + 0*t + 1/150*t**5 + 0*t**3 - 1/900*t**k + 19*t**2 + 0. Factor u(f).
-2*f*(f - 2)*(f - 1)/15
Let a(s) be the third derivative of s**6/540 + 16*s**5/15 - 289*s**4/108 - 2463*s**2. Factor a(h).
2*h*(h - 1)*(h + 289)/9
Let c be 5 - (-30)/42 - (-2)/7. Suppose -c*d + 3*d = 4*f - 34, 0 = 3*d - 4*f - 26. Factor -15*w - 25*w - 90 - 4*w**2 - d + 0*w**2.
-4*(w + 5)**2
Let i be ((-6)/(-8) - 2) + ((-900)/(-80))/9. Let x(p) be the first derivative of 0*p**2 - 21 + 2/35*p**5 + 0*p**3 + 1/42*p**6 + 1/28*p**4 + i*p. Solve x(k) = 0.
-1, 0
Let z(d) = -103*d**3 + 825*d**2 - 10913*d - 11737. Let u(y) = -65*y**3 + 550*y**2 - 7275*y - 7825. Let h(o) = -8*u(o) + 5*z(o). Let h(j) = 0. What is j?
-1, 27, 29
Let f(w) be the third derivative of -w**6/30 + 2*w**5/5 - 8*w**2 - 47. Factor f(n).
-4*n**2*(n - 6)
Let g be 8/6 + 22/(-9)*(-4455)/1188. Solve 11*x**2 - 1/2*x**5 - g*x**3 + 0 + 4*x**4 - 4*x = 0 for x.
0, 1, 2, 4
Let w be (((-18)/5)/(30/(-75)))/1. Let x(j) = 4*j**2 - 32*j + 60. Let d(i) = i**2 - 8*i + 15. Let o(p) = w*d(p) - 2*x(p). Factor o(k).
(k - 5)*(k - 3)
Let t(b) be the second derivative of -b**5/90 - 13*b**4/54 - 44*b**3/27 - 32*b**2/9 - 146*b + 2. Solve t(c) = 0.
-8, -4, -1
Let p be (-1 - -17)*(-5)/10*3. Let a be (-6)/p*(-12)/(-21). Solve 0 + 2/7*h + a*h**2 = 0.
-2, 0
Factor 14*k**2 - 28*k**3 - 59*k**3 - 244*k**2 + 6*k**2 - 16 + 11*k**3 + 316*k.
-4*(k - 1)*(k + 4)*(19*k - 1)
Let j(a) be the first derivative of -a**6/4 + 308*a**5 - 794631*a**4/8 + 1052161*a**3/3 - 459264*a**2 + 262144*a - 5427. Let j(i) = 0. What is i?
2/3, 1, 512
Suppose -109 = -11*c + 254. Let x = 585 + c. Suppose -x + 603 - 5*a**3 + 9*a - 5*a**2 + 16*a = 0. Calculate a.
-3, 1
Let w(y) = 15*y**4 + 27*y**3 - 55*y**2 + 25*y - 4. Let c(z) = 78*z**4 + 135*z**3 - 273*z**2 + 123*z - 21. Let j(v) = -4*c(v) + 21*w(v). Factor j(h).
3*h*(h - 1)**2*(h + 11)
Let b(x) = -13*x**2 - 104*x - 496. Let p = 10 - 6. Let f = -7157 + 7156. Let n(r) = -2*r**2 - r + 1. Let w(d) = f*b(d) + p*n(d). Solve w(u) = 0.
-10
Let z(d) be the third derivative of d**8/3920 + 2*d**7/2205 - d**6/1260 + 7*d**5/6 - 81*d**2. Let x(w) be the third derivative of z(w). Factor x(p).
4*(p + 1)*(9*p - 1)/7
Let m(l) be the second derivative of -l**7/21 - 50*l**6/3 + 506*l**5/5 - 508*l**4/3 + 68*l + 12. Let m(n) = 0. What is n?
-254, 0, 2
Let w(u) = u**3 - 6*u**2 - 6*u - 4. Let d be w(7). Suppose -8 = d*n - 7*n. What is r in 4*r**2 - n*r + r**3 - 4 + 0*r + 5*r**3 - 4*r**3 = 0?
-2, -1, 1
Factor -3/8*f**2 - 121203/2 - 603/2*f.
-3*(f + 402)**2/8
Let t(b) = 4*b**2 + 189*b + 95. Let f(n) = -2*n**2 - 86*n - 48. Let u(l) = -5*f(l) - 2*t(l). Factor u(z).
2*(z + 1)*(z + 25)
Factor -4/3*d**2 + 116*d - 680/3.
-4*(d - 85)*(d - 2)/3
What is y in 4720/3*y - 1/3*y**2 - 5569600/3