*m**6 - 1/6*m**5 + 5/189*m**7 + 8/27*m**4. Determine n, given that x(n) = 0.
-2, 0, 2/5, 1
Let l be (2*409/715)/(12/15). Let q = l + 43/22. Factor 242/13 + 2/13*n**2 + q*n.
2*(n + 11)**2/13
Let l(q) be the first derivative of -552*q**3 - 64*q - 64 + 308*q**2 + 405/2*q**4. Factor l(b).
2*(5*b - 8)*(9*b - 2)**2
Let s be 1*16/4 - (-206)/2. Factor -4*c**4 + 112*c**3 - 107*c + s*c.
-4*c**3*(c - 28)
Let q(g) be the third derivative of -g**8/168 - g**7/105 + g**6/20 + g**5/6 + g**4/6 + 1043*g**2. Factor q(p).
-2*p*(p - 2)*(p + 1)**3
Let a be 2208/322 + (-3)/(-21) - (-174)/(-25). Let c(n) be the first derivative of 0*n + 10 + 1/5*n**3 + 1/5*n**2 - a*n**5 + 0*n**4. Factor c(v).
-v*(v - 2)*(v + 1)**2/5
Let m = 1295 - 1291. Let d(c) be the first derivative of 3*c**2 + 2/3*c**3 + 21 + m*c. Find x, given that d(x) = 0.
-2, -1
Let b(s) be the third derivative of s**6/12 + 37*s**5/30 - 34*s**4/3 - 20*s**3 - 2351*s**2. Factor b(d).
2*(d - 3)*(d + 10)*(5*d + 2)
Let m(h) be the first derivative of -h**6/42 - 89*h**5/35 + 461*h**4/28 - 839*h**3/21 + 328*h**2/7 - 188*h/7 + 2473. Suppose m(o) = 0. What is o?
-94, 1, 2
Let r = -416567/4236 + 9/1412. Let f = r + 99. Suppose 0*n + 2/3*n**2 - f = 0. Calculate n.
-1, 1
Let p(r) be the first derivative of -r**6/21 + 48*r**5/35 - 199*r**4/14 + 416*r**3/7 - 64*r**2 - 2649. Determine n so that p(n) = 0.
0, 1, 7, 8
Let d = 546 - 542. Suppose -25*o**d - 42*o**4 + 1000*o**2 - 4*o**5 + 2500*o + 27*o**4 = 0. Calculate o.
-5, 0, 5
Let l(r) be the first derivative of -4*r**3/3 + 332*r**2 - 660*r - 2792. Factor l(s).
-4*(s - 165)*(s - 1)
Suppose -8*y = -12*y + 40. Suppose -122 = -y*a - 12. Factor -7*j**3 + a*j + 3*j**5 - 5*j - 2*j**3 + 3*j**2 - 3*j**4.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Let f(d) be the first derivative of 1 - 49/2*d**2 + 16*d + 5*d**3. Let y(l) = l**2 + l. Let p(n) = -f(n) + 3*y(n). Factor p(r).
-4*(r - 4)*(3*r - 1)
Suppose 0 = 40*y - 51*y + 341. Suppose y - 21 = 5*q. Factor 11/2*o**q - 7*o**3 - 1 + 5/2*o.
-(o - 1)*(2*o + 1)*(7*o - 2)/2
Let u(t) be the second derivative of t**5/5 - 2*t**4/3 - 182*t**3/3 - 176*t**2 - 12*t + 122. Factor u(i).
4*(i - 11)*(i + 1)*(i + 8)
Let t(m) be the third derivative of m**5/90 - 15*m**4/2 + 536*m**3/9 + m**2 + 7. Factor t(y).
2*(y - 268)*(y - 2)/3
Let n(t) = 5*t**2 + 172 - 4*t**2 - 177. Let d be n(-5). Factor d*c + 5*c**2 - 1 + 2 - 1.
5*c*(c + 4)
Let z(s) be the third derivative of 0*s**4 + 1/40*s**7 - 1/20*s**5 - 3/40*s**6 + 0*s**3 + 0*s - 100*s**2 + 0. Let z(r) = 0. Calculate r.
-2/7, 0, 2
Let v(t) be the third derivative of -256*t**6/15 + 96*t**5/5 + 133*t**4/4 + 49*t**3/3 - t**2 - 16. Factor v(r).
-2*(r - 1)*(32*r + 7)**2
Let m = 1024248 - 3072737/3. Suppose 3/2*h**2 + m*h + 1/6*h**3 + 0 = 0. Calculate h.
-7, -2, 0
Solve 1740/11*g + 126150/11 + 6/11*g**2 = 0.
-145
Suppose 0 = -2*o + 3*v + 25 + 159, -4*o = -5*v - 366. Suppose 2*j - 53 = 3*k - 6*k, -5*k = -3*j + o. Factor -63*t**3 - 3*t**2 + 18*t - 12 - 14*t + j*t + 16*t.
-3*(t + 1)*(3*t - 2)*(7*t - 2)
Let l(c) be the third derivative of -c**5/75 + 314*c**4/15 - 197192*c**3/15 - 1600*c**2. Factor l(h).
-4*(h - 314)**2/5
Suppose -5*m**4 - 38/3*m - 71/3*m**3 - 31*m**2 + 0 + 1/3*m**5 = 0. Calculate m.
-2, -1, 0, 19
Solve 4107/4*c + 225/4*c**3 + 0 + 4329/4*c**2 + 3/4*c**4 = 0.
-37, -1, 0
Solve 16/11 - 8/11*s**4 + 76/11*s - 26/11*s**3 + 42/11*s**2 = 0 for s.
-4, -1, -1/4, 2
Suppose 2/5*k**4 + 0 - 13/5*k**2 + 23/5*k**3 - 12/5*k = 0. What is k?
-12, -1/2, 0, 1
Let m(w) be the third derivative of -w**8/504 - w**7/15 - 109*w**6/180 - 53*w**5/30 - 35*w**4/18 - 845*w**2. Determine n, given that m(n) = 0.
-14, -5, -1, 0
Factor 356*z + 7980*z - 4*z**2 - 2737464 - 1605592.
-4*(z - 1042)**2
Let m(p) = -p**2 + 22*p - 21. Let d be m(21). Let b be (-15 + (18 - 4))*3/(-1). Factor -9/4*w**2 + 3/4*w**4 + 3/2*w**b + d + 0*w.
3*w**2*(w - 1)*(w + 3)/4
Let l(f) = -23*f**3 - 163*f**2 + 613*f - 600. Let a(q) = 4*q**3 - q**2 + q. Let w(j) = 7*a(j) + l(j). Find b, given that w(b) = 0.
2, 30
Suppose 0 = 36*d - 71*d. Let q(l) be the second derivative of d*l**2 + 0 + 2/105*l**6 + 0*l**3 + 3/35*l**5 + 2/21*l**4 + 4*l. Determine w, given that q(w) = 0.
-2, -1, 0
Let r(i) = i**3 - 2*i**2 + 4*i. Let t(u) = -45*u**3 + 85*u**2 - 160*u. Let c(o) = 40*r(o) + t(o). Let c(g) = 0. What is g?
0, 1
Factor -2/15*k**2 + 76/15*k - 208/5.
-2*(k - 26)*(k - 12)/15
Let b(q) be the third derivative of 1/110*q**5 + 19 + 0*q + 0*q**3 - 1/385*q**7 - 1/1848*q**8 + 1/132*q**6 - 1/33*q**4 - 2*q**2. Solve b(t) = 0.
-4, -1, 0, 1
Determine c, given that -3588 - 37 - 4112 - 6164*c + 1577 - 4*c**2 = 0.
-1540, -1
Let a(x) be the second derivative of -x**4/16 - 37*x**3/2 + 225*x**2/2 - 2*x + 865. Suppose a(k) = 0. What is k?
-150, 2
Let h(i) = i**3 + 5*i**2 + 13*i - 3. Let y(b) = -2*b**3 - 10*b**2 - 25*b + 5. Suppose 77 = -5*d - 2*d. Let s(x) = d*h(x) - 6*y(x). Factor s(j).
(j + 1)**2*(j + 3)
Let q = 3318 + -3315. Let g(j) be the second derivative of -j - 1/5*j**2 - 1/90*j**4 - 4/45*j**q + 0. Solve g(i) = 0.
-3, -1
Suppose -12*g = 3315*b - 3317*b + 20, 4*b + g - 15 = 0. Factor 0 - 2/9*l**2 + 2/9*l**b - 4/9*l + 4/9*l**3.
2*l*(l - 1)*(l + 1)*(l + 2)/9
Let w(i) be the first derivative of -i**8/10080 + i**7/504 + i**6/90 + 21*i**3 - 2*i + 64. Let c(p) be the third derivative of w(p). Factor c(z).
-z**2*(z - 12)*(z + 2)/6
Let r(p) be the third derivative of 35/3*p**4 + 5/12*p**6 + 0 + 40*p**2 - 80/3*p**3 - 3*p**5 + 0*p - 1/42*p**7. Factor r(t).
-5*(t - 4)*(t - 2)**3
Let c(g) = -g**3 + 462*g**2. Let z(y) = -y**3 - 3*y**2. Let o(w) = -c(w) + 6*z(w). Factor o(k).
-5*k**2*(k + 96)
Let r(q) be the second derivative of q**4/4 - 47*q**3 + 819*q**2/2 + 919*q. Factor r(u).
3*(u - 91)*(u - 3)
Find n such that 129*n + 366 + 267*n - 6*n**2 + 333*n = 0.
-1/2, 122
What is x in -11*x**4 + 214384*x - 1220*x**3 - 70422*x**2 + 6*x**4 - 8718*x**2 - 1113920 - 790224*x = 0?
-118, -4
Let f(g) be the third derivative of g**8/840 + g**7/105 - 13*g**6/50 - 102*g**5/25 - 18*g**4 + 6020*g**2. Solve f(n) = 0.
-6, -3, 0, 10
Find n such that 14/11*n**4 - 14/11*n**2 - 12/11*n - 6/11*n**5 + 0 + 18/11*n**3 = 0.
-1, -2/3, 0, 1, 3
Let l(w) = 46*w + 125. Let t be l(-5). Let h be 2/(7*(-10)/t). Factor 0 - 1/12*n**5 + 0*n**4 - 1/12*n + 0*n**2 + 1/6*n**h.
-n*(n - 1)**2*(n + 1)**2/12
Find m such that -24 - 81*m**3 + 81*m + 69/2*m**2 - 21/2*m**4 = 0.
-8, -1, 2/7, 1
Let v(j) = 4*j**2 - 27*j - 111. Let b(k) = 502*k**2 - 498*k**2 - 68 - 42 - 26*k. Let u(i) = -3*b(i) + 2*v(i). Let u(p) = 0. Calculate p.
-3, 9
Let q(i) = 5*i**4 + 439*i**3 + 425*i**2 - 433*i - 430. Let s(x) = 25*x**4 + 2197*x**3 + 2125*x**2 - 2164*x - 2150. Let w(z) = 11*q(z) - 2*s(z). Factor w(r).
5*(r - 1)*(r + 1)**2*(r + 86)
Factor 770884/11 - 388954/11*w - 2/11*w**3 + 160*w**2.
-2*(w - 439)**2*(w - 2)/11
Factor 4822 + 26*q**3 - 332*q - 9532 + 226*q**2 + 4790.
2*(q - 1)*(q + 10)*(13*q - 4)
Let n(w) be the third derivative of w**7/525 + 31*w**6/25 - 25*w**2 - 25*w. Let n(p) = 0. Calculate p.
-372, 0
Let r(z) be the third derivative of 1/350*z**7 - 13/100*z**6 - 39/2*z**4 + 91*z**2 + 229/100*z**5 + 90*z**3 + 0*z + 0. Factor r(a).
3*(a - 10)**2*(a - 3)**2/5
Let y(v) be the second derivative of 1/4*v**4 - 2 + 9/2*v**2 + 184*v + 2*v**3. Find p such that y(p) = 0.
-3, -1
Suppose -172*m = -170*m + 427*m - 858. Suppose -27/5 - 369/5*s - 285*s**m - 1083/5*s**3 = 0. Calculate s.
-1, -3/19
Let o(r) be the third derivative of 0*r - 1/5*r**6 + 0 + 16/3*r**4 - 80*r**2 + 0*r**5 - 2/105*r**7 + 0*r**3. Factor o(g).
-4*g*(g - 2)*(g + 4)**2
Let h(t) be the third derivative of -7*t**6/600 + 19*t**5/300 + 11*t**4/10 + 6*t**3/5 + 1345*t**2. Find k, given that h(k) = 0.
-3, -2/7, 6
Suppose -3*h = -3*y + 5*y - 30, 3*y - 15 = -2*h. Suppose 2*f - 4*a + a + 12 = 0, 3*f = -3*a + h. Factor f - 3/4*m**2 - 1/4*m**3 - 1/2*m.
-m*(m + 1)*(m + 2)/4
Let o(n) be the first derivative of 975/4*n**4 - 85 + 0*n + 5/6*n**6 - 375*n**3 + 29*n**5 + 0*n**2. Factor o(y).
5*y**2*(y - 1)*(y + 15)**2
Factor 14*v**4 + 3*v**4 - 21*v - 62*v**4 + 13*v**4 + 9*v**2 - 18 + 29*v**4 + 9*v**3.
-3*(v - 3)*(v - 2)*(v + 1)**2
Suppose h - 25 = 73*k - 78*k, -3*k + 15 = 4*h. Factor 3/2*g**3 + 0*g - 1/2*g**5 + 0*g**4 + g**2 + h.
-g**2*(g - 2)*(g + 1)**2/2
Let a(o) be the third derivative of o**6/100 - 971*o**5/300 - 1063*o**4/60 - 164*o**3