w) be the first derivative of -2*w**4 - 766*w**3/3 - 9120*w**2 + 4608*w - 1068. What is q in p(q) = 0?
-48, 1/4
Let s = 16966 - 16963. Let d(u) be the first derivative of 5/7*u - 30 + 1/21*u**s - 3/7*u**2. Factor d(m).
(m - 5)*(m - 1)/7
Let m(d) be the first derivative of -d**3/3 - 494*d**2 - 244036*d + 1803. Let m(l) = 0. What is l?
-494
Factor 2*q**2 - 218*q + 0*q**2 + 372*q + 40 + q**2 - 197*q.
(q - 1)*(3*q - 40)
Let b(r) = -49*r**3 + 584*r**2 + 2209*r - 40535. Let s(o) = -4*o**3 + 48*o**2 + 184*o - 3378. Let m(n) = -4*b(n) + 50*s(n). Factor m(x).
-4*(x - 13)**2*(x + 10)
Let m(s) = s**2 - 14*s - 29. Let t = 42 + -26. Let a be m(t). Determine n, given that -13*n - 3*n**2 - 2 + n**4 + 8*n + 0*n**3 + n**a = 0.
-1, 2
Factor 115*x + 5*x**3 - 179*x**2 + 42*x**2 + 59*x**2 - 75 + 33*x**2.
5*(x - 5)*(x - 3)*(x - 1)
Let y(z) = -408*z**3 - 828*z**2 - 417*z + 3. Let x(u) = -u**4 - 409*u**3 - 831*u**2 - 419*u + 4. Let g(c) = -3*x(c) + 4*y(c). Find r, given that g(r) = 0.
-1, 0, 137
Determine n, given that 16*n**2 + 24*n - 6723*n**3 + 3367*n**3 + 3358*n**3 = 0.
-6, -2, 0
Let z(t) = -145*t**3 + 17535*t**2 - 34770*t + 17335. Let l(g) = -13*g**3 + 1594*g**2 - 3161*g + 1576. Let n(k) = 45*l(k) - 4*z(k). Factor n(j).
-5*(j - 316)*(j - 1)**2
Suppose y + 3*t - 486 = 0, -350 = 2*y + 3*t - 1316. Let w = -303 + y. Let 16 - 68*m**4 - 40*m - 108*m**2 - 2*m**4 + w*m**3 + 25*m**3 = 0. Calculate m.
-2/5, 2/7, 1, 2
Let d(v) be the first derivative of v**6/3 - 34*v**5/5 + 39*v**4 - 284*v**3/3 + 113*v**2 - 66*v - 10194. Suppose d(c) = 0. Calculate c.
1, 3, 11
Let p(q) be the third derivative of -q**5/15 - 5*q**4/2 + 36*q**3 - 68*q**2 - 15*q. Find s, given that p(s) = 0.
-18, 3
Let w(g) be the second derivative of -g**5/50 - 1157*g**4/30 - 2311*g**3/15 - 231*g**2 - 19*g + 3. Factor w(q).
-2*(q + 1)**2*(q + 1155)/5
Suppose 45 = 583*i - 574*i. Let o be 264/55 - (9 + i/(-1)). Suppose 0*n + o*n**2 - n**4 - 8/5*n**3 + 0 = 0. What is n?
-2, 0, 2/5
Let u = -124 - -78. Let f = -42 - u. Solve -22*g**5 + 4 + 42*g**f - 33*g**2 - 27*g**3 - 4 - 6*g + 46*g**5 = 0 for g.
-2, -1/2, -1/4, 0, 1
Let u = -137 - -142. Factor -4*z**3 + 2*z**2 + 3 - 12 + z**u + 3*z + 7.
(z - 1)**3*(z + 1)*(z + 2)
Let -1260*v + 184*v**2 - 894*v + 270*v**2 - 58*v**4 + 40*v**2 + 504 - 8*v**5 + 242*v**3 + 20*v**4 = 0. Calculate v.
-7, -4, 1/4, 3
Suppose 4*o + 49 = 3*b + 8, 23 = 3*b + 5*o. Factor -5*j**3 + b*j**4 - 6*j - 37*j**2 - j**3 - 14*j**3.
j*(j - 3)*(j + 1)*(11*j + 2)
Let t(g) be the first derivative of -g**4/2 - 86*g**3/3 - 352*g**2 + 1606. Solve t(l) = 0 for l.
-32, -11, 0
Let v(j) be the third derivative of -j**5/150 - 19*j**4/60 - 139*j**2 - 2*j + 2. Factor v(h).
-2*h*(h + 19)/5
Let q = -4193301/5 + 838677. Solve -6/5*s**2 - q - 3/5*s**3 + 93/5*s = 0.
-7, 1, 4
Let q(h) = 1826*h**3 + 2*h**2. Let s be q(-1). Let w be s/(-352) + 1*-5. Factor -w*t**2 + 16/11*t - 32/11.
-2*(t - 4)**2/11
Suppose 5*w + 3*t = 42, 3*w - 14 = -0*t + t. Let -873 + 873 + 3*o**2 + w*o = 0. What is o?
-2, 0
Let a(g) be the first derivative of 74/39*g**3 - 27/13*g**2 + 166 - 18/13*g + 3/26*g**4 - 8/65*g**5. Determine d, given that a(d) = 0.
-3, -1/4, 1, 3
Determine v so that 8/17*v**5 + 62/17*v**4 - 36/17*v**2 + 54/17 + 128/17*v**3 - 216/17*v = 0.
-3, 1/4, 1
Solve 156/5*g**4 + 0 + 16/5*g**3 - 116/5*g**2 + 24/5*g = 0 for g.
-1, 0, 3/13, 2/3
Let v(s) be the third derivative of s**6/120 - 1153*s**5/30 + 1329409*s**4/24 - 70*s**2 - 3. Factor v(k).
k*(k - 1153)**2
Let p = 183 - 22. Let r(s) = -s**3 - 153*s - p*s - s**2 - 1 + 312*s + 5. Let k(j) = -j**3 - j**2 + j + 1. Let b(w) = 4*k(w) - r(w). Factor b(c).
-3*c*(c - 1)*(c + 2)
Let i be (-6)/(20 + -8)*0. Let z = -1161 + 1161. Solve 0*y - 1/7*y**2 + 1/7*y**4 + z*y**3 + i = 0 for y.
-1, 0, 1
Let i(m) = -94*m**3 - 363*m**2 - 312*m + 86. Let a(w) = -w**3 + 6*w - 1. Let k(u) = 2*a(u) + i(u). Factor k(q).
-3*(q + 2)**2*(32*q - 7)
Let d(w) = 7*w**3 - w**2 - w - 5. Let h(i) = -13*i**3 + i**2 + 5*i + 9. Let g(u) = -9*d(u) - 5*h(u). Factor g(n).
2*n*(n - 2)*(n + 4)
Suppose -4*l + 2092 = -u, 4*u = 39*l - 40*l + 506. Let -20 - 10*n**3 + 20*n - 507*n**2 - 7*n**4 + 2*n**4 + l*n**2 = 0. Calculate n.
-2, 1
Let v = 103 + -99. Find y, given that 7 - 21*y**v - 43*y - 1 + 27*y**3 + 15*y**2 + 16*y = 0.
-1, 2/7, 1
Let a(m) be the first derivative of -24336/5*m - 133 - 312/5*m**2 - 4/15*m**3. Suppose a(o) = 0. What is o?
-78
Let t = 1298345/9 - 435109/3. Let z = t - -776. Factor -2/3*f + z*f**3 + 8/9*f**2 - 4.
2*(f - 2)*(f + 3)**2/9
Let p(j) be the third derivative of -3*j**2 + 13/270*j**5 + 0*j**3 + 5*j - 1/1080*j**6 - 25/216*j**4 + 0. Let p(y) = 0. Calculate y.
0, 1, 25
Let r(b) = b**2 + 2*b + 1. Suppose 2*n + 8*v - 5*v = -17, -n = -3*v - 5. Let g(f) = 7*f**2 + 44*f + 64. Let t(m) = n*r(m) + g(m). Factor t(i).
3*(i + 2)*(i + 10)
Let v(h) be the first derivative of -h**6/33 + 4*h**5/11 + 9*h**4/11 - 712*h**3/33 + 623*h**2/11 - 588*h/11 - 1134. Solve v(z) = 0 for z.
-6, 1, 7
Let d(y) = 2*y**4 - 10*y**3 + 18*y**2 - 2*y - 8. Suppose -2*b + 6 = -0*b. Suppose 3*w - 6*w = b. Let z(p) = p - 1. Let c(a) = w*d(a) + 12*z(a). Factor c(i).
-2*(i - 2)*(i - 1)**3
Suppose 8*q - 4*q - 30 = -2*b, -5*q = -5*b - 15. Suppose 3*w + 6 = 6*w. Factor s**2 + 0*s**w - q*s**2 - 4*s - 11*s.
-5*s*(s + 3)
Let b(c) = -c**2 + 20*c - 72. Let t be b(5). What is y in -5/4*y**t + 15/4*y + 0*y**2 - 5/2 = 0?
-2, 1
Determine a so that -195*a - 1341/2*a**4 - 1071*a**2 + 21/4*a**5 + 0 - 6207/4*a**3 = 0.
-1, -2/7, 0, 130
Let b(g) be the second derivative of 3*g**6/2 + 9641*g**5/4 + 5738775*g**4/4 + 683763885*g**3/2 + 227496465*g**2 + 415*g - 4. Factor b(j).
5*(j + 357)**3*(9*j + 2)
Let c(s) be the third derivative of s**5/240 - 325*s**4/24 + 105625*s**3/6 - 104*s**2 + 15*s. Solve c(u) = 0 for u.
650
Let x = -88 + 88. Let g be 45/1 + (-2 - x). Factor -37*q**2 + 7 - 91*q**2 - 20*q**5 - 9*q - 88*q**4 - 15 - 152*q**3 - g*q.
-4*(q + 1)**4*(5*q + 2)
Factor 11*u**3 + 17*u**2 + 36 + 39 + 0 - 7 - 26 + u**4 - 71*u.
(u - 1)**2*(u + 6)*(u + 7)
Let p(r) = r**2 - r + 100. Let z(x) = -x**2 + 11759*x - 17287100. Let d(f) = 2*p(f) - 2*z(f). Determine u so that d(u) = 0.
2940
Let t(m) = m**3 + 2*m**2 - 7*m - 9. Let n be t(-3). Factor n*d**3 + 2*d**2 - 24*d + 2*d**2 - d**2 - 52 + 16.
3*(d - 3)*(d + 2)**2
Suppose 4*r = 9*r - 80. Determine t, given that 34*t**2 + 4*t**4 - 56*t**3 + r*t**2 + 12*t**3 - 14*t**2 + 44*t - 40 = 0.
-1, 1, 10
Solve 0*n + 78/5*n**2 + 0 + 2/5*n**3 = 0.
-39, 0
Let z(p) be the second derivative of -p**4 + 3403*p**3/2 + 2553*p**2/2 - 313*p. Factor z(w).
-3*(w - 851)*(4*w + 1)
Let p(f) be the third derivative of -f**6/900 + 7*f**5/10 - 207*f**4/20 + 309*f**3/5 + 2*f**2 + 58*f + 6. Let p(x) = 0. Calculate x.
3, 309
Let b be (-35)/(-10) - 4/8. Let n = -4917 + 24603/5. Factor 0 - 3/5*x**3 + b*x**2 - n*x.
-3*x*(x - 3)*(x - 2)/5
Let n = -323 + 326. Factor x**n + 6*x**2 - 3*x**5 + 25*x**2 - x**4 - 15*x**4 - 15*x**4 + 2*x**5.
-x**2*(x - 1)*(x + 1)*(x + 31)
Factor -84/5*o**3 - 4/5*o**4 + 0 + 0*o**2 + 0*o.
-4*o**3*(o + 21)/5
Let p = 663175/4 - 165793. Let -45/4*w**3 + 9/2*w + 15/4*w**5 - 9/4*w**4 - p*w**2 + 0 = 0. What is w?
-1, 0, 3/5, 2
Factor -4/3*q**5 + 0 - 2128*q**3 - 328/3*q**4 + 4704*q**2 + 0*q.
-4*q**2*(q - 2)*(q + 42)**2/3
Let m = -771 - -778. Suppose 4*a + m*j - 5*j = -4, 2 = -j. Suppose -9/2*v**2 + 0 - 21/4*v**3 - 2*v**4 - 1/4*v**5 + a*v = 0. Calculate v.
-3, -2, 0
Factor 136447*x**2 - x**5 - 100 + 209297*x**2 + 1177*x**4 + 28 + 72 - 346920*x**3.
-x**2*(x - 588)**2*(x - 1)
Let v = 71258/5 - 14251. Factor 33/5 + 6*t - v*t**2.
-3*(t - 11)*(t + 1)/5
Let n(k) be the first derivative of -k**5/360 - k**4/24 - k**3/4 + 28*k**2 - 2*k - 102. Let f(h) be the second derivative of n(h). Factor f(r).
-(r + 3)**2/6
Let b(f) = -21*f - 21. Let q be b(-9). Let a be ((-8)/(-6))/(q/2079). Suppose -21/2*n**2 - 3/2*n**3 - a*n - 15/2 = 0. What is n?
-5, -1
Let p = 240 + -561. Let u = p - -322. Factor -11/3*q**2 - 5/6*q**3 - u - 23/6*q.
-(q + 1)*(q + 3)*(5*q + 2)/6
Let 5/3*x**4 + 62/3*x + 19*x**2 - 16 - 16*x**3 = 0. Calculate x.
-1, 3/5, 2, 8
Let x(k) be the first derivative of 136*k**2 + 81 - 32*k - 568/3*k**3 + 55*k**4. Factor x(b).
4*(b - 2)*(5*b - 2)*(11*b - 2)
Let v(u) = 11*u**3 - 1895*u**2 + 178516*u + 180500. Let o(b) = -300*b**3 + 51165*b**2 - 4819890*b - 4873500. 