z**2 - 695520*z - 5/3*z**4 - 1080*z**3 = 0.
-322, -2
Suppose 3/5*f**2 + 273/5*f + 486 = 0. Calculate f.
-81, -10
Let f = 286 + -229. Factor 0*h + 3*h**5 + 39*h**2 + 16*h**4 - 9*h**3 + 30*h - f*h**4 + 26*h**4.
3*h*(h - 5)*(h - 2)*(h + 1)**2
Let t(c) be the second derivative of -c**5/5 - c**4/12 - c**3/6 - c**2/2 - 2*c. Let p be t(-1). Factor -4*u + u + 9*u**p + 3*u**4 - 6*u**3 - 3*u**2.
3*u*(u - 1)*(u + 1)**2
Let d be (-44)/(-9) - (484/99 + -5). Let p be (-49)/(-3) - (-11)/33. Find v, given that 0*v + 16/3*v**3 + 0 + 50/3*v**d + 8/15*v**2 + p*v**4 = 0.
-2/5, -1/5, 0
Suppose -273*x - 164*x - 484*x = 0. Factor -1/2*n**2 + 0 - 1/6*n**3 + x*n.
-n**2*(n + 3)/6
Let v = 41124/5 - 8224. Let i(n) be the first derivative of 1/5*n**4 + v*n**3 - 18/5*n**2 + 4*n - 23. Factor i(y).
4*(y - 1)**2*(y + 5)/5
Let l = -1306297 + 1306299. Determine s, given that 1/2*s**4 - l*s**5 - 6*s - 2*s**2 + 19/2*s**3 + 0 = 0.
-2, -3/4, 0, 1, 2
Let q be 13 + 4 - 3315/(-60). Solve -q - 153*o - 179/2*o**2 - 1/4*o**4 - 9*o**3 = 0 for o.
-17, -1
Let a = -72 + 79. Suppose a*s - 1447 = -257. Factor 2738*g**2 + 126*g + s*g + 829 - 821.
2*(37*g + 2)**2
Suppose 4*c + 3*a = 87, 5*a + 7 = -8. Factor -23*o**2 - c*o**2 - 35 + 48*o**2 - 55*o - 21*o**2.
-5*(o + 1)*(4*o + 7)
Let o(r) be the first derivative of r**3/3 - 129. Let k(h) = 2*h**3 + h**2 - 8*h + 40. Let a(p) = -2*k(p) + 22*o(p). Let a(i) = 0. Calculate i.
-2, 2, 5
Let w(m) be the first derivative of 121*m**5/120 - 55*m**4/24 + 4*m**3/3 - m**2/3 - 20*m - 20. Let c(t) be the first derivative of w(t). Factor c(y).
(y - 1)*(11*y - 2)**2/6
Let a(g) = g**3 - 50*g**2 + 378*g - 365. Let x be a(41). Factor -8/7*h - 12/7*h**x + 0 + 4/7*h**2 + 16/7*h**3.
-4*h*(h - 1)**2*(3*h + 2)/7
Let q be 5 - (-2)/(-12*(-16)/(-384)). Solve -q - 2*p**3 - 5/2*p**5 + 6*p**4 + 9/2*p - 5*p**2 = 0 for p.
-1, 2/5, 1
Suppose 0 = 47*d - 45*d + o - 3, 4*o = -5*d. Let f(g) be the first derivative of 4/3*g**3 - 9 - d*g**2 + 4*g. What is u in f(u) = 0?
1
Find a, given that -239/4 + 1/4*a**2 + 119/2*a = 0.
-239, 1
Let l = -320180 - -960542/3. Factor 8*x**2 + 0 - 24*x - l*x**3.
-2*x*(x - 6)**2/3
Suppose 100 - 38 - 2*v**4 - 2*v**3 - 110*v + 168*v**2 - 206*v - 2*v**3 + 92 = 0. What is v?
-11, 1, 7
Let t(d) be the third derivative of -d**6/300 + 13*d**5/30 + 17*d**4/5 + d**2 + 418. Factor t(j).
-2*j*(j - 68)*(j + 3)/5
Let k(h) be the third derivative of h**7/1260 - 5*h**5/72 + 5*h**4/12 - h**3 + 2630*h**2. Suppose k(i) = 0. Calculate i.
-6, 1, 2, 3
Let p(j) be the third derivative of -j**5/60 + 29*j**4/3 + 235*j**3/2 - 1403*j**2. Suppose p(g) = 0. What is g?
-3, 235
Suppose -4*k = -4*m - 156, 4*k = -23 + 3. Let s = -40 - m. Factor -6*o**2 - o**3 - o**2 - s - 8*o + 2*o**2.
-(o + 1)*(o + 2)**2
Let i = 1343 - 1323. Suppose -y + 3*y + 16 = 4*f, 5*f = i. Let y*v**2 + 1/6*v**3 - 1/2*v + 1/3 = 0. Calculate v.
-2, 1
Let d be (58/2)/((-1)/(-1)). Let q be 22 - (-180)/((-120)/10). Factor -d - o**2 + 20*o - 41 + q - 37.
-(o - 10)**2
Let w(a) be the second derivative of -30*a + 1 + 0*a**2 - 7/2*a**3 + 1/2*a**4. Find k, given that w(k) = 0.
0, 7/2
Let b(z) be the third derivative of z**8/63 - 2*z**7/21 - 4*z**6/5 + 79*z**5/45 + 28*z**4/3 + 8*z**3 + 11*z**2 + 3. Find r such that b(r) = 0.
-3, -1, -1/4, 2, 6
Factor 4608*z**3 - 2082*z**2 + 48*z + 381*z**5 + 70*z**4 - 582*z**4 - 357*z**4 - 1038*z**2 - 1423*z**4.
3*z*(z - 2)**3*(127*z - 2)
Let o(w) be the second derivative of w**7/14 + 14*w**6/15 - 23*w**5/20 - 7*w**4/3 + 10*w**3/3 - 1860*w. Determine c so that o(c) = 0.
-10, -1, 0, 2/3, 1
Let p(v) be the second derivative of -v**5/20 - v**4/6 + 9*v**3 + 111*v**2/2 - 318*v. Let a be p(-2). Factor -2/13*g**a - 8/13 - 12/13*g**2 - 18/13*g.
-2*(g + 1)**2*(g + 4)/13
Let u be 5/(140/(-8)) + (-212)/(-7). Factor -3282*h**2 + 13*h**3 - u*h - 43*h**3 + 3337*h**2 + 5*h**4.
5*h*(h - 3)*(h - 2)*(h - 1)
Let c(h) = -16*h - 184. Let w(l) = 59*l + 736. Let u(v) = -9*c(v) - 2*w(v). Let x be u(-7). Factor -2/3*b**x + 4/3*b**3 + 0 + 0*b - 2/3*b**4.
-2*b**2*(b - 1)**2/3
Let x(j) be the first derivative of -2 - 21/8*j**2 + 1/12*j**3 + 5*j. Factor x(t).
(t - 20)*(t - 1)/4
Let l(y) be the first derivative of -2*y**5/55 - 2*y**4/11 + 2*y**3/11 + 14*y**2/11 + 16*y/11 + 822. Determine x, given that l(x) = 0.
-4, -1, 2
Let k be 1192/3036 - 384/13248. Factor -14/11*t - k*t**4 - 4/11*t**3 + 2/11*t**5 + 16/11*t**2 + 4/11.
2*(t - 1)**4*(t + 2)/11
Let u = -28 - -43. Let d(z) = z**3 - 16*z**2 + 13*z + 34. Let x be d(u). Suppose -39 + 78 - 39 + 4*f**5 - x*f - 8*f**4 + 8*f**2 = 0. What is f?
-1, 0, 1
Factor -1/3*f**5 + 229/3*f**4 - 16843/3*f**3 + 347047/3*f**2 + 3644744/3*f + 7888624/3.
-(f - 79)**3*(f + 4)**2/3
Suppose 0 = 3*t + 10*t - 47515. Let k be ((-2)/(-5))/(129/t). Let -4*m - 10/3*m**3 + k*m**2 + 0 = 0. What is m?
0, 2/5, 3
Let a(u) = 5 + 3*u**3 + 0 - 27*u**4 + 30*u**4 + 6*u**2 + 10*u - 1. Let p(k) = 2*k**4 + 2*k**3 + 6*k**2 + 10*k + 4. Let h(n) = 4*a(n) - 5*p(n). Factor h(c).
2*(c - 2)*(c + 1)**3
Let d(a) be the second derivative of -a**6/135 + 16*a**5/45 - 58*a**4/27 + 112*a**3/27 + 1214*a. Find z such that d(z) = 0.
0, 2, 28
Let j(f) be the first derivative of -f**4/8 - 33*f**3 + 100*f**2 + 7407. Determine q, given that j(q) = 0.
-200, 0, 2
Let m = -37364/15 - -2491. Let i(h) be the third derivative of 11*h**2 - 4/3*h**3 + m*h**5 + 1/6*h**4 + 0*h + 0. Factor i(s).
4*(s - 1)*(s + 2)
Let m(n) be the first derivative of -72*n**3 - 278*n**2 - 40*n - 1724. Factor m(u).
-4*(2*u + 5)*(27*u + 2)
Let y be (-2)/(-10) + 4 + 30/(-25). Let o be y + 4 + 16/4 + -9. Factor -2/7*w + 0 - 9/7*w**4 + 9/7*w**o + 2/7*w**3.
-w*(w - 1)*(w + 1)*(9*w - 2)/7
Let v(r) be the third derivative of 0*r**4 - 68*r - 1/60*r**5 + r**2 + 2/3*r**3 + 0. Determine k so that v(k) = 0.
-2, 2
Determine n, given that 5892/5*n + 2352/5 + 6*n**2 = 0.
-196, -2/5
Let t be 0*((-1)/(-2))/1. Let j be 282/(-987) + (t - (-58)/56). Determine z, given that -1/2*z**2 - 1/4*z + j*z**3 + 0 = 0.
-1/3, 0, 1
Let 54*o**2 + 7761*o**3 - 228 - 7800*o**3 + 612 + 480*o + 3*o**4 = 0. What is o?
-2, -1, 8
Let r(k) be the second derivative of k**4/6 + 5*k**3/3 + 6*k**2 + 689*k. Factor r(w).
2*(w + 2)*(w + 3)
Let d = -767/658 + 123/94. Solve -400/7 - d*n**2 - 40/7*n = 0.
-20
Let r = 4/4433 - 204234/350207. Let k = 2673/158 - r. Factor 18*t - 177*t**2 + 20 + k*t**3.
(t - 10)*(5*t - 2)*(7*t + 2)/2
Solve -2/17*w**2 + 110/17*w - 76 = 0 for w.
17, 38
Let c(w) be the first derivative of -25*w**4/4 - 445*w**3 - 1540*w**2 - 1020*w + 214. Factor c(a).
-5*(a + 2)*(a + 51)*(5*a + 2)
Let i(f) be the first derivative of 1/38*f**4 - 12/19*f - 8/57*f**3 - 11/19*f**2 - 40. Factor i(k).
2*(k - 6)*(k + 1)**2/19
Let c(m) = 8*m + 26. Let r be c(-3). Factor 0*h**5 + 12*h**4 + 2*h**5 + 14*h**4 + 12*h**r + 90*h**2 + 112*h**3 + 58*h**2.
2*h**2*(h + 4)**2*(h + 5)
Let k(r) be the third derivative of r**6/24 - 11*r**5/2 + 80*r**4/3 + 4*r**2 - 13*r + 9. Suppose k(n) = 0. What is n?
0, 2, 64
Suppose -69*m - 3/2*m**2 - 792 = 0. Calculate m.
-24, -22
Let w(b) = -9*b - 13. Let i be w(-11). Let k = 94 - i. Factor 2*r**3 - 2*r**2 + 0*r**2 + 0*r**3 - 10*r**5 + k*r**5 + 2*r**4.
-2*r**2*(r - 1)**2*(r + 1)
Let m = 3776137/2795716 + -2037/1252. Let c = 3/319 - m. Factor -6/7*q + c*q**2 + 4/7.
2*(q - 2)*(q - 1)/7
Let x(n) be the second derivative of n**4/12 - n**3/2 - 8*n**2 - 2*n. Let g be x(6). Factor 35*c + 42 - 15 + c + 5 + 4*c**g.
4*(c + 1)*(c + 8)
Solve 0 + 1000/3*v**2 - 1984/3*v - 4/3*v**3 = 0 for v.
0, 2, 248
Let o(h) be the second derivative of h**5/60 - 15*h**4/8 + 22*h**3/3 + 183*h**2/2 - 6*h + 12. Let x(w) be the first derivative of o(w). Let x(r) = 0. What is r?
1, 44
Let g = -2305218/23 + 100228. Factor -8/23 - 6/23*n**3 - 32/23*n - g*n**2.
-2*(n + 2)**2*(3*n + 1)/23
Let d(u) be the second derivative of 4/3*u**3 - 1/3*u**4 + 11 - 2*u**2 + 4*u. Determine f so that d(f) = 0.
1
Let l = -602291/6 + 101199. Let b = l - 817. Suppose 1/3*y**4 - b*y**5 - 1/3*y**2 + 1/6*y**3 + 0*y + 0 = 0. Calculate y.
-1, 0, 1, 2
Let u(s) be the second derivative of -s**5/20 + 3*s**4/4 - 5*s**3/2 + 7*s**2/2 + 629*s. Factor u(k).
-(k - 7)*(k - 1)**2
Suppose 622*m + 80*m + 144*m - 1554 = 69*m. Factor -2/3*l**m - 1/6*l**3 + 0 + 5/6*l.
-l*(l - 1)*(l + 5)/6
Suppose 2 + 5/2*g + 1/2*g**2 = 0. Calculate g.
-4, -1
Let q be (21/42)/(3/(-12))