t k be (d/(-6))/(6/144). Factor s**2 + s**2 - k + s**2 - 4*s**2 + 8*s.
-(s - 4)**2
Let y(w) be the third derivative of -w**5/120 - 23*w**4/24 + 49*w**3/4 - w**2 + 341. Factor y(s).
-(s - 3)*(s + 49)/2
Let j(o) be the third derivative of 0*o - 1/480*o**6 - 17/32*o**4 - 13/240*o**5 - 4*o**2 - 21/8*o**3 + 0. Find z such that j(z) = 0.
-7, -3
Determine b so that 2374 + 6637*b**2 + 9363*b**2 + 14*b**5 + 1092 + 5520*b**3 + 1718 + 476*b**4 - 2*b**5 + 16128*b = 0.
-18, -2, -1, -2/3
Let f(q) be the first derivative of q**6/24 + 3*q**5/20 + q**4/8 - 4233. Let f(y) = 0. What is y?
-2, -1, 0
Suppose -5*a + 2*a = -5*f + 157, -5*f + 59 = -a. Let b = -46 - a. Factor -2*n**2 + 4*n**2 - 7*n**2 - 4*n + b*n**2.
-2*n*(n + 2)
Let d(j) be the third derivative of -j**5/12 + 695*j**4/6 - 193210*j**3/3 - 8*j**2 + 169*j. Factor d(b).
-5*(b - 278)**2
Let m(f) be the first derivative of -f**6/3 + 14*f**5/15 - 8*f**3/9 + 3726. Suppose m(v) = 0. What is v?
-2/3, 0, 1, 2
Let i(c) = -5*c**2 - 2*c + 2. Let a be i(-2). Let l be (-8)/a*42/36. Suppose -l*h**2 - 8/3 + 1/3*h**4 + 4*h - h**3 = 0. Calculate h.
-2, 1, 2
Let w = -205 + 207. Let h be (29 - 21) + (-12)/w. Factor 2/5*v**h - 2/5*v + 0.
2*v*(v - 1)/5
Factor -1/3*d**2 - 506763 + 822*d.
-(d - 1233)**2/3
Let r(l) = -l**4 + 2*l**2 - 2*l + 1. Let j be ((-2)/10)/(4/(-60) + 0). Let d(y) = y**4 + y**3 - 3*y**2 + 2*y - 1. Let k(t) = j*r(t) + 2*d(t). Factor k(c).
-(c - 1)**3*(c + 1)
Let x be 6/(-14) - 68/(-28). Suppose x*u = -4 + 14. Factor -647*r**2 + 667*r**2 + r**3 - 20*r**4 + u*r**5 - 20*r + 14*r**3.
5*r*(r - 2)**2*(r - 1)*(r + 1)
Let v(h) = -h**3 + 3*h**2 - 4*h + 1. Let l(r) = -6*r**3 + 3*r**2 - 220*r - 409. Let a(j) = 3*l(j) - 21*v(j). Factor a(y).
3*(y - 26)*(y + 4)**2
What is u in 16/3*u**4 - 178/3*u - 112/3*u**3 + 220/3*u**2 + 52/3 + 2/3*u**5 = 0?
-13, 1, 2
Let j = 535419 - 5889607/11. Factor 4*i + 0 + 18/11*i**2 - j*i**3.
-2*i*(i - 11)*(i + 2)/11
Factor -8*h**2 - 2*h**5 + 2142515*h + 6*h**3 + h**5 - 2142512*h.
-h*(h - 1)**3*(h + 3)
Determine y so that -5/3*y**3 + 765 + 495*y + 75*y**2 = 0.
-3, 51
Let b(t) be the second derivative of -7*t**5/60 + 521*t**4/12 - 590*t**3/3 + 442*t**2/3 + 2146*t. Factor b(c).
-(c - 221)*(c - 2)*(7*c - 2)/3
Let o(i) = -i**2 + i. Let a be (4 - (6 - 0)) + -3. Let g(n) = -3*n**2 + n. Let j(m) = m**3 + 1. Let w be j(0). Let v(t) = a*o(t) + w*g(t). Factor v(b).
2*b*(b - 2)
Let w(o) be the third derivative of -o**6/200 - 2*o**5/5 - 39*o**4/40 - 62*o**2 + 10*o. Factor w(l).
-3*l*(l + 1)*(l + 39)/5
Let a = 143/16 + -20767/2320. Let s = a + 70/29. Factor 9/5*w**2 + s*w + 3/5.
3*(w + 1)*(3*w + 1)/5
Let j(y) be the first derivative of 1/90*y**5 + 0*y + 0*y**3 + y**2 + 1/360*y**6 + 1/72*y**4 + 20. Let s(b) be the second derivative of j(b). Factor s(i).
i*(i + 1)**2/3
Let f = 74689 + -74685. Determine r, given that -8/3*r**3 - 5/3*r**f + 0*r + 0 + 4/3*r**2 = 0.
-2, 0, 2/5
Let h be (0 - -72)*(464/168 - 2). Let p = -3428/63 + h. Let 8/9*y**2 - p*y - 2/3 + 4/9*y**3 - 2/9*y**4 = 0. What is y?
-1, 1, 3
Determine j so that 14/13*j**3 - 64/13*j + 24/13 - 74/13*j**2 = 0.
-1, 2/7, 6
Let a(j) be the second derivative of -j**7/14 + 33*j**6/10 - 447*j**5/20 + 259*j**4/4 - 99*j**3 + 84*j**2 + 274*j. Factor a(w).
-3*(w - 28)*(w - 2)*(w - 1)**3
Let a = -21 + 23. Let n be (-30 - a/(-2))*(5 - 6). Suppose -m**2 - m**3 + n - 29 - m**2 = 0. What is m?
-2, 0
Let m = -21140678/11 - -1921880. Let -80/11 - m*p**2 - 4*p = 0. Calculate p.
-20, -2
Let y(b) be the second derivative of -1/20*b**6 + 0 + 61*b + 0*b**2 + b**3 + 1/8*b**4 - 3/10*b**5. Suppose y(n) = 0. Calculate n.
-4, -1, 0, 1
Let w(u) = -6*u - 200. Let s be w(-33). Let q(d) = -8*d**2 + 51*d - 91. Let p(o) = 4*o**2 - 26*o + 46. Let v(h) = s*q(h) - 5*p(h). Factor v(l).
-4*(l - 4)*(l - 3)
Let h(t) = -t**3 + 15*t - 2. Let m = -211 + 207. Let z be h(m). Solve 10/9*r**5 - 2/3*r**3 + 2/9*r + 11/9*r**4 + 0 - 5/9*r**z = 0.
-1, 0, 2/5, 1/2
Let p(w) be the second derivative of -w**6/9 + 2*w**5/5 + 491*w**4/18 - 22*w**3 - w - 1052. Find k, given that p(k) = 0.
-9, 0, 2/5, 11
Find d, given that 17 - 11 - 10*d**5 + 16*d**4 - 20*d**2 - 13*d + 5*d**2 + 23*d**3 - 7*d**4 = 0.
-1, 2/5, 1, 3/2
Factor -4/15*y**3 + 0 - 58/15*y**2 + 2/15*y**4 - 28/5*y.
2*y*(y - 7)*(y + 2)*(y + 3)/15
Factor 957*n**3 + 194*n + 288 - 152*n**3 + 62*n**3 + 20604*n**2 - 1538*n - 3540*n.
3*(n + 24)*(17*n - 2)**2
Suppose -178 = -510*h + 230 + 612. Factor -25/4*q + 1/4*q**3 - 3/2*q**h - 9/2.
(q - 9)*(q + 1)*(q + 2)/4
Let -86*q + 164*q**2 + 165*q**3 - 283*q**3 + q**4 + 27*q**4 + 12 = 0. Calculate q.
3/14, 1, 2
Let q(m) be the first derivative of -m**6/3 + 168*m**5/5 + 218*m**4 + 1588*m**3/3 + 621*m**2 + 356*m - 5933. Solve q(f) = 0.
-2, -1, 89
Let c(t) be the third derivative of -t**6/40 + 8*t**5/5 + 40*t**4 + 6*t**2 + 255*t + 1. Factor c(k).
-3*k*(k - 40)*(k + 8)
Let f(r) be the third derivative of -r**5/60 - r**4/12 + r**3/2 - 113*r**2. Let o(q) = 3*q - 3. Let l(y) = 3*f(y) + 4*o(y). Factor l(w).
-3*(w - 1)**2
Let x(c) be the first derivative of 2*c**5/75 - 7*c**4/30 - 8*c**3/45 + 28*c**2/15 - 1196. Solve x(l) = 0 for l.
-2, 0, 2, 7
Factor 5/2*a - 1/2*a**5 + a**2 + 1 - 2*a**4 - 2*a**3.
-(a - 1)*(a + 1)**3*(a + 2)/2
Let m(l) = l**5 + l**4 - l**3 + 2*l**2 + l. Let r(w) = -4*w**5 - 6*w**4 - 4*w**3 - 21*w**2 - 9*w. Let s(c) = -5*m(c) - r(c). What is p in s(p) = 0?
-1, 0, 4
Factor 488 + 2/5*d**2 + 1224/5*d.
2*(d + 2)*(d + 610)/5
Let p(j) be the second derivative of -j**4/36 - 85*j**3/18 - 200*j**2/3 - 1650*j. Solve p(o) = 0 for o.
-80, -5
Suppose 5*d + 27 = -4*s + 5, 28 = -s - 5*d. Solve -6/7*r**5 + 0 - 10/7*r**4 + 0*r**s + 4/7*r**3 + 0*r = 0 for r.
-2, 0, 1/3
Let k(g) be the third derivative of g**7/210 - g**6/60 - 9*g**5/20 + 9*g**4/2 - 18*g**3 + 1417*g**2. What is c in k(c) = 0?
-6, 2, 3
Suppose 13*y - 12*y + 2*j = -6, 4*j + 12 = 0. Let h(o) be the third derivative of 0*o - 1/32*o**4 + 0 + y*o**3 + 1/80*o**5 - 3*o**2. Factor h(i).
3*i*(i - 1)/4
Solve 184/13 - 38/13*v - 2/13*v**2 = 0.
-23, 4
Let t(j) be the second derivative of 19/18*j**4 + 1/15*j**5 + 0*j**2 - 111*j + j**3 + 0. Find o, given that t(o) = 0.
-9, -1/2, 0
Let v(j) = -j**2 - 5*j + 9. Let w be v(-6). Factor -13 + 13 + 170*f**w - f**4 - 175*f**3.
-f**3*(f + 5)
Factor 1/5*b**4 + 97/5*b**2 + 0 + 10*b**3 + 48/5*b.
b*(b + 1)**2*(b + 48)/5
Let l be (-6)/(-14) - 154/(-98). Factor 44*h + 112 - 3*h**2 - 4*h**2 + 9*h**2 - 6*h**l + 8*h**2.
4*(h + 4)*(h + 7)
Suppose 64*p + 57*p + 14*p - 84 = 93*p. Factor -2/7*b**3 - 44/7 - 48/7*b**p - 90/7*b.
-2*(b + 1)**2*(b + 22)/7
Let d = 1197837/1497290 + -1/299458. Solve -9/5*v**4 + 0 + 0*v - 7/5*v**5 + d*v**2 + 12/5*v**3 = 0 for v.
-2, -2/7, 0, 1
Let r = -52705 + 263636/5. Suppose 2268/5*o**5 + 432*o**4 + r*o**2 + 0 + 6/5*o + 747/5*o**3 = 0. Calculate o.
-1/3, -2/7, -1/6, 0
Let d(t) = 3*t**4 + 418*t**3 + 84*t**2 - 1600*t - 474. Let n(f) = 2*f**4 + 208*f**3 + 42*f**2 - 800*f - 240. Let o(h) = 4*d(h) - 9*n(h). What is a in o(a) = 0?
-33, -2, -1/3, 2
Let c(s) be the first derivative of 3*s**4 + 9968*s**3/3 - 1662*s**2 - 552. Find h such that c(h) = 0.
-831, 0, 1/3
Suppose s - 52*t = -829, 5*s + 17 = 112*t - 110*t. Suppose -10*g**4 + 10*g**s - 8*g + 0 + 40/3*g**2 + 4/3*g**5 = 0. Calculate g.
-1, 0, 1/2, 2, 6
Let m(x) be the second derivative of -2/7*x**3 - 11/28*x**4 + 2 - 3/70*x**5 + 15/14*x**2 - 3*x. Solve m(h) = 0 for h.
-5, -1, 1/2
Let m = 4795 - 4793. Let q(d) be the third derivative of 0*d + d**4 + 1/210*d**7 + 11/30*d**5 + 3/2*d**3 + 18*d**m + 0 + 1/15*d**6. Solve q(t) = 0 for t.
-3, -1
Let t(m) = 18*m - 1473. Let z be t(82). Let j(u) be the second derivative of 3/20*u**4 + 3/10*u**2 + 8*u - 3/100*u**5 - 3/10*u**z + 0. Solve j(a) = 0.
1
Let n(j) be the second derivative of -j**6/255 + 6*j**5/17 - 29*j**4/17 + 172*j**3/51 - 57*j**2/17 - 108*j + 1. Find p, given that n(p) = 0.
1, 57
Let b(j) = -j**3 - 76*j**2 + 328*j + 640. Let p be b(-80). Suppose p*l - 1/3*l**2 + 0 - 1/3*l**3 = 0. What is l?
-1, 0
Let w = 308 + -304. Factor -20*k**2 - 37*k**2 - 28*k + 33*k**2 + w*k**3.
4*k*(k - 7)*(k + 1)
Find q such that 24*q**2 + q - 123*q**3 - 24 + 158*q**3 - 36*q**3 = 0.
-1, 1, 24
Let x(g) = g**4 - g**3 + g - 1. Let c be (6/18)/(-2 + 74/36). Let n(h) = -h**4 - 29*h**3 + 85*h**2 - 91*h + 36. Let b(t) = c*x(t) + n(t). Solve b(q) = 0.
1, 2,