o) = -2*o**2 + 70*o + 3. Let j be q(35). What is c in -15800*c - 97*c**j + 32768 + 1599*c**2 + 1569*c**2 - 20040*c + c**4 = 0?
1, 32
Let s = 106 + -108. Let t be (-24)/(-9) + s - (-16)/3. Solve 3*z**2 + 3*z**3 - 6*z**2 - t*z**2 + 3*z**2 = 0 for z.
0, 2
Factor -8*k**2 - 131*k + 17*k + 123*k - k**3.
-k*(k - 1)*(k + 9)
Let d = 157414 + -157412. Find g, given that 39/5*g - 21/5 - 18/5*g**d = 0.
1, 7/6
Suppose -2*o - 2*q + 946 = 0, 550 = 2*o - q - 387. Let l = -470 + o. Let -1/3*k**2 + l - k = 0. Calculate k.
-3, 0
Let t(v) be the first derivative of v**4/90 + 14*v**3/15 + 147*v**2/5 - 49*v - 60. Let y(h) be the first derivative of t(h). Factor y(a).
2*(a + 21)**2/15
Let l(h) be the third derivative of h**6/180 + 26*h**5/45 + 49*h**4/36 - 34*h**3/3 + 5*h**2 - 72. Factor l(n).
2*(n - 1)*(n + 2)*(n + 51)/3
Suppose 3 = 4*h + 5*d, 0*h + 9 = 2*h - 5*d. Suppose 3*j + h*j - 20 = 0, 0 = -3*c + 3*j - 3. Factor 5*a**3 + 5 - 9 + 6*a + 6*a - a**c - 12*a**2.
4*(a - 1)**3
Let m be (-2)/11 - (-1440)/176. Suppose m*r - r - 14 = 0. Factor -24 + r*z**2 + 20*z - 8*z - 14*z.
2*(z - 4)*(z + 3)
Let o(m) be the first derivative of -2*m**5/25 - 259*m**4/10 - 2958*m**3 - 613089*m**2/5 + 2634012*m/5 + 924. Let o(l) = 0. Calculate l.
-87, 2
Let u = -1 + 13. Suppose 0*g - g - 4*c + u = 0, 4*g = -5*c + 70. Find o, given that g*o + 7*o - 30*o + 13*o - 5*o**2 = 0.
0, 2
Find i such that 15/7*i**4 + 480/7*i - 384/7*i**2 + 54/7*i**3 - 3/7*i**5 + 0 = 0.
-5, 0, 2, 4
Let t(k) be the second derivative of -62/3*k**3 + 0 - 1/18*k**4 - 210*k - 2883*k**2. Suppose t(z) = 0. Calculate z.
-93
Let a be (-300)/(-550) + 8/(-36) + 2775/(-9504). Let f(i) be the second derivative of -a*i**4 - 1/16*i**3 + 0*i**2 + 0 - 18*i. Suppose f(b) = 0. What is b?
-1, 0
Let a(y) = -5*y**3 + 100*y**2 + 416*y + 388. Let p(j) = 9*j**3 - 200*j**2 - 831*j - 783. Let w(u) = -7*a(u) - 4*p(u). Let w(b) = 0. What is b?
-2, 104
Suppose 5*s + 1858198*s**2 - 1858027*s**2 + 12*s**3 + 37*s = 0. What is s?
-14, -1/4, 0
Factor -4/3*x**2 - 504 - 764/3*x.
-4*(x + 2)*(x + 189)/3
Let a(o) = -o**2 - 5*o + 3. Let n be a(-6). Let f(l) = -12*l**2 - 4*l + 25. Let s(y) = 7*y**2 + 3*y - 13. Let h(z) = n*f(z) - 5*s(z). Factor h(u).
(u - 5)*(u + 2)
Suppose -10*h = 82*h + 17*h. Let n(q) be the first derivative of -1/10*q**5 + h*q - 1/8*q**4 + 1/4*q**2 + 1/6*q**3 - 11. Factor n(x).
-x*(x - 1)*(x + 1)**2/2
Solve 0 - 70/3*y**2 - 80/3*y**4 - 58*y**3 - 8/3*y + 32/3*y**5 = 0.
-1, -1/4, 0, 4
Let w = -553 - -388. Let r be w/44 - (-2 + -2). Suppose -c**4 + 0 + 1/2*c**2 + 3/4*c**3 - c**5 - r*c = 0. Calculate c.
-1, 0, 1/2
Let v = 979 + -973. Let q be (v/(-10))/((-297)/165). Suppose 0*h + 1/6*h**4 - q*h**3 + 1/6*h**2 + 0 = 0. What is h?
0, 1
Let m(l) = -2*l**4 - 88*l**3 - 128*l**2 + 228*l - 50. Let j(s) = 4*s**4 + 88*s**3 + 129*s**2 - 241*s + 50. Let v(c) = 4*j(c) + 3*m(c). Factor v(n).
2*(n - 1)*(n + 5)**2*(5*n - 1)
Let m(q) be the third derivative of 5*q**8/84 - 27*q**7/14 + 131*q**6/6 - 455*q**5/6 - 245*q**4 + 1715*q**3/6 + 143*q**2. Factor m(g).
5*(g - 7)**3*(g + 1)*(4*g - 1)
Let j(n) be the third derivative of n**6/360 - n**5/40 - n**4/6 - n**3/2 + 20*n**2. Let x(m) be the first derivative of j(m). Suppose x(q) = 0. What is q?
-1, 4
Suppose -5*b - 63 = -s + 16, -4*s + 44 = -3*b. Let h be (95/(-40) - -2)/(24/b). Factor -h*t**2 + 5/4*t - 3/2.
-(t - 3)*(t - 2)/4
Find y such that 321*y - 3222/5 + 3/5*y**3 + 1614/5*y**2 = 0.
-537, -2, 1
Let h(y) be the first derivative of -y**6/24 - 11*y**5/20 + 29*y**4/16 + 35*y**3/12 - 7*y**2 - 13*y + 3809. What is w in h(w) = 0?
-13, -1, 2
Let f(v) be the first derivative of v**3/6 - 3*v**2/2 - 8*v - 993. Factor f(r).
(r - 8)*(r + 2)/2
Suppose -225/2 - 63/2*b**2 - 291/2*b + 3/2*b**3 = 0. Calculate b.
-3, -1, 25
Let v be (-2 - 91/(-39))/((-2)/30) + 10. Let 4/5*l - 14/5*l**2 + 2/5*l**v - 2*l**4 + 0 + 18/5*l**3 = 0. What is l?
0, 1, 2
Factor -1296/7*d + 2/7*d**3 - 318/7*d**2 - 1304/7.
2*(d - 163)*(d + 2)**2/7
Let v(u) be the third derivative of u**6/1440 + u**5/160 - 5*u**3/6 + u**2 - 13. Let a(k) be the first derivative of v(k). Factor a(i).
i*(i + 3)/4
Factor -22*r - 79*r**2 - 81*r**2 + 161*r**2 - 72 + 43*r.
(r - 3)*(r + 24)
Let y be ((-10)/(-8) - 2) + (-22 - 67)/(-89). Factor -y*u**2 + 5/4*u + 3/2.
-(u - 6)*(u + 1)/4
Let r(m) be the first derivative of -m**4/20 + 196*m**3/15 - 4589*m**2/10 + 5746*m + 929. Factor r(y).
-(y - 170)*(y - 13)**2/5
Let k(s) be the second derivative of s**6/120 - s**5/4 - 11*s**3/6 - s**2/2 - s + 2. Let w(t) be the second derivative of k(t). Let w(p) = 0. Calculate p.
0, 10
Factor 25/2*l**2 + 26*l - 3/2*l**3 - 10.
-(l - 10)*(l + 2)*(3*l - 1)/2
Let r(n) be the second derivative of n**4/4 - 54*n**3 + 4374*n**2 + 356*n. Factor r(i).
3*(i - 54)**2
Let p be 5/25*(-18380)/6. Let b = p + 613. Factor -4*q**3 - 2*q**4 - q + 0 - b*q**5 - 10/3*q**2.
-q*(q + 1)**3*(q + 3)/3
Let h be 2/(((-1428)/(-189))/(-17)) + 2*3. Factor h*l**2 - 15 + 43/2*l.
(l + 15)*(3*l - 2)/2
Let c(p) = 4*p**3 - 120*p**2 + 85*p + 528. Let d(t) = -2*t**3 + 62*t**2 - 44*t - 264. Let b(q) = -4*c(q) - 7*d(q). Factor b(n).
-2*(n - 22)*(n - 3)*(n + 2)
Let m(g) = 3*g**2 - 4*g**2 + 0*g + 5*g. Let h be (-212)/(-318) - 66/(-9). Let a(n) = -3*n**2 + 14*n. Let k(u) = h*m(u) - 3*a(u). Find r such that k(r) = 0.
0, 2
Suppose 7*n - 95 = 2*n + 5*p, 3*p = -10*n + 151. Let f(h) be the first derivative of 1/5*h**2 + 1/15*h**3 + 0*h - n. Find l such that f(l) = 0.
-2, 0
Let b(o) be the first derivative of o**4/22 + 1102*o**3/33 - 1106*o**2/11 - 7337. Solve b(x) = 0 for x.
-553, 0, 2
Factor -3/8*b**2 + 627/8 - 3*b.
-3*(b - 11)*(b + 19)/8
Let h = -101298 + 101300. What is s in 0 + 2/15*s**3 + 12/5*s - 38/15*s**h = 0?
0, 1, 18
Let d be 79/(158/16) - 50/7. Solve 2/7*u - 6/7*u**2 + d - 2/7*u**3 = 0 for u.
-3, -1, 1
Suppose -126*r = 2*s - 131*r - 83, -3*s + r = -53. Factor -8/3 - s*u**2 + 88/3*u.
-2*(u - 2)*(21*u - 2)/3
Let u = 40419/8978 + -9/4489. Solve 3/4*o**4 + 0*o + 0 - u*o**3 + 0*o**2 = 0.
0, 6
Let c(k) be the first derivative of 124 + 13*k**2 - 60*k - 2/3*k**3. Factor c(s).
-2*(s - 10)*(s - 3)
Suppose 12*z + 1 + 35 = 0. Let l be 19/(-19)*z/7. Determine y so that -l*y**2 - 3 - 24/7*y = 0.
-7, -1
Let v(c) = 19*c + 135. Let r be v(-7). Factor -3*h**r - 18*h**3 + 52*h**3 - 18*h**3 - 15*h**3.
h**2*(h - 3)
Let g(c) = c**4 + 232*c**3 + 12769*c**2 + 2. Let u(i) = -2*i**4 - 467*i**3 - 25538*i**2 - 5. Let n(p) = -10*g(p) - 4*u(p). Find f, given that n(f) = 0.
-113, 0
Suppose 28 = -4*k, 2557*r - 2563*r = -2*k - 26. Let i be (-4)/(-3) + 0/(-2). Solve 16/9*b - 4/9*b**r - i = 0.
1, 3
Let t be (-130229)/33 - (-42)/18. Let i be t/(-406) + (-16)/2. Factor -i*z**2 + 24/7 + 4*z.
-4*(z - 3)*(3*z + 2)/7
Suppose 6*j + 5*j + 43 = 208. Let d(o) be the first derivative of 0*o + 90*o**2 - j - 20*o**3 + 5/4*o**4. Factor d(p).
5*p*(p - 6)**2
Let l = -38/35989 + 216200/251923. Let -34/7*p**3 + 6*p + 38/7*p**2 + l*p**4 - 36/7 = 0. What is p?
-1, 2/3, 3
Let i be (-106)/477*(60/(-8) - 0). Determine h, given that 0*h**2 - i*h**3 + 5*h - 10/3 = 0.
-2, 1
Let c(p) = p**3 + 11*p**2 - p - 1. Let k be c(-11). Factor -a**2 - 3*a - a + 12*a + 4*a + k + 3.
-(a - 13)*(a + 1)
Let y be (6/12)/(2/96). Suppose -4*c - y = -2*m, -4*c = -5*m - 7*c - 5. Find v, given that v**3 - 2*v**3 - 4*v**m + 6*v**2 = 0.
0, 2
Suppose -92*m = -80*m - 48. Let i(u) be the second derivative of u - 1/5*u**3 - 1/5*u**2 - 1/50*u**5 + 0 - 1/10*u**m. Factor i(a).
-2*(a + 1)**3/5
Factor 29*v - 3/8*v**2 + 39/2.
-(v - 78)*(3*v + 2)/8
Let t(l) be the third derivative of l**6/180 + 47*l**5/90 - 313*l**4/36 + 265*l**3/9 + 4*l**2 - 163. What is i in t(i) = 0?
-53, 1, 5
Suppose 144*i + 68*i - 109*i = -144*i. Let d(h) be the third derivative of 0 - 5/12*h**3 - 5*h**2 - 1/24*h**5 + i*h - 5/24*h**4. Find s, given that d(s) = 0.
-1
Let l(b) be the second derivative of -b**6/45 + 157*b**5/15 + 124*b**4 + 534*b**3 + 963*b**2 - 6928*b. Let l(a) = 0. Calculate a.
-3, -1, 321
Let a(u) = 14*u**3 + 31*u**2 - 14*u + 20. Let v(n) = 5*n**3 + 11*n**2 - 5*n + 7. Suppose 0 = 137*j - 132*j + 85. Let f(y) = j*v(y) + 6*a(y). Factor f(x).
-(x - 1)*(x + 1)**2
Determine g, given that 125/4 - 1/4*g**2 + 5*g = 0.
-5, 25
Let j(i) be the third derivative of -3/8*i**3 + 3*i**2 + 1/160*i**5 + 1 - 1/64*i**4 + 0*i. Factor j(f).
3*(f - 3)*(f + 2)/8
Le