 Calculate j.
1, 2
Let j = 82 - 54. Let o be ((-2376)/77)/((-30)/j). Factor 48/5*u + o + 4/5*u**2.
4*(u + 6)**2/5
Let o(t) = 8*t**2 + 227*t + 660. Let w(k) = -95*k**2 - 2725*k - 7915. Let i(j) = 35*o(j) + 3*w(j). Solve i(s) = 0 for s.
-43, -3
Suppose 4*h = -6 + 10, -b + 2 = 2*h. Let w(x) be the first derivative of 3/32*x**4 - 9/16*x**2 + 1/4*x**3 + b*x + 8. Let w(u) = 0. What is u?
-3, 0, 1
Factor 406*d - 95454 - 1695*d**2 + 95454 - 229*d**3 + 439*d + 1084*d**3 - 5*d**4.
-5*d*(d - 169)*(d - 1)**2
Let d be (-6)/(-11) - 64/(-528). Suppose -2*n + 2*s = -3*n + 6, 0 = 3*s - 3. What is v in d*v**n - 32/21*v - 8/21 - 2/7*v**2 + 32/21*v**3 = 0?
-2, -1, -2/7, 1
Let o(r) be the third derivative of -r**8/32 + 4*r**7/35 + 3*r**6/10 - 11*r**5/20 - 17*r**4/16 + 3*r**3/2 - 22*r**2 + 27*r - 1. Solve o(v) = 0.
-1, 2/7, 1, 3
Let y be 6/12*(-1 - -9). Suppose 39*v - 37*v - y = 0. Factor -173*g**2 - 13*g - 16 + 180*g**v + 5*g - g**3.
-(g - 4)**2*(g + 1)
Let a(d) be the second derivative of -2*d**6/9 - 57*d**5/4 - 625*d**4/36 + 35*d**3/3 - d - 1072. Determine v, given that a(v) = 0.
-42, -1, 0, 1/4
Factor 1/4*m**3 - 19/2*m + 0 + 17/4*m**2.
m*(m - 2)*(m + 19)/4
Let i be (1/158)/(4 + (-2490)/624). Let a = 2/237 + i. Factor a*m**2 - 4/9*m + 0 - 2/9*m**3.
-2*m*(m - 2)*(m - 1)/9
Suppose 8*f - 13*f + 3*m - 23 = 0, 3*m - 43 = -5*f. Find l such that 1/7*l**4 - 8/7 - 4/7*l + 5/7*l**3 + 6/7*l**f = 0.
-2, 1
Let d be ((-147)/14 + 11)*(-2 + -6) + 88/5. Factor -12/5*o**2 + 58/5*o - d.
-2*(o - 2)*(6*o - 17)/5
Find h, given that -6/11 - 2/11*h**2 + 8/11*h = 0.
1, 3
Let b = 1214 + -1194. Let w be ((-9)/6)/((-6)/(144/b)). Find a such that 2/5*a - a**4 + w*a**3 + 0 - 7/5*a**2 + 1/5*a**5 = 0.
0, 1, 2
Let m(r) be the first derivative of 5*r**6/6 - 21*r**5 - 245*r**4/4 + 325*r**3/3 + 240*r**2 - 460*r - 5243. Solve m(c) = 0.
-2, 1, 23
Let m be (40 - (-6 + -6))*16/(-2). Let x = m + 416. Suppose 3/4*k**2 + x - 3/4*k**4 + 3/2*k - 9/4*k**3 + 3/4*k**5 = 0. Calculate k.
-1, 0, 1, 2
Let w(x) = -x**3 + 4*x**2 + 61*x - 244. Let s be w(4). Let -1/3*d**3 + 0 + 1/3*d**5 + 0*d + 0*d**4 + s*d**2 = 0. What is d?
-1, 0, 1
Let n(d) be the first derivative of -d**6/48 - 83*d**5/20 - 4773*d**4/16 - 52205*d**3/6 - 1092701*d**2/16 - 446631*d/4 - 4483. Factor n(x).
-(x + 1)*(x + 6)*(x + 53)**3/8
Let q(z) be the third derivative of -z**7/280 + z**6/120 + z**5/40 - z**4/8 + 19*z**3/2 - 7*z**2 + 3. Let w(a) be the first derivative of q(a). Factor w(r).
-3*(r - 1)**2*(r + 1)
Find o, given that 32/3*o + 4/3*o**2 + 64/3 = 0.
-4
Let q(s) be the second derivative of -s**5/5 - 8*s**4 - 120*s**3 - 800*s**2 - 1369*s. Factor q(g).
-4*(g + 4)*(g + 10)**2
Let f(r) be the first derivative of r**5/30 - 185*r**4/24 - 187*r**3/6 - 563*r**2/12 - 94*r/3 + 31. Suppose f(m) = 0. Calculate m.
-1, 188
Let x = 1046 - 1043. Suppose 0 = -3*d + 9, -60 + 57 = x*b - 3*d. Determine o so that -3/4 + 3/2*o - 3/4*o**b = 0.
1
Let q(j) be the third derivative of 1/1575*j**7 + 1/180*j**6 - 32*j**2 + 0 + 0*j - 7/450*j**5 + 2/15*j**3 - 1/36*j**4. Suppose q(k) = 0. What is k?
-6, -1, 1
Suppose -5*g + 24 = -3*q, -g - 2*q + 6 = 3*g. Let j be (-9)/3 - (-16 + (4 - -6)). Factor -6*k + 19*k**g + 18*k**2 + 2*k**4 - 7*k**j + 0*k**4 + 14*k.
2*k*(k + 1)**2*(k + 4)
Let l(j) be the first derivative of j**5/3 + 295*j**4/12 + 120*j**3 - 590*j**2/3 - 4400*j/3 + 8637. Let l(m) = 0. What is m?
-55, -4, -2, 2
Let q(w) = -w**5 - 4*w**4 - w**3 - w**2 + 2. Let s(n) = -4*n**5 + 30*n**4 - 182*n**3 + 142*n**2 + 4. Let x(k) = 2*q(k) - s(k). Suppose x(l) = 0. What is l?
0, 1, 6, 12
Suppose 0 = 2*p - 212 + 204. Suppose -4*q = q + 10, -q + p = 2*z. Determine i so that -24/13*i - 6/13*i**2 - 8/13 + 10/13*i**z = 0.
-1, -2/5, 2
Let d(j) be the first derivative of 7/4*j**4 - 2450*j - 164*j**3 + 50 + 8715/2*j**2. Determine c so that d(c) = 0.
2/7, 35
Let u be ((-8 - -7)/((-2)/1468))/(-2). Let f = -365 - u. Factor c**3 + 0*c - 3/4*c**f - 1/4*c**4 + 0.
-c**2*(c - 3)*(c - 1)/4
Suppose 3*b - 4*q - 1193 = 0, -7*b + 2*q + 401 = -6*b. Let -d**4 + 2*d + b*d**3 + d**2 - 4*d - 389*d**3 = 0. What is d?
-1, 0, 1, 2
Let z(n) be the second derivative of 2*n**7/63 + 26*n**6/15 + 394*n**5/15 + 58*n**4/3 - 3382*n**3/9 + 722*n**2 - 1624*n. Suppose z(u) = 0. Calculate u.
-19, -3, 1
Let f(i) be the third derivative of -4/9*i**3 + 1/270*i**5 - 19*i**2 - 1/27*i**4 + 0 + 0*i. Suppose f(u) = 0. What is u?
-2, 6
Let u = -661/121 - -6433/1089. Find y, given that -u*y**5 + 0 + 0*y**3 + 0*y + 0*y**2 + 4/9*y**4 = 0.
0, 1
Let h(b) = 4*b - 5. Let p(j) = 18*j**2. Let w be p(-1). Let z(i) = -i**2 - i - 1. Let v(n) = w*z(n) - 2*h(n). Suppose v(f) = 0. Calculate f.
-1, -4/9
Factor -484128 - 1/2*o**2 - 984*o.
-(o + 984)**2/2
Factor -15*t**3 + 6*t**3 + 7*t**3 + 7*t**3 + 136 + 62*t**2 - 3*t**3 - 200*t.
2*(t - 2)*(t - 1)*(t + 34)
Let f(l) be the second derivative of -l**4/66 - 548*l**3/33 - 547*l**2/11 - 27*l - 44. Factor f(p).
-2*(p + 1)*(p + 547)/11
Suppose -6*d + 108 = -4*d. Suppose 5*s - d = -44. Factor 0 - 636*c**s + 640*c**2 + 8 + 12*c.
4*(c + 1)*(c + 2)
Find c such that 38*c**3 - 36*c**2 - 35*c**3 + 105*c - 12191 + 12191 = 0.
0, 5, 7
Determine c so that -54/7 + 25/7*c + 4*c**2 + 1/7*c**3 = 0.
-27, -2, 1
Let t(r) be the second derivative of -r**8/36960 + r**6/3960 + 7*r**4/2 - 2*r + 44. Let f(g) be the third derivative of t(g). Factor f(m).
-2*m*(m - 1)*(m + 1)/11
Let i(k) be the second derivative of -k**4/36 + 17*k**3/3 - 99*k**2/2 - 3051*k. Factor i(t).
-(t - 99)*(t - 3)/3
Let d(h) be the second derivative of h**6/24 + 7*h**5/12 - 15*h**4/4 + 78*h**2 + 36*h. Let s(t) be the first derivative of d(t). Find u such that s(u) = 0.
-9, 0, 2
Let m(r) be the first derivative of r**5/2 + r**4/6 + r**3/45 - 99*r**2/2 + 38. Let q(o) be the second derivative of m(o). Find p such that q(p) = 0.
-1/15
Let m(l) be the second derivative of 0 - 2/45*l**6 + 1/30*l**5 + 0*l**3 + 50*l + 0*l**2 + 1/9*l**4 - 1/63*l**7. Solve m(b) = 0 for b.
-2, -1, 0, 1
Let c(j) be the second derivative of j**7/42 + j**6/12 - 2*j**5/3 + 7*j**2 - 8*j - 4. Let y(u) be the first derivative of c(u). Let y(t) = 0. What is t?
-4, 0, 2
Let o(t) = -11*t**2 + 55*t + 18. Let x(b) be the third derivative of -b**5/15 + 3*b**4/4 + b**3 + 57*b**2. Let i(a) = 4*o(a) - 14*x(a). Solve i(l) = 0 for l.
-1/3, 3
Let i(j) be the second derivative of 5/2*j**2 + 7/12*j**3 - 7/40*j**5 + 0 - 3/8*j**4 - 5*j - 1/60*j**6. Find u, given that i(u) = 0.
-5, -2, -1, 1
Let y(f) be the third derivative of f**6/30 + f**5/15 - 5*f**4/6 + 2*f**3 - 1191*f**2. Factor y(l).
4*(l - 1)**2*(l + 3)
Suppose -1863*m + 2411 = -1315. Suppose 12 + 1/3*i**m - 4*i = 0. What is i?
6
Let s(z) be the third derivative of 0*z + 0*z**3 + 2/15*z**5 - 1 - 1/105*z**7 - 1/168*z**8 - 2/3*z**4 + 1/10*z**6 - 233*z**2. Determine m, given that s(m) = 0.
-2, 0, 1, 2
Let k(t) = -24*t - 228. Let b be k(-10). Let d be ((-7)/(-5) + -2)/((-18)/b). Factor 36/5 - 8/5*m**2 + 6/5*m - d*m**3.
-2*(m - 2)*(m + 3)**2/5
Let x = -5/4513 - -13574/31591. Let m be (-72)/(-39) - (-2)/13. What is n in 0*n - x + 3/7*n**m = 0?
-1, 1
Let -720*s**2 + 15200*s**3 - 1420*s - 7601*s**3 - 7604*s**3 = 0. Calculate s.
-142, -2, 0
Let y(l) = -3*l**2 + l - 28. Let s be y(-8). Let c = s + 231. Find w such that 4/3 + 4*w**2 - 4/3*w**c - 4*w = 0.
1
Factor 603/2*f + 321/2*f**2 + 33/2*f**3 - 189/2.
3*(f + 3)*(f + 7)*(11*f - 3)/2
Let 370/13*u**3 - 1502/13*u**2 - 756/13 + 1886/13*u + 2/13*u**4 = 0. What is u?
-189, 1, 2
Suppose -3 + 5 = z. Suppose -4*s - 33 = -5*o, 2*s + z = 8. Factor -6*n**2 + 13*n - 2*n**4 - o*n + 4*n**4.
2*n*(n - 1)**2*(n + 2)
Factor 346*r + 59858 + 1/2*r**2.
(r + 346)**2/2
Let k(x) be the first derivative of 3*x**2 + 44 + 0*x - 3/4*x**4 + x**3. Let k(j) = 0. What is j?
-1, 0, 2
Solve -41/6*r**4 - 167/3*r**3 + 374*r**2 + 1452*r + 0 - 1/6*r**5 = 0.
-22, -3, 0, 6
Let t be (8/15)/4 + 8104/(-30). Let n = 1621/6 + t. Let -n - 1/6*v + 1/3*v**2 = 0. What is v?
-1/2, 1
Let l = 27/457 - -1263/1828. Find c, given that 3/4*c**2 + 0 - 3/4*c**4 + l*c - 3/4*c**3 = 0.
-1, 0, 1
Let h(q) be the third derivative of q**8/784 + 27*q**7/490 + 113*q**6/280 + 61*q**5/140 - 57*q**4/28 - 44*q**3/7 + 940*q**2 - q. Let h(d) = 0. What is d?
-22, -4, -1, 1
Suppose -1116*c + 5*q - 20 = -1111*c, 0 = c - 4*q + 16. Factor c + 123/7*r**2 + 0*r - 3/7*r**3.
-3*r**2*