). Factor k(c).
(c - 460)**2
Suppose 5*h - 508*f - 28 = -505*f, 3*h = 2*f + 18. Factor -1/3*c**4 + c**2 - h*c**3 - 4 + 16/3*c.
-(c - 1)**2*(c + 2)*(c + 6)/3
Let m(h) be the first derivative of 66 + 10/9*h**3 - 55/6*h**2 - 35*h. Factor m(l).
5*(l - 7)*(2*l + 3)/3
What is b in 162*b + 21*b**4 - 4860*b**3 - 85439*b**2 + 91997*b**2 - 6*b**5 + 312*b**4 - 2187 = 0?
-1/2, 1, 27
Let a(j) be the first derivative of j**6/24 - 9*j**5/20 - 21*j**4/16 - 11*j**3/12 + 367. Factor a(b).
b**2*(b - 11)*(b + 1)**2/4
Let o be 44/(-33)*(134/100*5 + -7). Suppose 38/5 - o*d**2 + 36/5*d = 0. What is d?
-1, 19
Let z(d) be the second derivative of 1/21*d**4 + 26/21*d**3 + 105*d + 44/7*d**2 + 0. Factor z(a).
4*(a + 2)*(a + 11)/7
Let p(x) = -8*x**3 - 9*x**2 + 14*x + 132. Let u be p(-6). Let i = 11617/8 - u. Factor i*s**2 + 0*s - 1/8.
(s - 1)*(s + 1)/8
Let i = 369766 - 4067425/11. Find v such that v**2 + 0 + 25/11*v**4 + i*v + 35/11*v**3 = 0.
-1, -1/5, 0
Let p(b) be the first derivative of 8*b**4 + 140*b**3 - 198*b**2 - 56*b + 5. Determine x so that p(x) = 0.
-14, -1/8, 1
Let d(q) be the first derivative of -q**4/4 - 2108*q**3/3 + 4219*q**2/2 - 2110*q + 13963. Factor d(k).
-(k - 1)**2*(k + 2110)
Let f(j) = -3*j**2 + 73*j + 78. Let x be f(26). Let k be -6*32/(-780) + (-8)/x. Factor -k*i**3 + 1/5*i**4 - 3/5*i**2 - 4/5 + 8/5*i.
(i - 2)*(i - 1)**2*(i + 2)/5
Factor 28512720*q + 11940*q**2 + 5/3*q**3 + 22696125120.
5*(q + 2388)**3/3
Solve -1/10*r**3 + 66/5*r**2 - 26*r + 0 = 0 for r.
0, 2, 130
Let t(o) be the first derivative of 5*o**2/2 - 83*o - 5. Let k be t(17). Determine f so that -9/4*f**k + 9/4*f - 3/4 + 3/4*f**3 = 0.
1
Suppose 3002 = 12*k + 8402. Let u = k - -1351/3. Solve u*q**2 - 4/3*q + 4/3 = 0 for q.
2
Let x = -42 + 36. Let p be (-6)/(-4) - 399/x. Factor -k + 418*k**4 - 310*k**4 + 180*k**3 + 9*k + p*k**2 - 108*k**5.
-4*k*(k - 2)*(3*k + 1)**3
Let o(x) be the second derivative of -2*x**4/27 + 41*x**3/27 - 10*x**2/9 + 611*x. Find r, given that o(r) = 0.
1/4, 10
Let w(r) = 0 + 23 - 10*r + 1 + 8*r**3 + 18*r**2. Let c(h) = h - 1. Suppose 0 = -309*u + 319*u + 440. Let k(j) = u*c(j) - 2*w(j). Solve k(o) = 0.
-1, -1/4
Let m(w) be the first derivative of -w**5/30 - 123*w**4/8 + w**3/18 + 123*w**2/4 - 4942. Factor m(i).
-i*(i - 1)*(i + 1)*(i + 369)/6
Let b = -1165 - -1172. Let i be (-2)/24 - 4*b/(-84). What is u in u + 0 + i*u**4 - 1/4*u**2 - u**3 = 0?
-1, 0, 1, 4
Let i(r) = -13*r + 32. Let t(v) = v**2 + 14*v - 30. Let y(q) = -3*i(q) - 4*t(q). Let h(n) = -n**2 - 4*n + 6. Let k(z) = 26*h(z) - 6*y(z). Factor k(g).
-2*(g - 2)*(g + 3)
Suppose 6*v - 12*v + 234 = 0. Let o be ((-72)/v)/(-4 + 2). Solve 18/13 + 2/13*i**2 - o*i = 0 for i.
3
Let i = 68 + -66. Let y be 845*i/(-10)*-5. Factor -103*d**2 - 3*d**2 + 5*d**3 + 540*d + y + 16*d**2 - 1925.
5*(d - 6)**3
Let f(b) be the first derivative of 52/5*b**2 - 86 - 88/15*b - 14/45*b**3. Suppose f(y) = 0. What is y?
2/7, 22
Let g = -1/1618303 + 4854911/3236606. Solve 12 + g*r**2 + 9*r = 0.
-4, -2
Determine o, given that 114/5*o**2 + 102 - 2/5*o**3 - 622/5*o = 0.
1, 5, 51
Let g(s) be the third derivative of 1/90*s**5 - 4/9*s**3 + 1/12*s**4 + 0*s - 9*s**2 - 4. Suppose g(l) = 0. What is l?
-4, 1
Let t(v) be the first derivative of 5*v**4/12 + 1150*v**3 + 1190250*v**2 + 547515000*v - 1033. Factor t(w).
5*(w + 690)**3/3
Let j(m) = -m**3 - 10*m**2 + 14*m + 29. Let c be j(-11). Let x be ((-6)/c)/(54/(-20) - -3). Solve -8*i**3 + 0*i**4 - x*i**4 - 9*i**3 + 2*i**3 = 0.
-3, 0
Let b(s) be the third derivative of 0 + s + 0*s**4 + 1/455*s**7 - 5*s**2 + 0*s**3 + 1/390*s**5 - 1/260*s**6 - 1/2184*s**8. Solve b(j) = 0 for j.
0, 1
Let u(p) be the third derivative of 14*p**2 - p - 1/56*p**4 + 1/21*p**3 + 1/420*p**5 + 0. Factor u(w).
(w - 2)*(w - 1)/7
Let x(y) be the first derivative of -y**3/5 + 102*y**2/5 + 219*y - 21. Find p such that x(p) = 0.
-5, 73
Suppose 0 = 5*a - 3*h - 19, 2*a - 2*h + 9 - 15 = 0. Let -239*g**4 + 481*g**4 - 241*g**4 - g**a = 0. What is g?
0, 1
Let t(c) be the second derivative of c**7/14 + 9*c**6/10 + 9*c**5/4 + 7*c**4/4 - 2486*c. Factor t(w).
3*w**2*(w + 1)**2*(w + 7)
Let b(q) be the second derivative of q**6/90 + 4*q**5/15 + 5*q**4/2 + 107*q**3/2 - 2*q + 191. Let w(l) be the second derivative of b(l). Factor w(p).
4*(p + 3)*(p + 5)
Suppose 0 = -35*d - 754*d + 44*d - 222*d. Factor d + 2/5*r**3 + 4/5*r - 6/5*r**2.
2*r*(r - 2)*(r - 1)/5
Let j(z) = -61 - 541*z + 308*z + z**2 + 293*z. Let s be j(1). Factor -2/5*a**2 + s + 2/5*a**4 + 2/5*a - 2/5*a**3.
2*a*(a - 1)**2*(a + 1)/5
Let d(b) be the first derivative of -b**4/16 + 14*b**3 - 165*b**2/2 + 164*b + 6. Factor d(s).
-(s - 164)*(s - 2)**2/4
Let b(o) be the first derivative of o**7/315 - o**6/20 + 4*o**5/15 - 4*o**4/9 - 17*o**2/2 + 65. Let n(m) be the second derivative of b(m). Factor n(p).
2*p*(p - 4)**2*(p - 1)/3
Let q(s) be the third derivative of 1/105*s**7 + 0 + 847/6*s**4 + 1331/3*s**3 + 66/5*s**5 + 47*s**2 + 17/30*s**6 + 0*s. Factor q(t).
2*(t + 1)*(t + 11)**3
Let q(a) be the second derivative of -a**5/270 + a**4/18 + 219*a**2/2 - 188*a. Let f(w) be the first derivative of q(w). Factor f(y).
-2*y*(y - 6)/9
Let c(y) = -13*y**2 + 40*y + 939. Let o(g) = 15*g**2 - 42*g - 968. Let a(t) = 7*c(t) + 6*o(t). Determine i, given that a(i) = 0.
-17, 45
Let u = 1687754 + -3375503/2. Solve 1/2*m**2 - u*m + 0 = 0 for m.
0, 5
Let z(u) be the first derivative of 2*u**3/69 + 152*u**2/23 - 1248*u/23 + 5223. Suppose z(a) = 0. What is a?
-156, 4
Let n(k) = -k**3 + 122*k**2 - 504*k + 2640. Let f be n(114). Find t such that -13440*t**2 - f + 1200*t**3 + 3/4*t**5 - 195/4*t**4 + 61440*t = 0.
1, 16
Find q such that -394/13*q - 336/13 - 2/13*q**3 - 60/13*q**2 = 0.
-21, -8, -1
Find g such that -2592 - 159*g**2 + 57*g**3 + 12300*g + g**4 - 4*g**4 + 12*g**3 - 417*g**2 - 10248*g = 0.
3, 6, 8
Let g be 96/(-12) + -1*363/(-45). Let i(k) be the second derivative of 1/9*k**4 + 0 + 0*k**2 - 2/9*k**3 + g*k**5 - 2/45*k**6 + 15*k. Factor i(u).
-4*u*(u - 1)**2*(u + 1)/3
Suppose -43*h - 6 = -38*h - 3*m, -5 + 1 = -2*m. What is d in 3/2*d**5 - 3*d**4 + 0*d**2 + 0 + h*d**3 + 0*d = 0?
0, 2
Solve -3/4*y**2 - 6*y + 0 = 0.
-8, 0
Suppose -24*d**3 - 1910 + 5*d**3 + 682*d - 36*d**2 + 1850 - 27*d**3 + 132*d**2 = 0. Calculate d.
-3, 2/23, 5
Let h(f) be the first derivative of 73 + 200/3*f + 2/9*f**3 - 20/3*f**2. Factor h(b).
2*(b - 10)**2/3
Let k = -3724 - -78224/21. Let v = 16/7 - k. Suppose 0*r**2 + 0 + 4/3*r**5 + 0*r + 0*r**3 - v*r**4 = 0. What is r?
0, 1
Let r be ((1 + 0)*-3)/(9/(-15)). Suppose -h + 81 = 4*c - 22, 128 = r*c + h. Factor 42*o**4 + 5*o**5 - 54*o**4 + c*o**3 + 32*o**4 + 10*o**2.
5*o**2*(o + 1)**2*(o + 2)
Let z = 1/555450 + 1110887/7220850. Factor -16/13 + 8/13*d + 4/13*d**2 - z*d**3.
-2*(d - 2)**2*(d + 2)/13
Let p = 292192/81165 + 2/81165. Find t such that p - 3/5*t - 4/5*t**2 + 1/5*t**3 = 0.
-2, 3
Let b = 122 + -16. Factor 29*t**2 - 15*t - 38*t**2 - 44*t**3 - b*t**2 + 10 - 46*t**3.
-5*(t + 1)*(2*t + 1)*(9*t - 2)
Let n(i) = -3*i**2 + 366*i - 96. Let d(k) be the third derivative of -k**5/6 + 183*k**4/4 - 145*k**3/3 - 30*k**2 + 2. Let l(s) = -4*d(s) + 11*n(s). Factor l(t).
(t - 52)*(7*t - 2)
Let l(n) = 49 - 35*n**2 - 3 - 208*n - 81*n**2. Let m(t) = 1. Let d(k) = l(k) + 2*m(k). Determine i, given that d(i) = 0.
-2, 6/29
Let m(r) be the third derivative of -1/210*r**7 + 60*r**2 - 11/24*r**6 + 0 - 243/8*r**4 - 261/20*r**5 + 0*r + 0*r**3. Factor m(v).
-v*(v + 1)*(v + 27)**2
Let i(b) = -2*b**2 - 23*b + 4. Suppose -94*q = -106*q - 132. Let p be i(q). Solve -4 + 18*j - p*j**2 + 7/2*j**3 = 0.
2/7, 2
Let d(g) = g**2 + 8*g + 8. Let m be d(-8). Suppose -m + 4 = -2*u. Factor -u*o - o + o + 0*o + 2*o**2.
2*o*(o - 1)
Let t(v) = -9*v**2 - 26*v + 39. Let k(a) = 8*a**2 + 27*a - 38. Suppose -2*r = -2*f + r + 4, 3*f - 2*r + 4 = 0. Let x(q) = f*k(q) - 3*t(q). Factor x(n).
-5*(n - 1)*(n + 7)
Suppose 202*d = -3*c + 200*d + 42, -3*c - 3*d = -57. Let 32/15*s - 8/15*s**3 + 56/15*s**2 - 26/15*s**c + 0 + 2/5*s**5 = 0. What is s?
-1, -2/3, 0, 2, 4
Factor 395605*s + 3559/8*s**2 - 396050 + 1/8*s**3.
(s - 1)*(s + 1780)**2/8
Factor -144*x**2 - 5*x + 193*x - 78 + 84*x**4 - 4*x**3 - 86*x**4 + 40*x**3.
-2*(x - 13)*(x - 3)*(x - 1)**2
Let m = 53/6440 + -1/920. Let t(c) be the third derivative of -m*c**5 + 1/56*c**4 + 0*c + 0 + 0*c**3 - 16*c**2. What is n i