*r**3 + 205/4 + 1641/4*r.
(r + 205)*(4*r + 1)**2/4
Let y be (-122)/(-12) - 12/(-36). Let q(n) = -n**2 + 2*n + 52. Let o be q(8). Let 1/2*z**2 - 9/2*z + 9/2*z**o + y*z**3 + 1 = 0. Calculate z.
-2, -1, 1/3
Let w = -28097/15 + 9374/5. Let k(b) be the first derivative of -1/5*b - w*b**3 + b**2 + 21. Factor k(q).
-(5*q - 1)**2/5
Suppose -7 = 9*m + 11. Let b be 9 - (-2 + m + 9). What is d in 12*d**2 + 4 + 4*d**3 + 4 - 990*d + 970*d - b*d**4 = 0?
-2, 1
Let d be (-202)/(-9) + 32/(-72). Let 4 + 2*y - 38*y**2 + 33*y**2 - d*y + 79 + 22 = 0. What is y?
-7, 3
Factor -59280*r**2 + 300 + 59365*r**2 + 5*r**3 + 158*r + 222*r.
5*(r + 1)*(r + 6)*(r + 10)
Let c(s) = -4*s**3 + 51*s**2 + 133*s - 1554. Let r be c(8). Find v such that -33*v + r + 3/8*v**2 = 0.
44
Suppose -3*b = -2*c + 4106, 40*b = 36*b + 3*c - 5475. Let i = b + 1368. Factor i + 3/5*w**2 + 18/5*w.
3*w*(w + 6)/5
Let f(m) = 939*m**2 + m - 18. Let b(a) = 938*a**2 + 2*a - 21. Let s(u) = -6*b(u) + 7*f(u). Factor s(h).
5*h*(189*h - 1)
Let r(s) = s**3 + 54*s**2 + 153*s + 25. Let u be r(-51). Factor 53*o + 65*o**2 - u*o**3 - 61*o - 32*o.
-5*o*(o - 1)*(5*o - 8)
Determine k so that 1185*k - 8 - 955*k + 458*k**2 + 226*k**3 - 2*k**4 + 8 + 0 = 0.
-1, 0, 115
Let c(z) = 21*z**2 - 6018*z + 3024042. Let x(g) = 24*g**2 - 6017*g + 3024041. Let u(i) = -7*c(i) + 6*x(i). Find m such that u(m) = 0.
1004
Determine y, given that 11/10*y**3 - 5*y - 31/10*y**2 - 4/5 = 0.
-1, -2/11, 4
Let w(x) be the second derivative of -2/7*x**3 + 9/28*x**4 - 4*x - 18/7*x**2 + 1/70*x**6 + 9/70*x**5 + 4. Factor w(o).
3*(o - 1)*(o + 2)**2*(o + 3)/7
Let a = -377 - -400. Suppose -17*v = a - 74. Factor 0 - 2*d - 10/3*d**v + 2/3*d**4 + 14/3*d**2.
2*d*(d - 3)*(d - 1)**2/3
Let u be ((-462)/(-14))/(-11)*12/(-6*12). Factor -u*m**2 + 0 + 0*m.
-m**2/2
Let o(h) be the first derivative of -23/8*h**2 - 50 - 1/24*h**3 - 529/8*h. Factor o(r).
-(r + 23)**2/8
Let q(k) be the first derivative of -2*k**5/15 + 29*k**4/6 + 62*k**3/3 - 1743*k**2 - 3528*k - 313. Suppose q(n) = 0. Calculate n.
-12, -1, 21
Let s(d) be the first derivative of 13*d + 0*d**2 + 1/30*d**6 + 1/10*d**5 + 14 + 0*d**3 + 1/12*d**4. Let c(m) be the first derivative of s(m). Factor c(n).
n**2*(n + 1)**2
Let q be 24*((-2)/(-8) + 1). Factor -14*n - 3*n - 4*n + 3*n**2 + q.
3*(n - 5)*(n - 2)
Let v(s) be the third derivative of -s**5/30 - 67*s**4/6 - 133*s**3/3 + 12*s**2 - s. Find l, given that v(l) = 0.
-133, -1
Let u(q) = -6*q**2 - 32*q - 28. Let g(p) be the first derivative of -5*p**3/3 - 29*p**2/2 - 29*p + 149. Let f(a) = 4*g(a) - 3*u(a). Factor f(r).
-2*(r + 2)*(r + 8)
Let z be (90/20)/((-3)/4). Let y be (-6)/9 + (-16)/z. Factor c + c**3 + 3*c**2 - 7*c**y + 3*c.
c*(c - 2)**2
Let p(k) be the third derivative of -k**7/70 + 11*k**6/40 - 11*k**5/5 + 19*k**4/2 - 24*k**3 + k**2 + 532*k. Determine j so that p(j) = 0.
2, 3, 4
Let z be ((-6)/(-2))/(36/24). Determine f, given that 62*f**3 + 11 - 42*f**3 + 2*f**z - 34*f + 1 = 0.
-3/2, 2/5, 1
Let m = 2330 - 6988/3. Let k(p) be the third derivative of 0*p - m*p**4 + 2/5*p**5 - 1/10*p**6 + 0 + 1/105*p**7 + 0*p**3 - 17*p**2. Let k(w) = 0. Calculate w.
0, 2
Factor -111879*q + 3*q**2 + 111837*q - 48 - 48.
3*(q - 16)*(q + 2)
Let d be 3 - 42/18 - (-97)/3. Suppose 2*g + 0*l - l = d, -5*l + 27 = 2*g. Factor -14*q**2 + 2*q**3 + 32 - 4*q**3 + 0*q**3 - g*q.
-2*(q - 1)*(q + 4)**2
Let n(i) = 41 + 37293*i - 74587*i - i**2 + 37298*i. Let x(m) = 8 - 14 - 5*m - 34. Let s(w) = -5*n(w) - 4*x(w). Factor s(r).
5*(r - 3)*(r + 3)
Suppose -60 = -2*q - 5*t, 4*q + t = -89 + 119. Solve 12/7*c**3 + 0*c + 3/7*c**4 - 12/7*c**2 - 3/7*c**q + 0 = 0 for c.
-2, 0, 1, 2
Suppose -6*t = -9*t - 5*s + 11, -5*t + 15 = 5*s. Factor -6*b**3 + 2*b**2 + b + 6*b**3 - b**3 - 4*b**2 + t.
-(b - 1)*(b + 1)*(b + 2)
Let l(j) be the second derivative of -j**6/240 - 11*j**5/160 + 55*j**4/96 - 73*j**3/48 + 15*j**2/8 + 559*j. Factor l(m).
-(m - 2)*(m - 1)**2*(m + 15)/8
Let w(c) = c**2 - 170*c + 6072. Let z be w(51). Factor -1/2*u**2 + 8 + z*u.
-(u - 8)*(u + 2)/2
Let g = -92434 - -462172/5. Factor -4/5*z**3 + 0 + 2/5*z**2 - g*z**4 + 4/5*z.
-2*z*(z - 1)*(z + 1)*(z + 2)/5
Let n(r) be the third derivative of -r**8/84 - 26*r**7/315 - 7*r**6/90 + 17*r**5/45 + r**4/3 - 4*r**2 - 308*r. Find c, given that n(c) = 0.
-3, -2, -1/3, 0, 1
Let j = -3/7 + 19/28. Let m(g) be the first derivative of 0*g**2 + 1/12*g**3 - j*g + 12. Factor m(p).
(p - 1)*(p + 1)/4
Let s = -701 - -703. Suppose -2 + 6 = -c + b, -c - s*b + 8 = 0. Let 1/3*m - m**2 - 1/3*m**4 + m**3 + c = 0. What is m?
0, 1
Let k = -11054 - -11058. Let n(a) be the second derivative of 0*a**2 - 15*a + 0 + 1/3*a**4 - k*a**3. Find w such that n(w) = 0.
0, 6
Let r(d) = -2*d**4 - 7*d**3 - 145*d**2 - 17*d + 3. Let l(a) = -a**4 - 39*a**2 + a + 1. Let j(h) = 15*l(h) - 5*r(h). Factor j(u).
-5*u*(u - 10)*(u + 1)*(u + 2)
Let v(p) = p**2 + 41*p + 351. Let o be v(-12). Let w(c) be the second derivative of 0 + 15*c + 0*c**o - 1/6*c**2 + 1/36*c**4. Factor w(y).
(y - 1)*(y + 1)/3
Suppose -1/4*d**2 + 32*d + 0 = 0. Calculate d.
0, 128
Let d(l) be the third derivative of -l**5/15 - 779*l**4/6 - 47*l**2 - 7*l + 3. Factor d(y).
-4*y*(y + 779)
Let t(r) = r**2 - 1. Let h(x) = -3*x**2 - 94*x - 2114. Let g(u) = h(u) + 4*t(u). Let c(o) = 7*o**2 - 565*o - 12709. Let l(d) = 6*c(d) - 39*g(d). Factor l(i).
3*(i + 46)**2
Suppose -1009*g + 2051*g - 138 = 996*g. What is a in -60/7*a**2 + 6*a**4 - 12/7*a + 0 - 51/7*a**g = 0?
-1/2, -2/7, 0, 2
Let m be (2565/9)/(8/(-24)). Let l = m - -2567/3. Determine s, given that -16/3*s - 14/3 - l*s**2 = 0.
-7, -1
Let p(g) = 8*g**4 - 2260*g**3 + 566245*g**2 - 47812505*g + 78125005. Let x(i) = i**4 - i**3 - i**2 - i + 1. Let f(w) = 2*p(w) - 10*x(w). Factor f(v).
2*(v - 250)**3*(3*v - 5)
Let r(l) = -l**3 - 2*l**2 + 2*l. Let j be 2/(-3) - ((-39)/(-9) - 2). Let x be r(j). Factor -4*u**3 + 0*u**x + 2*u**4 + u - 2 + 3*u**2 - 3*u**4 + 3*u**3.
-(u - 1)**2*(u + 1)*(u + 2)
Let x be -35*53/((-42665)/46). Suppose 0 - 8/5*n - 8/5*n**x + 2/5*n**3 + 2/5*n**4 = 0. Calculate n.
-2, -1, 0, 2
Suppose -24 = 2*w - 2*i, 125*w - 121*w + i - 12 = 0. Suppose 0*m**4 + 0*m + 0*m**2 + 5/2*m**5 - 5/2*m**3 + w = 0. What is m?
-1, 0, 1
Factor 706/3*b + 2/3*b**2 + 700.
2*(b + 3)*(b + 350)/3
Let f be 36/8*((-176)/144)/(21/(-18)). Let 0 - 36/7*b**2 + f*b**3 - 108/7*b + 6/7*b**4 - 3/7*b**5 = 0. Calculate b.
-2, 0, 3
Let q = -23649 - -47355/2. Factor -75/4*c**3 - 21*c - 6 - 6*c**4 - q*c**2 - 3/4*c**5.
-3*(c + 1)**2*(c + 2)**3/4
Let -2/13*l**3 - 66/13*l + 0 - 68/13*l**2 = 0. What is l?
-33, -1, 0
Let f(c) be the second derivative of 10/3*c**3 + 11/3*c**4 - 65*c + 0*c**2 + 2/15*c**6 + 7/5*c**5 + 0. Factor f(k).
4*k*(k + 1)**2*(k + 5)
Let m(p) be the third derivative of -2*p**7/805 + p**6/60 - 2*p**5/69 - p**4/69 + 764*p**2 + 1. Factor m(w).
-2*w*(w - 2)**2*(6*w + 1)/23
Let d(y) = -25*y**3 - 560*y**2 - 15*y + 570. Let t(b) = 2*b**3 + 2*b - 1. Let v(z) = -d(z) - 10*t(z). Factor v(k).
5*(k - 1)*(k + 1)*(k + 112)
Let s = -853 + 855. Factor 6*x**2 - 7*x**s + 49 - 15 - 4*x**2 - 30*x + 166.
-5*(x - 4)*(x + 10)
Let p(l) be the third derivative of l**7/840 - 13*l**6/120 - 199*l**5/120 - 73*l**4/8 - 177*l**3/8 + 3191*l**2. Factor p(c).
(c - 59)*(c + 1)*(c + 3)**2/4
Let v(t) = -7*t + 60. Let q be v(10). Let o be 2*(1 - 5/q). Factor 22*h + 9/2*h**4 - 24*h**o + 7/2*h**2 - 10.
(h - 5)*(h + 1)*(3*h - 2)**2/2
Let i(f) = 1247*f - 1215*f + 61 + 579. Let y be i(-20). What is n in -2/5 - 1/5*n**3 + 3/5*n + y*n**2 = 0?
-2, 1
Let r(o) be the first derivative of -10*o**3 + 7/4*o**4 - 27/2*o**2 + 92 + 10*o. Factor r(f).
(f - 5)*(f + 1)*(7*f - 2)
Suppose -h = 10 - 6. Let i be (-3)/(6/h) + 0. Factor -26 - 12*w + 19 + 15 + 4*w**i.
4*(w - 2)*(w - 1)
Let z(r) be the third derivative of -r**6/60 - 136*r**5/15 - 18221*r**4/12 + 37538*r**3/3 + 717*r**2. Determine m, given that z(m) = 0.
-137, 2
Let l(y) = -2*y**2 - 16*y - 11. Let q be l(-7). Factor -7*p**4 + 7*p**3 - 12*p**2 - 23*p**q + 3*p**5 - 4*p**5.
-p**2*(p + 2)**2*(p + 3)
Let s(j) be the first derivative of j**4/10 + 442*j**3/15 + 438*j**2/5 + 3661. Suppose s(n) = 0. Calculate n.
-219, -2, 0
What is i in -93/7*i**2 + 183/7*i**3 - 3/7*i**5 + 0 - 87/7*i**4 + 0*i = 0?
-31, 0, 1
Suppose -42*p - 3*z - 3 = -47*p, -5*z - 5 = -4*p. Let k(y) be the second derivative of p + 0*y**2 + 0*y**3 + 