**2 - 44*i + 7. Let z(v) = 28*v**2 - 29*v + 5. Let d(h) = 5*c(h) - 7*z(h). Factor d(y).
-y*(y + 17)
Determine n, given that -38/15*n**2 + 4/15*n**3 - 8/5 + 56/15*n + 2/15*n**4 = 0.
-6, 1, 2
Let u be (19 - 10)*(-9 + (-252)/(-27)). Let b(p) be the second derivative of -5*p - 1/15*p**u - 1/10*p**2 - 1/60*p**4 + 0. Factor b(j).
-(j + 1)**2/5
Let o(m) be the second derivative of 23/2*m**2 + 25*m + 1/270*m**5 + 0 - 1/27*m**3 + 0*m**4. Let f(v) be the first derivative of o(v). Factor f(n).
2*(n - 1)*(n + 1)/9
Let c(r) = -r**3 - 249*r**2 + 1050*r + 1287. Let l(t) = -t**3 - t**2 - 8*t + 3. Let d(z) = -c(z) - l(z). Factor d(s).
2*(s - 5)*(s + 1)*(s + 129)
Let s be ((-216)/30)/(24/80). Let o be (-23)/(-9) - s/54. Factor 18/5*y**o + 2/5*y + 8/5*y**4 + 12/5*y**2 + 0.
2*y*(y + 1)**2*(4*y + 1)/5
Suppose -10*p = -55 + 15. Suppose p*g + 23 - 23 = 0. Factor 0 - 1/3*d**2 + g*d.
-d**2/3
Let t(h) be the second derivative of 3*h**6 + 83/8*h**4 - 627/80*h**5 + 0 - 25/56*h**7 - 15/2*h**3 + 3*h**2 + 91*h. Find f such that t(f) = 0.
2/5, 1, 2
Let l(d) be the second derivative of 2*d**5/135 + 41*d**4/108 + 10*d**3/27 - 2*d**2 - 45*d. Let s(o) be the first derivative of l(o). Factor s(x).
2*(x + 10)*(4*x + 1)/9
Suppose -5*g = 3*n - 119, -3*g + 0*g - n = -65. Let v(u) be the second derivative of 0 + g*u + 1/28*u**4 + 3/7*u**3 + 27/14*u**2. Suppose v(x) = 0. Calculate x.
-3
Factor -2/13*c - 526/13*c**2 + 526/13 + 2/13*c**3.
2*(c - 263)*(c - 1)*(c + 1)/13
Let k(i) be the third derivative of i**6/240 - 257*i**5/150 + 613*i**4/240 + 41*i**3/6 - 862*i**2. Factor k(u).
(u - 205)*(u - 1)*(5*u + 2)/10
Let f be ((-1720)/(-248) - 2) + (-2)/(-31). Let j be 14 + (-884)/65 + 13/f. Factor -9*m - 15*m**2 - 1/4*m**5 - 13/4*m**j + 0 + 5/2*m**4.
-m*(m - 6)**2*(m + 1)**2/4
Let n(x) be the second derivative of 0*x**4 + 0 + 35*x + x**3 - 1/10*x**5 - 2*x**2. Factor n(y).
-2*(y - 1)**2*(y + 2)
Factor -1825*v**3 + 868*v + 99*v**2 - 3*v**2 + 3653*v**3 - 1832*v**3.
-4*v*(v - 31)*(v + 7)
Let x(i) = -i**2 + i + 1. Let k(p) = 1098500*p**3 + 354904*p**2 + 38216*p + 1368. Let l(r) = -k(r) - 4*x(r). Let l(m) = 0. Calculate m.
-7/65
Let j(z) = -5*z**2 - 3*z + 6. Let k(x) = -x**2 - x. Suppose 3*c - 112 = 5*c. Let u = c + 53. Let s(o) = u*j(o) + 12*k(o). Factor s(l).
3*(l - 3)*(l + 2)
Let i(n) = n**3 + 4*n**2 + 2*n + 1. Let f be i(-3). Factor f*b**4 + 31*b**2 - 18*b**2 - 33*b**2 + 16*b**3.
4*b**2*(b - 1)*(b + 5)
Let m be (15/(-9) - 3)*(-6)/7. Suppose -2*u = -23*u + m*u. Factor 1/3*d**3 - d**2 + u + 2/3*d.
d*(d - 2)*(d - 1)/3
Find h, given that -2/17*h - 840/17 + 2/17*h**2 = 0.
-20, 21
Let r be (-12)/82*(-85567)/20870. Factor -14/5*c + 4/5*c**3 + 7/5*c**2 + r.
(c - 1)*(c + 3)*(4*c - 1)/5
Let b(g) be the third derivative of -g**8/588 + 31*g**6/210 + 106*g**5/105 + 22*g**4/7 + 16*g**3/3 - 2*g**2 - 1149*g. Suppose b(f) = 0. Calculate f.
-2, -1, 7
Let v = 2750125/4 + -687530. Solve -v*c**4 + 0 + 1/4*c**2 + 1/4*c - 3/4*c**3 - 1/2*c**5 = 0.
-1, 0, 1/2
Let a(u) be the third derivative of 0*u**3 - 3/40*u**5 + 9/280*u**7 - 110*u**2 + 5/32*u**6 + 0*u + 0 + 0*u**4. Let a(b) = 0. Calculate b.
-3, 0, 2/9
Let l be (-5)/(-30)*-98 - 8188/(-356). Factor 8/3*z + 28/3*z**2 + l*z**3 + 0.
4*z*(z + 1)*(5*z + 2)/3
Suppose 2*d = d + 3, -d + 43 = 4*j. Suppose j*q - 3 = 27. What is a in -45*a - 3*a**3 + 48*a + 0*a**q + 9*a**2 - 9 = 0?
-1, 1, 3
Let s(h) = 15*h**2 + 4057*h + 2043969. Let f(z) = -7*z**2 - 2028*z - 1021995. Let k(t) = -13*f(t) - 6*s(t). Factor k(l).
(l + 1011)**2
Let w be (-592)/28*189/(-1026) - (-4)/38. Let h(n) be the second derivative of 1/3*n**3 - 1/9*n**w - 4/9*n**2 + 0 + 39*n + 1/90*n**5. What is q in h(q) = 0?
1, 4
Let h(l) = -10*l**2 - 334*l + 2593. Let v(m) = 3*m**2 + 111*m - 864. Let s(a) = -6*h(a) - 19*v(a). Factor s(t).
3*(t - 22)*(t - 13)
Let z(x) = -x**2 + 9*x - 6. Let r be z(8). Factor 12*d + 15 + 2 - 17 + 2*d**2 - r*d**3.
-2*d*(d - 3)*(d + 2)
Let x(i) = 29*i**2 + 867*i - 517. Let s(b) = 14*b**2 + 434*b - 258. Let g(q) = -11*s(q) + 6*x(q). Determine d so that g(d) = 0.
-22, 3/5
Suppose -3*n - 4*r + 127 = 0, -193 = -10*n + 5*n - 4*r. Let z(l) be the first derivative of n - 16*l**3 + 9/2*l**4 + 13*l**2 - 4*l. Factor z(k).
2*(k - 2)*(3*k - 1)**2
Let o(b) = -b**2 + 66*b - 477. Let d be o(13). Let v = d + -210. What is c in 2/5*c**v - 2/5*c + 12/5*c**3 + 0 = 0?
-1/2, 0, 1/3
Suppose -3*s = -5*z - 8, -268*z - 2*s = -266*z - 16. Let c = 2561/3 + -849. Factor -158/3*h - c*h**z - 44/3.
-2*(h + 11)*(7*h + 2)/3
Suppose 0 = 5*f, 3*z - 3*f - 9 = -6*f. Factor 2*j**4 + 12 - 2*j**3 + 80*j**2 + 12*j**2 - 38*j - 16*j**z - 50*j**2.
2*(j - 6)*(j - 1)**3
Let g(x) be the first derivative of -x**6/720 + 19*x**5/360 + 5*x**4/36 + 37*x**2/2 + x + 47. Let a(p) be the second derivative of g(p). Factor a(q).
-q*(q - 20)*(q + 1)/6
Let h be 2/(-10) + (-15)/((-40200)/(-844)). Let w = -1/67 - h. What is u in -5/4*u - 1/4*u**3 - w - u**2 = 0?
-2, -1
Let l be -94 + 107 + (-33)/6. Let 27/4*k**4 - 3 - 141/4*k**2 + 18*k + 21*k**3 - l*k**5 = 0. Calculate k.
-2, 2/5, 1/2, 1
Let c(j) be the second derivative of 0*j**2 - 3/50*j**6 - 1/4*j**5 + 0 - 74*j - 4/15*j**3 + 7/10*j**4. Let c(f) = 0. Calculate f.
-4, 0, 2/9, 1
Suppose -269*s + 1 - 2 = -1. Let q(x) be the second derivative of 0 + 3/28*x**5 + 1/70*x**6 + 12*x + s*x**3 + 0*x**2 + 1/7*x**4. Let q(t) = 0. Calculate t.
-4, -1, 0
Suppose 0 = -3*l - 554 - 538. Let z be 152/l - (-6 + 228/42). Factor -8/13*h**2 + 0 + 8/13*h + z*h**4 - 2/13*h**3.
2*h*(h - 2)*(h - 1)*(h + 2)/13
Let c(f) = -3*f**2 + 189*f - 720. Let p(y) = -3*y**2 + 188*y - 718. Let b(t) = 7*c(t) - 6*p(t). Factor b(n).
-3*(n - 61)*(n - 4)
Suppose -81*w + 80*w + 70 = 0. Let k = w + -69. Let m(q) = -q**2 - q. Let y(d) = -2*d**3 - 12*d + 2. Let u(h) = k*y(h) - 6*m(h). Factor u(s).
-2*(s - 1)**3
Let o(m) = 20*m - 461. Let n be o(25). Let x be 2 + n/(-15) + 12/15. Determine s, given that -x*s**2 + 2/5*s + 0 = 0.
0, 2
Let l = 89/36 + -19/12. Let y(c) be the first derivative of l*c + 1/18*c**4 + 24 + 4/27*c**3 - 7/9*c**2. Factor y(o).
2*(o - 1)**2*(o + 4)/9
Let -67240*h**3 - 68921/6*h**4 + 10004*h**2 - 1472/3*h + 8 = 0. Calculate h.
-6, 2/41
Let i(v) be the third derivative of 0*v**3 + 3*v + 1/20*v**6 + 0*v**4 + 4*v**2 + 0 - 1/30*v**5. Solve i(g) = 0 for g.
0, 1/3
What is o in -4*o**2 - 4*o**2 + 6*o**2 + 49*o + 104*o + 85*o = 0?
0, 119
Let u(p) = -3*p**2 + 5. Let h(w) = -w**4 + 9*w**3 - 80*w + 172. Let a(c) = h(c) + 4*u(c). Let a(f) = 0. Calculate f.
-3, 4
Suppose 0 = -3*t - 12*t. What is l in t + 0 - 7*l**5 + 23096*l**4 - 23093*l**4 - 2*l**5 = 0?
0, 1/3
Let v = 323/23 - 601/69. Let 2/3*l**2 - v*l + 8 = 0. Calculate l.
2, 6
Let x be (-126)/(-36)*(-56)/(-49). Let t(o) be the third derivative of 2*o**x + 0*o + 11/30*o**5 - 12*o**3 + 0 + 1/60*o**6 + 24*o**2. Let t(l) = 0. Calculate l.
-6, 1
Let g(r) be the third derivative of -r**6/660 - 2*r**5/165 - 5*r**4/132 - 2*r**3/33 + 23*r**2 + 5*r. Determine s, given that g(s) = 0.
-2, -1
Let u = 71711 - 430261/6. Factor u*t**3 - 15/2*t + 5/6*t**2 - 15/2.
5*(t - 3)*(t + 1)*(t + 3)/6
Suppose -3*f - 29 + 44 = 0. Suppose -5*q = -2*s - 0*s - 19, 2*q + 4 = -f*s. Factor 5*a**q + 13*a - 10*a**2 + 10 + 6*a - 24*a.
5*(a - 2)*(a - 1)*(a + 1)
Let k(c) be the third derivative of 1/204*c**4 + 1/1020*c**6 + 1/255*c**5 + 0*c**3 + 0 + 40*c**2 + 0*c. Factor k(r).
2*r*(r + 1)**2/17
Factor -347*d + 122*d + 1166 + 4 - 11825495*d**2 + 11825500*d**2.
5*(d - 39)*(d - 6)
Suppose -20*o**2 - 4/9*o**3 + 80 + 16/9*o = 0. What is o?
-45, -2, 2
Factor -34*x**3 + 3136 - x**4 + 2215*x - 3135*x**2 + 146*x**3 - 2327*x.
-(x - 56)**2*(x - 1)*(x + 1)
Suppose 0 = -3*r - 3*m, -3*r + 6 = -2*r - m. Factor 5*y**r - 3468 - 2*y**3 + 31660*y**2 + 3264*y - 31459*y**2.
3*(y - 1)*(y + 34)**2
Solve -34/9*g**4 + 2/9*g**5 - 358/9*g**3 + 0 - 100*g - 338/3*g**2 = 0.
-3, -2, 0, 25
What is l in -9/2 - 41/8*l**3 - 105/8*l**2 - 13*l - 3/8*l**4 + 1/8*l**5 = 0?
-2, -1, 9
Factor 2/3*d**4 - 8*d**2 + 32/3*d + 0 + 0*d**3.
2*d*(d - 2)**2*(d + 4)/3
Let m be (1 - (-30)/(-4))*-2. Factor -6*v**4 + 0*v**5 + m*v**2 - v**5 + 5*v**5 - 11*v**2.
2*v**2*(v - 1)**2*(2*v + 1)
Let i = 772 - 704. Let u = 68 - i. Factor -1/2*d**4 - 1/2*d**3 + u*d + 0 + 0*d**2.
-d**3*(d + 1)/2
Let i(u) = -2*u**5 + 528*u**4 - 46990*u**3 + 1454292*u**2 - 4041822*u + 2634060. Let y(x) = -x**3 + 4*x