/7*j - 22/7*j**3 + z + 9/7*j**4 - 19/7*j**2.
j*(j - 3)*(j + 1)*(9*j - 4)/7
Let c(q) = 5*q**3 + 1042*q**2 - 4294*q + 4320. Let u(y) = 5*y**3 + 1048*y**2 - 4296*y + 4320. Let w(v) = -2*c(v) + 3*u(v). Find z such that w(z) = 0.
-216, 2
Let y(v) be the second derivative of -v**6/30 + v**4/6 - v**3/6 - v + 12. Let w(m) = -m**4 + 3*m**3 - 3*m**2 + m. Let u(r) = -5*w(r) - 20*y(r). Factor u(b).
5*b*(b - 1)*(b + 1)*(5*b - 3)
Let s = -2493/10 - -1249/5. Determine i so that -5/2*i**3 + 9/2*i - 3/2*i**2 + 0 - s*i**4 = 0.
-3, 0, 1
Let t(w) = 5*w + 40. Let b be t(-7). Suppose -4*k - b*s - 7 = 0, 4*k - 5*k = 2*s + 4. Factor k*z + 1/2*z**2 + 3/2.
(z + 1)*(z + 3)/2
Factor 298 - 24*s**3 - 20*s**2 - 178 - 3*s**4 + 186*s + 29*s**2 - 17*s**3 - 19*s**3.
-3*(s - 2)*(s + 1)**2*(s + 20)
Let k(l) = 15*l**3 - 30*l**2 - 35*l + 120. Let i(q) = -7*q**3 + 15*q**2 + 18*q - 60. Let w be 12/(-9) + (-33)/9. Let s(d) = w*i(d) - 2*k(d). Factor s(j).
5*(j - 3)*(j - 2)*(j + 2)
Let g = -61 - -61. Suppose -10*v + 28 + 2 = g. Factor -327*h**v + 322*h**3 - 5*h + h**2 - 11*h**2.
-5*h*(h + 1)**2
Let j(f) be the second derivative of f**7/1680 - 7*f**6/720 + f**5/24 - 5*f**3/6 - f**2 + 43*f - 2. Let v(w) be the second derivative of j(w). Factor v(c).
c*(c - 5)*(c - 2)/2
Let i(u) be the first derivative of u**5/30 + 49*u**4/12 + 95*u**3/18 - 97*u**2/6 - 7736. Solve i(k) = 0 for k.
-97, -2, 0, 1
Let z = 3878 - 3873. Let t(h) be the first derivative of h**z + h + 5/2*h**2 + 5/2*h**4 - 13 + 10/3*h**3 + 1/6*h**6. Factor t(q).
(q + 1)**5
Let n(y) be the first derivative of -3*y + 94 + 3*y**2 + 66 - 15 - y**3 - 33. Factor n(m).
-3*(m - 1)**2
Suppose -201*i = 1290*i. Factor 48/7*y**2 + i*y + 0 + 4/7*y**4 + 40/7*y**3 - 2/7*y**5.
-2*y**2*(y - 6)*(y + 2)**2/7
Let i = 168 - 177. Let j be 40/(-45)*i/6. Factor -j*k**2 + 0*k + 0 - 8/3*k**4 - 2/3*k**5 - 10/3*k**3.
-2*k**2*(k + 1)**2*(k + 2)/3
Determine r, given that -2588/3*r + 864 - 4/3*r**2 = 0.
-648, 1
Let c(z) be the first derivative of -z**4/18 - 172*z**3/27 - 631*z**2/9 - 364*z/3 + 2702. Find l, given that c(l) = 0.
-78, -7, -1
Factor -748/7*m - 2/7*m**2 - 746/7.
-2*(m + 1)*(m + 373)/7
Let f be (-325)/1848 - 6/(-33). Let s = 47/168 + f. Factor -4/7*d**2 - s*d**3 + 0*d + 0.
-2*d**2*(d + 2)/7
Solve 202/7*d**2 - 2/7*d**3 + 0 + 0*d = 0 for d.
0, 101
Let v(a) be the first derivative of 169*a**6/60 - 52*a**5/5 + 12*a**4 - 10*a**2 + a - 177. Let z(d) be the second derivative of v(d). Factor z(q).
2*q*(13*q - 12)**2
Let 4149/2*m**2 + 293916543/2 + 3/2*m**3 + 1912689/2*m = 0. Calculate m.
-461
Let t(m) be the third derivative of -m**4/24 - 17*m**3/6 - 6*m**2. Let g be t(-19). Factor 2*h + 3*h + h**g - 5*h - 3 + 2*h.
(h - 1)*(h + 3)
Let r = -3438/145 + 705/29. Let t(u) be the second derivative of -r*u**3 + 1/30*u**4 + 8/5*u**2 + 1 + 14*u. Solve t(w) = 0 for w.
1, 8
Let h(k) be the first derivative of 1867563*k**6/2 - 8007561*k**5/5 + 661000*k**4 - 235064*k**3/3 - 2024*k**2 - 16*k - 2090. Suppose h(w) = 0. What is w?
-2/263, 2/9, 1
Let l(o) be the second derivative of -961*o**5/240 - 2945*o**4/72 - 187*o**3/18 - o**2 - 43*o + 5. Factor l(s).
-(s + 6)*(31*s + 2)**2/12
Suppose 0 = -36*i - 67*i - 8034. Let k be 832/624 - (-44)/i. Factor -8/13*t - 12/13*t**2 + 16/13 - 2/13*t**4 + k*t**3.
-2*(t - 2)**3*(t + 1)/13
Let w be 10/30 + 14/(-6). Let n be -1*(w + (-2 - -4)) + 4. Factor 294*c**3 - 54*c**3 - 192*c - 6*c**4 - 72*c**2 - 69*c**n - 48.
-3*(c - 2)**2*(5*c + 2)**2
Let w(v) be the second derivative of -1/12*v**4 + 0*v**5 + 0 + 0*v**3 + 1/30*v**6 + 0*v**2 - 42*v. Factor w(d).
d**2*(d - 1)*(d + 1)
Let r(w) be the second derivative of w**4/102 - 1574*w**3/51 + 619369*w**2/17 + 3671*w. Factor r(f).
2*(f - 787)**2/17
Let h(n) = 7*n + 17. Let p(z) = 4*z + 8. Let o(s) = 3*h(s) - 5*p(s). Let j be o(-8). Let j*c**2 + 0*c**2 - c**3 + 2*c**3 - 2*c**2 = 0. Calculate c.
-1, 0
Let y(v) = -1192*v - 57214. Let u be y(-48). Solve 21*s + 0 + 3/5*s**u = 0.
-35, 0
Suppose -354 + 524 = 565*k - 982 - 543. Determine o, given that 0 + 0*o**2 + 116/3*o**k + 4/3*o**4 + 0*o = 0.
-29, 0
Let k(r) be the first derivative of 39 - 25/2*r**2 + 6*r - 3*r**3. Factor k(n).
-(n + 3)*(9*n - 2)
Let l(s) be the second derivative of -1/150*s**6 - 128/15*s**3 - 1 + 31/100*s**5 - 56/15*s**4 + 0*s**2 + 119*s. Find n, given that l(n) = 0.
-1, 0, 16
Let y be (5/(-130) + 736/(-2496))*0/(-1). Determine h, given that 0*h + 1/3*h**2 + 1/6*h**3 + y = 0.
-2, 0
Let r = 35353/435 + -11736/145. Factor r*u**2 + 7*u - 22/3.
(u - 1)*(u + 22)/3
Suppose -4*f + 3*f + 5*o + 15 = 0, -2*f = -2*o - 46. Determine q so that 23*q**2 + 2*q**2 - 24*q + 29*q + 125*q + f = 0.
-5, -1/5
Let z(n) be the first derivative of -50*n**6 - 552*n**5 + 15057*n**4/4 + 1031*n**3 + 78*n**2 - 2613. What is v in z(v) = 0?
-13, -1/10, 0, 4
Determine y, given that 6232*y**4 + 1081*y**3 + 224*y - 1112*y**2 + 279*y**3 - 12395*y**4 + 6213*y**4 = 0.
-28, 0, 2/5
Solve 56*g**2 + 32*g + 49/2*g**3 + 0 = 0.
-8/7, 0
Let r(g) be the third derivative of 2*g**2 - 1/840*g**7 + 0*g**3 - 1/48*g**4 + 1/240*g**5 + 8*g + 1/240*g**6 + 0. What is w in r(w) = 0?
-1, 0, 1, 2
Suppose -b + 3 = -0*b. Suppose 0 = 4*l + b*d - 61, -l + 4*l = -d + 42. Factor -24 - 5*z**2 + l + 11 - 10*z.
-5*z*(z + 2)
Let y(c) be the third derivative of 0*c - 6/5*c**3 + 0 + 16/15*c**4 - 7/300*c**5 + 91*c**2. Factor y(o).
-(o - 18)*(7*o - 2)/5
Let a(z) = 5*z**3 + 2*z**2 - 7*z. Suppose 4*n = 4*b + 8, 0*b - 11 = 3*b - 4*n. Let r(y) = -4*y**3 - 2*y**2 + 6*y. Let x(c) = b*a(c) + 4*r(c). Factor x(v).
-v*(v - 1)*(v + 3)
Suppose 2*h - 3187 = -b, -3*h + 6392 = 2*b - 8*h. Determine n, given that -b*n**2 + 25*n**4 - 5*n**5 - 20*n**3 + 3191*n**2 = 0.
0, 1, 4
Let h(l) = 2*l - 24. Let v be h(9). Let x be ((-4)/42)/(v/27). Suppose 12/7*q**4 + 0 + x*q**3 + 0*q**2 + 0*q = 0. Calculate q.
-1/4, 0
Suppose -2*t + 0*t = -2*y - 2670, -y = 4*t + 1340. Let m = y - -1336. Factor 3/5 + m*j - 3/5*j**2.
-3*(j - 1)*(j + 1)/5
Suppose -4*r - 6*r = -20. Suppose 12*k - 5600 = r*k. What is f in -221*f + 111*f + k*f**5 + 76*f**4 + 86*f - 416*f**3 - 196*f**2 = 0?
-3/5, -2/7, -1/4, 0, 1
Suppose 0 = 5*x + 2*t - 14, -2*t + 4*t + 18 = 3*x. Factor 4*b**3 - 500*b - x*b**2 + b**4 - b**5 + 500*b.
-b**2*(b - 2)*(b - 1)*(b + 2)
Factor -9457*c**3 - 28 + 8328*c - 8915*c + 343*c**4 - 4090*c**2 - 5*c**2.
(c - 28)*(7*c + 1)**3
Factor 3*x**3 + 110006 + 33681*x - 8840 + 24*x**2 - 669*x**2 + 5763.
3*(x - 109)**2*(x + 3)
Let o(t) be the third derivative of -t**5/270 + 77*t**4/108 + 5120*t**2. Solve o(h) = 0 for h.
0, 77
Let l(v) = -3*v - 97. Let a(d) = -4*d - 96. Let p(b) = 3*a(b) - 2*l(b). Let o be p(-16). Factor -1/2*s**2 - o + 2*s.
-(s - 2)**2/2
Let b(c) be the first derivative of 4*c**6/3 - 362*c**5/5 + 221*c**4/2 - 88*c**3/3 - 6825. Determine j, given that b(j) = 0.
0, 1/4, 1, 44
Suppose -62*q + 65*q + 234 = 0. Let i = q - -83. Let 25 - 42*p - 65*p + 177*p - i*p**2 - 50*p = 0. Calculate p.
-1, 5
Let w(j) be the first derivative of 2*j**3/3 + 7444*j**2 + 27706568*j + 7844. Determine u so that w(u) = 0.
-3722
Let n(w) = 5*w**2 + 75*w - 408. Let h(f) = 5*f**2 + 75*f - 404. Let t(b) = 7*h(b) - 6*n(b). Determine k so that t(k) = 0.
-19, 4
Let q = 1970 + -1932. Suppose 2*t + 36*z - q*z - 10 = 0, 4*z = 3*t - 18. Factor -1/2*r**t + 13*r - 169/2.
-(r - 13)**2/2
Let a(w) be the second derivative of -1/8*w**5 - 5/24*w**4 + 1/3*w**3 + 153*w + 1/60*w**6 + 1/84*w**7 + w**2 + 0. Solve a(g) = 0 for g.
-2, -1, 1, 2
Let p(k) be the second derivative of k**7/210 + k**6/90 - k**5/15 + 3*k**3 - 37*k - 1. Let m(s) be the second derivative of p(s). Factor m(v).
4*v*(v - 1)*(v + 2)
Suppose -156 = 128*u + 54*u - 234*u. Let o(h) be the second derivative of -40*h + 1/16*h**4 + 0 + 0*h**2 + 1/2*h**u. Suppose o(r) = 0. What is r?
-4, 0
Factor 145283*o**2 - 18670176*o - 134699*o**2 + 15667028308 - 2*o**3 - 4688964820.
-2*(o - 1764)**3
Let a(b) be the second derivative of -b**4/12 + 17*b**3/6 + 1459*b. Let a(d) = 0. Calculate d.
0, 17
Let h(m) be the third derivative of m**8/784 - 2*m**7/49 + 9*m**6/70 + m**5/70 - 37*m**4/56 + 9*m**3/7 + 1361*m**2. Let h(j) = 0. Calculate j.
-1, 1, 18
Suppose n - 5 = -26. Let d = 68/3 + n. Factor 0*t + 0 + d*t**2.
5*t**2/3
Let y(f) be the first derivative of 0*f**2 - 1/60*f**5 + 0*f**4 + 0*f + 11 - 7/3*f**3 + 1/1080*f**6. Let s(v) be the thi