. Let z(w) = 28*w**2 + 210*w + 33. Suppose 7*a = -3*g + 4*a - 27, -2*g = -5*a - 17. Let k(o) = g*z(o) + 11*h(o). Factor k(p).
-2*p*(p + 35)
Let t(a) be the third derivative of -a**6/30 - 7*a**5/30 + 7*a**4/12 - 2*a**3/3 - 45*a**2 + a. Let b(z) = z**3 + z + 2. Let p(m) = 4*b(m) + 2*t(m). Factor p(q).
-4*q*(q - 1)*(q + 8)
Let y(g) be the first derivative of g**5/30 - 2*g**4/3 - 3*g**3 - 14*g**2/3 + 32*g - 70. Let x(o) be the first derivative of y(o). Factor x(j).
2*(j - 14)*(j + 1)**2/3
Find w such that 42/5*w**4 + 10 + 8/5*w**5 - 8/5*w**3 + 0*w - 92/5*w**2 = 0.
-5, -5/4, -1, 1
Let y(b) = -3*b**2 + 12*b + 49. Let q(w) = 2*w**2 + w. Let j be 3 - -16*(-6)/12. Let f(d) = j*y(d) - 10*q(d). Solve f(u) = 0.
-7
Factor -88/3 - 2/3*n**2 + 16*n.
-2*(n - 22)*(n - 2)/3
Let v(t) be the third derivative of -t**8/196 + 52*t**7/735 - 38*t**5/35 - 109*t**4/42 - 16*t**3/7 - 932*t**2. What is x in v(x) = 0?
-1, -1/3, 3, 8
Let i = 31 + -30. Let p(x) = 12*x - 7. Let q be p(i). Determine j, given that 9*j + q*j + 0*j**2 - 18*j - 4*j**2 = 0.
-1, 0
Let g(z) be the first derivative of -10*z**3 - 7 - 5/4*z**4 - 40*z + 75/2*z**2. Factor g(i).
-5*(i - 1)**2*(i + 8)
Let d = -417 - -430. Let d*x**3 + 783*x**3 + 20*x**5 - 780*x**2 - 260*x**4 + 169*x**3 + 180*x = 0. Calculate x.
0, 1/2, 6
Let r(x) be the third derivative of x**8/26880 + 13*x**7/10080 - 29*x**4/12 - 85*x**2. Let j(d) be the second derivative of r(d). Factor j(o).
o**2*(o + 13)/4
Let k be 138/5 - (-120798)/(-4474). Factor -7/5*l**3 - k*l - 12/5*l**2 + 2/5.
-(l + 1)**2*(7*l - 2)/5
Let w(p) be the third derivative of 5*p**7/189 + 179*p**6/216 + 259*p**5/180 + 205*p**4/216 + 17*p**3/54 + 45*p**2 + 4*p. Suppose w(a) = 0. What is a?
-17, -1/2, -1/5
Let p(j) = 10*j**2 + 7627*j + 1444000. Let k(f) = -5*f**2 - 3812*f - 722000. Let i(z) = 9*k(z) + 4*p(z). Solve i(u) = 0 for u.
-380
Solve 512/7 + 20/7*i**2 + 184*i = 0 for i.
-64, -2/5
Let z(s) be the second derivative of 7*s**7/6 - 7*s**6/3 - 101*s**5/20 + 31*s**4/6 + 26*s**3/3 + 4*s**2 + 4253*s. Let z(l) = 0. Calculate l.
-1, -2/7, 1, 2
Find i, given that -96/5 - 52/5*i + 2/5*i**3 + 46/5*i**2 = 0.
-24, -1, 2
Let j(w) = w**2 - 469*w - 7260. Let h be j(-15). Find x such that 0 + h*x**2 - 6*x**4 + 20/3*x**3 - 2/3*x**5 + 0*x = 0.
-10, 0, 1
Let k(a) be the third derivative of -a**6/40 + 407*a**5/20 + 15*a**2 + 10*a. Factor k(z).
-3*z**2*(z - 407)
Let s(y) be the second derivative of -y**7/294 - 268*y**6/105 - 3808*y**5/5 - 2293504*y**4/21 - 130803712*y**3/21 + 1368408064*y**2/7 + 1026*y. Factor s(x).
-(x - 8)*(x + 136)**4/7
Let i be 9/(-3) - (-1 + -2). Let h(c) = i - 5 - 7*c**2 + 4*c - 4. Let p(m) = -3*m**2 + 2*m - 4. Let a(b) = 4*h(b) - 9*p(b). Factor a(u).
-u*(u + 2)
Let c = -31413 - -31438. Let w(z) be the first derivative of -21/4*z**2 + c - 9/4*z**3 + 6*z. Factor w(r).
-3*(r + 2)*(9*r - 4)/4
Suppose -9 = 3*g, -2*v - 2*g + 4*g = -26. Factor 0*m**3 + v*m**2 + 18*m**2 + 24 - 74*m + 36*m**2 - 14*m**3.
-2*(m - 3)*(m - 1)*(7*m - 4)
Let w(i) = -21*i + 7 + 11 + 38*i + 18. Let o be w(-2). Determine y so that -2*y**o - 2/3 - 2*y - 2/3*y**3 = 0.
-1
Let o(z) = 124*z + 151. Let l be o(-6). Let n = l + 3563/6. Solve 5/3*q**2 + 0*q**3 + 0 - 5/3*q**4 + 5/6*q - n*q**5 = 0.
-1, 0, 1
Let s(c) be the second derivative of 1/165*c**6 - 1/11*c**2 + 0*c**4 - 3 + 9*c - 1/55*c**5 + 2/33*c**3. Solve s(i) = 0 for i.
-1, 1
Suppose 6*v = 14*v + 9*v - 119. Factor 0 - v*d + 1/3*d**2.
d*(d - 21)/3
Let i(k) be the second derivative of -k**5/105 + 13*k**4/42 - 40*k**2 - 10*k - 1. Let d(b) be the first derivative of i(b). Let d(x) = 0. What is x?
0, 13
Suppose 179*d = -149*d + 656. Factor 20/13*t**d + 18/13*t + 0 + 2/13*t**3.
2*t*(t + 1)*(t + 9)/13
Let f be (-390)/(-567) + (-2898)/(-39123). Factor f*x + 10/7 + 2/21*x**2.
2*(x + 3)*(x + 5)/21
Let x(o) = 13*o**2 - 70*o + 1024. Let j(t) = 24*t**2 - 139*t + 2048. Suppose 19*f = 51 + 63. Let z(l) = f*j(l) - 11*x(l). Factor z(a).
(a - 32)**2
Solve -2691 - 1744 - 5764*d - 765 + 868 + 16*d**2 = 0 for d.
-3/4, 361
Let c(u) be the first derivative of u**6/6 - 17*u**5/5 + 22*u**4 - 200*u**3/3 + 104*u**2 - 80*u + 610. Find b such that c(b) = 0.
1, 2, 10
Let m(r) = 9*r**2 + 10*r - 7. Let f be m(-3). Factor -f*s - 93*s - 17*s - 48*s + 10*s - 9216 - s**2.
-(s + 96)**2
Let s be 1070/963 + 12*3/(405/10). Factor 3/2*c**4 + 33/2*c - 9/2*c**s - 9/2*c**3 - 9.
3*(c - 3)*(c - 1)**2*(c + 2)/2
Let a(g) be the third derivative of -g**6/300 - 6*g**5/25 - 27*g**4/4 - 486*g**3/5 - 33*g**2 - 4*g. Factor a(h).
-2*(h + 9)**2*(h + 18)/5
Let v(g) be the second derivative of -34*g + 1/24*g**4 + 12*g**3 + 0 + 1296*g**2. Solve v(w) = 0 for w.
-72
Factor 0 - 198/7*w + 199/7*w**2 - 1/7*w**3.
-w*(w - 198)*(w - 1)/7
Let g(u) be the third derivative of -1/48*u**6 - 1/420*u**7 + 0*u + 0 - 57*u**2 - 1/2*u**3 + 5/48*u**4 + 7/120*u**5. Factor g(q).
-(q - 1)**2*(q + 1)*(q + 6)/2
Factor 547*q**3 + 62994*q**2 - q**4 - 48*q**3 + 185504*q + 23494 + 99514 + 2*q**4.
(q + 1)*(q + 2)*(q + 248)**2
Let x be (-336)/(168/6) - (-10 + -2). Let g(h) = -4*h - 3. Let n be g(-2). Factor 3/8*k**n + 0*k + 0*k**4 + 0*k**2 - 3/2*k**3 + x.
3*k**3*(k - 2)*(k + 2)/8
Suppose 4127*v - 78 - 6338 - 1838 = 0. Factor n**3 - 73/5*n**v - 6*n + 0.
n*(n - 15)*(5*n + 2)/5
Factor -1809/2*s**2 - 597/2*s**3 - 303 - 1815/2*s + 3/2*s**4.
3*(s - 202)*(s + 1)**3/2
Let y(k) = -2*k**2 - 13*k + 5. Let m(z) = 3*z**2 + 3*z - 4. Let q(l) = 9*l**2 + 8*l - 11. Let b(n) = -8*m(n) + 3*q(n). Let v(c) = 6*b(c) + 3*y(c). Factor v(r).
3*(r - 3)*(4*r - 1)
Let w(g) be the third derivative of g**6/540 + 41*g**5/108 - 311*g**4/216 + 52*g**3/27 + 752*g**2. Factor w(t).
(t - 1)*(t + 104)*(2*t - 1)/9
Let x = -106 + 108. Determine z so that 2883*z**4 - 2879*z**4 - x*z + 4*z**3 - 2*z - 4*z**2 = 0.
-1, 0, 1
Let u be (-416)/(-3120) - (-3 - (-1 + 4/(-5))). Factor 0 + u*y**2 + 4/3*y.
4*y*(y + 1)/3
Let o be -1 - (-4 + 13)/(-3). Let v(h) = -3*h**3 + 58*h**2 - 119*h + 3. Let n be v(17). Determine w so that 2/3 - 2/3*w**n - 2*w + 2*w**o = 0.
1
Solve -50/9*d + 2/9*d**2 + 44/3 = 0 for d.
3, 22
Factor -80*m**4 - 191*m**3 - 1923*m**5 + 46*m**3 + 1918*m**5 - 70*m**2.
-5*m**2*(m + 1)**2*(m + 14)
Let m be 328 - 293 - (-636)/(-20). Determine g so that 12*g**2 - m + 8*g - 14/5*g**4 - 2*g**3 = 0.
-2, -1, 2/7, 2
Let j(x) be the first derivative of -x**6/40 + x**5/2 - 181*x**2/2 + 149. Let c(t) be the second derivative of j(t). Find p, given that c(p) = 0.
0, 10
Suppose 112/13*g**3 - 18*g**2 - 1890/13*g - 8/13*g**4 + 5400/13 = 0. What is g?
-4, 3, 15/2
Let x(r) be the first derivative of -4*r - 2/3*r**3 + 2/3*r**2 - 4/9*r**4 + 21. Let u(a) be the first derivative of x(a). Factor u(q).
-4*(q + 1)*(4*q - 1)/3
Suppose 263 = -5*k + 3*a, a + 0*a - 51 = k. Let u be (0 + 1)*((-44)/k - -1). Determine f, given that u*f**2 - 9/5*f - 3/5*f**3 + 3/5 = 0.
1
Let o(l) = l**4 + l**2. Let z(m) = -14*m**4 - 50*m**3 - 80*m**2 - 54*m - 14. Let c(u) = -4*o(u) - 2*z(u). Suppose c(k) = 0. Calculate k.
-7/6, -1
What is c in -88/3*c**2 - 8/21*c**5 - 202/21*c**3 + 234/7*c + 136/21*c**4 - 60/7 = 0?
-2, 1/2, 3, 15
Determine d, given that -44/7*d - 30 - 2/7*d**2 = 0.
-15, -7
Let c(b) be the second derivative of -b**5/20 + b**4 + 23*b**3/3 - 13*b**2/2 - b + 1. Let m be c(15). Find n, given that -m*n + 2/3*n**2 + 4/3 = 0.
1, 2
Let z = 21064 - 21064. Let a(w) be the second derivative of 4/33*w**4 + 0*w**2 + 1/330*w**6 - 2*w + z - 2/11*w**3 - 7/220*w**5. Let a(v) = 0. What is v?
0, 2, 3
Let i(y) = 344*y**3 - 2082*y**2 + 3060*y + 138. Let z(j) = 690*j**3 - 4165*j**2 + 6120*j + 275. Let c(n) = 5*i(n) - 3*z(n). Factor c(f).
-5*(f - 3)**2*(70*f + 3)
Solve 2/3*l**3 - 26/3*l**2 - 40/3 + 64/3*l = 0.
1, 2, 10
Let c(k) be the first derivative of k**3/8 + 87*k**2/16 + 75*k/2 + 348. Factor c(o).
3*(o + 4)*(o + 25)/8
Let d(q) be the third derivative of -q**6/24 - 13*q**5/12 + 25*q**4/3 + 1750*q**3/3 + 4*q**2 - 107. Factor d(h).
-5*(h - 7)*(h + 10)**2
Let h(t) = -t**2 - 43*t - 216. Let l be h(-6). Let w(s) be the second derivative of -9/8*s**4 - 1/3*s**2 + s**3 + 0 - l*s. Solve w(g) = 0.
2/9
Let w(u) = 2*u**3 - 8*u**2 + 2*u + 8. Let i(a) = a**2 + 10*a - 1. Let n(v) = -2*v. Let s(c) = -i(c) - 6*n(c). Let m(b) = -4*s(b) + 2*w(b). Factor m(o).
4*(o - 3)*(o - 1)*(o + 1)
Let b(y) be the second derivative of -y**8/6720 + y**7/630 - 