he first derivative of l**5/150 + l**4/90 - l**3/45 - l**2/15 - 9*l - 10. Let i(c) be the first derivative of o(c). Factor i(y).
2*(y - 1)*(y + 1)**2/15
Suppose 5*s + 10 = -5*i, 4*s + i - 6 - 1 = 0. Let c = 9 - s. Solve k**5 + 17*k**2 + 9*k + 14*k**3 - 2 + c*k**4 - k**2 + 4 = 0.
-2, -1
Let a(u) be the second derivative of 3*u**5/100 - 3*u**4/20 + 6*u**2/5 + 311*u. Factor a(c).
3*(c - 2)**2*(c + 1)/5
Factor 3/2*s**2 - 327/2 + 162*s.
3*(s - 1)*(s + 109)/2
Let z(a) be the first derivative of a**4/4 - 4*a**3/3 + 2*a**2 + 7. Factor z(o).
o*(o - 2)**2
Let b(q) be the third derivative of q**7/5040 + q**6/288 + q**5/60 - 13*q**4/12 + 3*q**2. Let o(z) be the second derivative of b(z). Let o(l) = 0. Calculate l.
-4, -1
Let u be (1/(-2))/(9/(-54)). Let y be (12 - 9)*1/u. Suppose l + 1 - l**2 + y - 2 = 0. What is l?
0, 1
Factor 7/2*o - 3/2 + 1/2*o**3 - 5/2*o**2.
(o - 3)*(o - 1)**2/2
Let k be (-74)/18 + 26/234. Let d(p) = 7*p**2 + 8*p + 3. Let b(w) = 8*w**2 + 8*w + 4. Let l(y) = k*d(y) + 3*b(y). Factor l(n).
-4*n*(n + 2)
Suppose -70 = -4*t - 2*n, -3*n + 2*n = 3*t - 52. Let d = t + -13. Factor -49*j**d - 6 + 6 + 4*j + 21*j**3 + 0 + 24*j**2.
-j*(j - 1)*(7*j + 2)**2
Let y(l) = 19*l - 41*l - 12*l**3 + 2 - 2*l**2 - 5*l**2 - l**2. Let i(b) = -11*b**3 - 9*b**2 - 21*b + 1. Let a(s) = -7*i(s) + 6*y(s). Let a(m) = 0. Calculate m.
-1
Suppose 326 = 150*p + 26. Factor 1/3 + 2*l + 5/3*l**p.
(l + 1)*(5*l + 1)/3
Let i(g) = 3 - g + 4 - 5. Let s be i(0). Let 2*t**3 + 7*t**s - 8*t - 8*t**3 + 5*t**2 + 2*t**3 = 0. Calculate t.
0, 1, 2
Let q(s) be the second derivative of -7/30*s**4 + 4/15*s**3 + 1/25*s**5 + 0 + 0*s**2 - 9*s + 1/75*s**6. Solve q(f) = 0 for f.
-4, 0, 1
Let i(h) = -18*h**4 + 31*h**3 + 3*h**2 - 14*h + 7. Let w(m) = 17*m**4 - 30*m**3 - 2*m**2 + 12*m - 6. Let x(q) = -6*i(q) - 7*w(q). Solve x(g) = 0 for g.
0, 2/11, 2
Let g be -5 - -2 - -5 - (5 + 0). Let z be -3 - (-3 + (92/(-28) - g)). Factor -z*m + 4/7*m**2 + 0 - 2/7*m**3.
-2*m*(m - 1)**2/7
Let l(m) be the first derivative of -m**5/25 - 9*m**4/10 - 11*m**3/5 - 8*m**2/5 + 219. Determine w, given that l(w) = 0.
-16, -1, 0
Find h, given that 17/3*h**2 - 2/3*h + 0 = 0.
0, 2/17
Factor -6*p**3 - 185109 + 185109 + p**4 - 19*p**2 + 24*p.
p*(p - 8)*(p - 1)*(p + 3)
Solve -b**2 - 5*b**2 + 2*b**4 + 8 + 2 + 0*b**2 + 6*b**3 - 14*b + 2 = 0 for b.
-3, -2, 1
Let b be (-615)/1025 - ((-8)/5 + 1). Find i, given that b + 3/5*i**2 + 3*i = 0.
-5, 0
Let p = -393 - -394. Let x(g) be the first derivative of p + 0*g - 1/18*g**4 + 1/9*g**2 + 0*g**3. Factor x(q).
-2*q*(q - 1)*(q + 1)/9
Solve -2/7*t**5 + 66/7*t**4 - 96*t - 504 + 2110/7*t**2 - 678/7*t**3 = 0 for t.
-1, 3, 14
Let v = -6002 - -6002. Find o, given that v + 0*o - 1/3*o**3 - 4/3*o**2 = 0.
-4, 0
Let t(n) = n**3 - 3*n**2 - n. Let u be t(4). What is p in -24*p - 15 + 1 - 1 + 31 + u*p**2 - 2*p**3 = 0?
2
Let z(j) be the first derivative of 1/30*j**5 - 5 + 0*j**2 - 1/180*j**6 - 5/72*j**4 + 4*j + 1/18*j**3. Let c(l) be the first derivative of z(l). Factor c(m).
-m*(m - 2)*(m - 1)**2/6
Let y be (-6)/(-9) - (-2)/6. Let d be y/4*-2 - (-2)/4. Let -15/2*h**5 + d + 9/2*h**4 + 0*h + 18*h**3 + 6*h**2 = 0. Calculate h.
-1, -2/5, 0, 2
Let c(k) be the first derivative of 9 + 0*k**5 + 0*k**2 - 1/360*k**6 + 0*k + 1/6*k**4 - 1/3*k**3. Let z(g) be the third derivative of c(g). Factor z(v).
-(v - 2)*(v + 2)
Let i = 51 + -47. Let a(w) = -5*w**3 - w**2 - 4. Let c(x) = -6*x**3 - 2*x**2 - 4. Let k(u) = i*c(u) - 5*a(u). Determine q so that k(q) = 0.
-1, 2
Let y(u) = -3*u**4 + 16*u**3 + 36*u**2. Let p(r) = -r**4 + r**3. Let w(q) = 4*p(q) - y(q). Find i such that w(i) = 0.
-6, 0
Suppose 5*q + 5*j = 45, 3*j - 28 = -13. Factor -3*b**q + 0 + 3*b**2 - 3/2*b + 0*b**3 + 3/2*b**5.
3*b*(b - 1)**3*(b + 1)/2
Let z(q) be the second derivative of -q**6/540 - q**5/27 + q**4/108 + 10*q**3/27 - 27*q**2/2 - 7*q. Let c(f) be the first derivative of z(f). Factor c(j).
-2*(j - 1)*(j + 1)*(j + 10)/9
Suppose 0 = -6*d + d + 25. Suppose -3*i - 21 = -3*m, i + 18 = -m - 3*i. Factor -x**3 + x - d + 0 + m*x**2 + 0*x + 3.
-(x - 2)*(x - 1)*(x + 1)
Let z be 40/84 - 13/(-1183)*-13. Factor -2/3 - 4/3*l**2 + 5/3*l + z*l**3.
(l - 2)*(l - 1)**2/3
Let w = -10 - -12. Let r(x) = 43*x**3 - 91*x**2 - 84*x + 29. Let c(q) = -14*q**3 + 30*q**2 + 28*q - 10. Let l(v) = w*r(v) + 7*c(v). Factor l(y).
-4*(y - 3)*(y + 1)*(3*y - 1)
Let l(f) = -6*f**3 - 263*f**2 - 2893*f + 6899. Let n(b) = -b**3 - 44*b**2 - 482*b + 1150. Let m(o) = 2*l(o) - 13*n(o). Factor m(q).
(q - 2)*(q + 24)**2
Factor -96 + 80*c - 3*c**3 + 37*c - c**3 - 8*c**2 - 37*c.
-4*(c - 2)**2*(c + 6)
Let i(u) be the first derivative of 196*u**5/5 + 98*u**4 + 60*u**3 - 16*u**2 - 16*u - 115. Suppose i(q) = 0. What is q?
-1, -2/7, 2/7
Let l(h) be the first derivative of h**4/15 - 2*h**3/15 - 14*h + 1. Let f(d) be the first derivative of l(d). Factor f(w).
4*w*(w - 1)/5
Let d be ((-2 - -3) + -1)/(-9 - -6). Factor 0 - 2/7*r**2 + d*r.
-2*r**2/7
Let p = -14 + 16. Suppose p = 2*f - f. Factor -6*j**2 + 12*j**3 + j**2 + 2*j + 2*j**5 - 8*j**4 - 3*j**f.
2*j*(j - 1)**4
Let u(k) be the second derivative of -k**7/10080 + k**6/1440 + k**5/160 + 5*k**4/4 - 22*k. Let w(o) be the third derivative of u(o). Let w(t) = 0. What is t?
-1, 3
Let y = 58 + -39. Suppose 33*k**4 - y*k - 8 - 3*k**4 + 52*k**3 + 6*k**2 + 0 - 5*k = 0. What is k?
-1, -2/5, 2/3
Suppose 0 = 2*z + 5*q + 136, -5*z - 4*q - 260 = 80. Let b = z + 341/5. Factor 0*o + b*o**2 - 1/5.
(o - 1)*(o + 1)/5
Let i(s) be the third derivative of -s**7/945 + s**6/180 - s**5/90 + s**4/108 - 60*s**2. Factor i(h).
-2*h*(h - 1)**3/9
Let j = 79 - 80. Let d(f) = -f**2 - 2*f + 4*f - f. Let l(w) = -3*w**3 + 4*w**2 - w. Let g(b) = j*d(b) + l(b). Determine y so that g(y) = 0.
0, 2/3, 1
Suppose -3*l + 2*x + 30 = -3*x, 3*x = 2*l - 19. Suppose -s + 16 = l*q - 4*s, -2 = s. Factor 5*v + 3 + v**3 + v**q - 1 + 3*v**2.
(v + 1)**2*(v + 2)
Let n = -63 - -68. Let 8 + 10*z + 26*z**3 - 14*z + 16*z**4 - 10*z**3 - 24*z**2 - 12*z**n = 0. What is z?
-1, -2/3, 1
Let g(b) be the second derivative of -b**7/42 + 3*b**5/20 - b**4/6 - 47*b + 4. Find p, given that g(p) = 0.
-2, 0, 1
Let s(w) = -w**2 + w + 10. Let r be s(5). Let f = 16 + r. Factor -2*x**2 - 4*x**2 + 0*x**3 - 2*x**3 - x**3 + 3*x + f.
-3*(x - 1)*(x + 1)*(x + 2)
Let a(l) be the third derivative of 9/20*l**5 + 0 - 3/4*l**4 - 25*l**2 + 1/2*l**3 - 1/10*l**6 + 0*l. Factor a(m).
-3*(m - 1)**2*(4*m - 1)
Let p = -1532 + 7664/5. Factor -4/5 - 2/5*u + p*u**2 + 2/5*u**3.
2*(u - 1)*(u + 1)*(u + 2)/5
Let r(p) = 23*p**3 - 26*p**2 + 65*p - 38. Let f(t) = 120*t**3 - 129*t**2 + 324*t - 189. Let a(m) = -4*f(m) + 21*r(m). Let a(x) = 0. What is x?
1, 2, 7
Let t = 31 + -30. Let a = t + 1. Let 6*s + 8 - 4*s**a - 8*s - 2*s = 0. Calculate s.
-2, 1
Let r(l) = -10*l**4 + 25*l**3 + 420*l**2 + 1000*l + 720. Let y(v) = 15*v**4 - 37*v**3 - 630*v**2 - 1500*v - 1080. Let w(m) = 8*r(m) + 5*y(m). Factor w(k).
-5*(k - 9)*(k + 2)**3
Suppose -16*k = -47*k + 372. Find w, given that 0 + 3*w**5 + k*w**2 + 6*w - 15/2*w**4 - 9/2*w**3 = 0.
-1, -1/2, 0, 2
Factor -26/7*p - 60/7 - 2/7*p**2.
-2*(p + 3)*(p + 10)/7
Let s = 4284 + -4284. Solve -2/7*o**4 - 10/7*o**3 + 0 + 4/7*o**5 - 4/7*o**2 + s*o = 0 for o.
-1, -1/2, 0, 2
What is j in -48*j**4 + 9*j**2 + 192*j**3 - 6 - 69/2*j = 0?
-1/4, 1/2, 4
Let o be ((-4)/14)/((-95)/285). Factor 4/7*n - 2/7 + o*n**2.
2*(n + 1)*(3*n - 1)/7
Let p(j) be the second derivative of j**5/10 - 4*j**4/3 + 20*j**3/3 - 16*j**2 - 11*j - 8. Factor p(g).
2*(g - 4)*(g - 2)**2
Suppose 7136*q = 7145*q. Factor q*z + 3/4*z**3 - 3/4*z**2 + 3/4*z**4 - 3/4*z**5 + 0.
-3*z**2*(z - 1)**2*(z + 1)/4
Let v(i) be the first derivative of i**5/35 - i**4/7 - 65. Solve v(j) = 0 for j.
0, 4
Let k(c) be the first derivative of 1/720*c**6 + 0*c**2 + 0*c**4 - c**3 - 1/120*c**5 + 0*c - 2. Let a(h) be the third derivative of k(h). Factor a(y).
y*(y - 2)/2
Suppose -177*s = 269*s - 1338. Factor -9/4 - 15/4*b - 1/4*b**s - 7/4*b**2.
-(b + 1)*(b + 3)**2/4
Let x = 2591 + -5173/2. Factor 3/2*s**3 + x*s**2 + 0 + 3*s.
3*s*(s + 1)*(s + 2)/2
Let g = 47525/21 + -2263. Let y(j) be the first derivative of -1 + 2/7*j - 2/7*j**2 + g*j**3. Factor y(m).
2*(m - 1)**2/7
Let v(x) = -8415*x**2 + 815*x - 25. Let t(d) = -8413*d**2 + 816*d - 24. Let q(n) = 5*t(n) - 4*v(n). Let q(p) = 0. What is p?
2/41
Let i(s) = -3