*2 + 3/25*b**5. Suppose j(l) = 0. Calculate l.
-1, 1, 2
Factor 6 + 3/8*k**2 + 15/4*k.
3*(k + 2)*(k + 8)/8
Let d(s) be the first derivative of -s**6/2 + 9*s**5 - 81*s**4/2 - 108*s**3 + 972*s**2 - 428. Factor d(h).
-3*h*(h - 6)**3*(h + 3)
Let y(c) be the third derivative of c**5/180 - 91*c**4/36 + 8281*c**3/18 - 10*c**2 - 10*c. Factor y(s).
(s - 91)**2/3
Let z(l) be the third derivative of l**8/2352 + 11*l**7/1470 + 13*l**6/280 + 61*l**5/420 + 11*l**4/42 + 2*l**3/7 + 38*l**2. Let z(t) = 0. Calculate t.
-6, -2, -1
Suppose 3*b = -0*b - b. Let r(w) be the second derivative of 1/40*w**5 + 1/12*w**3 + 1/12*w**4 - 2*w + 0*w**2 + b. Find v such that r(v) = 0.
-1, 0
Let a be ((-80)/(-45))/8*9. Factor -2*t**a + 6*t**2 + 28*t**5 - 8*t + 87*t**4 - 25*t**4 + 60*t**3 + 14*t**4.
4*t*(t + 1)**3*(7*t - 2)
Let o(c) be the second derivative of -c**9/3024 - c**8/672 - c**7/504 - c**4/4 + 10*c. Let m(z) be the third derivative of o(z). Suppose m(b) = 0. What is b?
-1, 0
Suppose 30*l - 32*l + 4 = 0. Let z(k) be the third derivative of 0 + 0*k**5 + 5*k**l - 1/35*k**7 + 0*k**3 + 0*k**4 + 0*k - 1/40*k**6 - 1/112*k**8. Factor z(j).
-3*j**3*(j + 1)**2
Let z(k) be the third derivative of -k**5/90 + k**4/9 - 47*k**2. Factor z(d).
-2*d*(d - 4)/3
Let s(y) be the first derivative of -12*y**5/55 - 37*y**4/44 - 13*y**3/11 - 15*y**2/22 - y/11 - 628. Let s(z) = 0. What is z?
-1, -1/12
Let w(m) be the first derivative of m**3/15 + m**2/10 + 29. Determine y so that w(y) = 0.
-1, 0
Let i be (-13)/(156/(-160)) + (-2)/6. Let z = i + -13. Factor -1/2*n**3 + z*n + 0 + 1/2*n**2.
-n**2*(n - 1)/2
Let s be 4/(-18) - 12/(-54). Factor 20*p + 5*p**4 + 77*p**3 + 11*p**2 + 5 + 19*p**2 + s - 57*p**3.
5*(p + 1)**4
Let x(f) be the third derivative of -f**6/24 - 25*f**5/12 - 715*f**4/24 + 845*f**3/6 + 51*f**2. Suppose x(s) = 0. Calculate s.
-13, 1
Let g be (-2)/6*(1/(-2))/((-55)/(-66)). Determine l so that -g*l + 1/5*l**3 + 2/5 - 3/5*l**2 + 1/5*l**4 = 0.
-2, -1, 1
Let t(k) = k**3 - 4*k**2 - 7*k + 10. Let h(j) = -3*j - 3*j + 9 - 4*j**2 + 2*j**3 + 2*j**3 - 3*j**3. Let g(b) = -6*h(b) + 5*t(b). Factor g(u).
-(u - 4)*(u - 1)*(u + 1)
Let f(s) be the second derivative of s**3/3 + 23*s**2 + 3*s + 4. Let x be f(-23). Suppose -3/4*p + x*p**3 + 3/4*p**5 - 3/2*p**2 + 3/2*p**4 + 0 = 0. Calculate p.
-1, 0, 1
Let q be -21*(396/(-77) + 4 + 1). Suppose 6/5*t**q + 24/5*t**4 - 4/5*t**2 + 0*t + 14/5*t**5 + 0 = 0. What is t?
-1, 0, 2/7
Let y(v) be the first derivative of -v**3/3 + v**2 + 3*v - 74. Factor y(r).
-(r - 3)*(r + 1)
Factor 49*j - 62*j - 38*j - 9*j - 63 + 3*j**2.
3*(j - 21)*(j + 1)
Factor -3/2*u**4 - 537*u**2 - 1323/2 - 60*u**3 + 1260*u.
-3*(u - 1)**2*(u + 21)**2/2
Let w(n) be the second derivative of n**5/450 + n**4/15 + 11*n**3/45 - 5*n**2/2 + 5*n. Let x(h) be the first derivative of w(h). Let x(b) = 0. What is b?
-11, -1
Let l = 14 - 17. Let g be 1 + -2 - (l + -3). Let -3*u**4 - u**2 + 3*u**5 + 0*u**2 + g*u**2 - u**2 - 3*u**3 = 0. Calculate u.
-1, 0, 1
Factor -6*b - 16/3 - 2/3*b**2.
-2*(b + 1)*(b + 8)/3
Let x be 10/(-25) - (-26)/40. Suppose z - 5 = 22*p - 21*p, -19 = -2*z + 5*p. Find r, given that -1/4*r - 3/2*r**z + x = 0.
-1/2, 1/3
Let w(y) = -y**2 - 5*y + 38. Let d be w(-9). Let 0*l + 1/3 - 1/3*l**d = 0. What is l?
-1, 1
Let h(l) = -3*l - 5. Let u be h(-13). Suppose u*p = 40*p. Determine j so that 0*j**3 - 2/9*j**4 + 0*j + 0*j**2 + p = 0.
0
Factor -72/7*f + 2/7*f**2 + 648/7.
2*(f - 18)**2/7
Let y be (-7)/(21/(-9)) - -4. Suppose -2*k - l - 3 = -y, -3*l - 2 = -k. Suppose 5*d - 5 - 30*d + 25*d**3 + 53*d**2 - 48*d**k = 0. What is d?
-1, -1/5, 1
Let j(t) = 5*t**3 - 4*t**2 + 7*t - 4. Let d(z) = z**3 + z - 1. Suppose 12 = 6*y + 18. Let h(p) = y*j(p) + 4*d(p). Let h(n) = 0. What is n?
0, 1, 3
Suppose 4*k - i = -k + 17, 0 = -4*k - 2*i + 22. Suppose 10*s - 326 = -86. Factor 8 + k*c**2 - s - 8*c**2 + 15*c + c.
-4*(c - 2)**2
Let a(i) be the second derivative of -i**6/10 - 3*i**5/5 - i**4/2 + 2*i**3 + 9*i**2/2 - 2*i - 7. Factor a(s).
-3*(s - 1)*(s + 1)**2*(s + 3)
Let x(o) be the third derivative of -o**6/80 - 3*o**5/20 - 2*o**2 + 27. Let x(j) = 0. Calculate j.
-6, 0
Let k(s) be the second derivative of 5*s**8/336 + s**7/6 + 11*s**6/24 + 5*s**5/12 - 11*s**2/2 - 35*s. Let g(p) be the first derivative of k(p). Factor g(f).
5*f**2*(f + 1)**2*(f + 5)
Let k be (2/(-31))/(3/24). Let w = 134/341 - k. Factor -8/11 - 2/11*q**2 + w*q.
-2*(q - 4)*(q - 1)/11
Let p(d) be the second derivative of d**7/210 - d**6/60 + d**5/60 + 11*d**2/2 - d. Let o(w) be the first derivative of p(w). Find q, given that o(q) = 0.
0, 1
Let k be 3/9*6 + 3. Factor 2*y**2 + 5*y - 3*y - k*y - 5*y + 6.
2*(y - 3)*(y - 1)
Let b(n) be the third derivative of 0 - 27/2*n**4 - 1/84*n**8 + 22/105*n**7 - 3*n**2 + 0*n + 6*n**5 + 18*n**3 - 23/15*n**6. Factor b(a).
-4*(a - 3)**3*(a - 1)**2
Factor -37309 + 13058 - 5*x**2 + 268*x - 26754 + 742*x.
-5*(x - 101)**2
Let x = 56 + -39. Let a = -17 + x. Determine z so that 6/7*z**3 + 2/7*z**4 + a + 6/7*z**2 + 2/7*z = 0.
-1, 0
Let k be 35/5 + 61*(-2)/18. Determine v so that -16/9 - 4/3*v**2 + k*v**3 + 8/3*v = 0.
2
Let u(b) be the first derivative of -9*b**2 - 12 + 15/2*b**4 - b**3 + 0*b - 9/5*b**5. Solve u(a) = 0 for a.
-2/3, 0, 1, 3
Let k(x) be the second derivative of 25*x**7/28 + 19*x**6/24 + x**5/20 - x**4/12 - 4*x + 3. Factor k(s).
s**2*(5*s + 2)**2*(6*s - 1)/4
Let h be -1 - ((1 - 1) + -6). Let j = -1397 - -1402. Suppose 1/2 + 13/4*c - 9/4*c**h - j*c**4 - c**3 + 9/2*c**2 = 0. What is c?
-1, -2/9, 1
Let b(h) be the first derivative of 2/3*h**3 - 4*h**2 + 23 + 0*h. Find o, given that b(o) = 0.
0, 4
Let z be ((-158)/3)/(-1) - 4/6. Factor -z*u + 24 + 16*u - 18*u**2 - 80*u + 54*u**2.
4*(u - 3)*(9*u - 2)
Let c(x) = -6*x - 27. Let d be c(-5). Factor 100*a**d - 32 + 265*a**2 + 140*a + 23 + 29.
5*(a + 2)*(4*a + 1)*(5*a + 2)
Let u = 27/14 - 3/7. Suppose 1 + 1/2*v**2 + u*v = 0. What is v?
-2, -1
Let g(p) = p**2 - 11*p + 22. Let a(s) = s**2 - 10*s + 19. Let i(x) = -6*a(x) + 5*g(x). Factor i(d).
-(d - 4)*(d - 1)
Let u be (-648)/(-66) + -10 - (-156)/11. Let j(h) be the first derivative of -7/26*h**4 - 4/13*h - 32/39*h**3 - u - 11/13*h**2. Factor j(l).
-2*(l + 1)**2*(7*l + 2)/13
Let n = -175 - -181. Let h(w) be the third derivative of 0*w + 0*w**3 - 1/15*w**5 + 6*w**2 + 0 + 1/336*w**8 + 1/24*w**4 + 1/20*w**n - 2/105*w**7. Factor h(b).
b*(b - 1)**4
Let i(n) = n**2 + 11*n + 3. Let w be i(-11). Factor 2*k**2 + 12*k**2 + 3*k**w - 6*k**3 - 7*k**2 - 4*k.
-k*(k - 1)*(3*k - 4)
Solve -1/2*t**2 - 5*t + 28 = 0.
-14, 4
Let g(v) = 9*v**2 - 21. Let m(w) = -2*w**2 + 5. Let b(u) = 5*g(u) + 21*m(u). Let l = 1 - 0. Let d(z) = -z**3 - z**2. Let o(t) = l*b(t) + 3*d(t). Factor o(h).
-3*h**3
Let t(m) be the second derivative of -m**4/4 - 7*m**3/2 - 283*m - 1. Factor t(d).
-3*d*(d + 7)
Factor 28*k**2 + 196*k + 23 - 132*k + 25 + 4*k**3.
4*(k + 2)**2*(k + 3)
Let f(x) be the third derivative of -x**8/90720 - x**7/7560 + x**6/324 - x**5/60 - 2*x**2. Let m(u) be the third derivative of f(u). Factor m(o).
-2*(o - 2)*(o + 5)/9
Let f be (14 + -12)/(1/20). Suppose -44*l + f*l = -8. Factor -7/4*o - 9/2*o**l + 3/2 - 5/4*o**3.
-(o + 1)*(o + 3)*(5*o - 2)/4
Suppose 0 = 3*r - 7*b + 19, 15 = 20*r - 19*r + 3*b. Factor 0*u - 1/2*u**4 + 1/8*u**r + 0 + 0*u**2.
-u**3*(4*u - 1)/8
Let a(m) be the third derivative of -m**9/12096 + m**8/1680 - m**7/672 + m**6/720 - 2*m**3 + 15*m**2. Let y(n) be the first derivative of a(n). Factor y(p).
-p**2*(p - 2)*(p - 1)**2/4
Let l be -1 + 4 + (-2 - 105/69). Let i = 106/115 + l. Factor 2/5*h**3 + 0 - 2/5*h**4 + 0*h - 2/5*h**5 + i*h**2.
-2*h**2*(h - 1)*(h + 1)**2/5
Let n(v) = -v**4 + v**3 - 2*v**2. Let j(c) = 44*c**4 - 1264*c**3 - 810*c**2 + 470*c - 52. Let g(b) = -j(b) + 6*n(b). Suppose g(h) = 0. Calculate h.
-1, 1/5, 26
Let w(c) = -c**3 - 3*c**2 - 2*c - 5. Let d be w(-3). Let n be d + (-19)/15 + 6/9. What is j in -1/5*j**2 + n*j - 1/5 = 0?
1
Let g(o) be the second derivative of 21/4*o**3 - 15/4*o**2 + 0 + 16*o - 1/2*o**4. Factor g(m).
-3*(m - 5)*(4*m - 1)/2
Let i(q) be the third derivative of q**7/210 - q**6/45 - q**5/10 + q**3/6 + 25*q**2. Let x(l) be the first derivative of i(l). Solve x(y) = 0 for y.
-1, 0, 3
Factor 247/4*m**2 - 18 + 91/2*m - 7/4*m**3.
-(m - 36)*(m + 1)*(7*m - 2)/4
Suppose 2*o + 5*f - 69 + 5 = 0, -5*o - 2*f = -118. Deter