 44/(-1045)*(-5)/2. Let y = d - -11/76. Suppose -1/4*j**5 + 0*j + 0 - y*j**2 - 3/4*j**4 - 3/4*j**3 = 0. Calculate j.
-1, 0
Let b(i) be the first derivative of 0*i + 4/9*i**3 - 5/6*i**4 + 2 + 0*i**2. Factor b(j).
-2*j**2*(5*j - 2)/3
Let b(l) = 3*l**3 - 9*l - 2. Let z(y) = -21*y**3 + 63*y + 15. Let j(x) = 27*b(x) + 4*z(x). Factor j(c).
-3*(c - 2)*(c + 1)**2
Let t = -162 + 490/3. Let j(f) be the first derivative of 2 + 2*f**2 - f**3 - t*f. Factor j(u).
-(3*u - 2)**2/3
Let k(o) = -o**2 - 7*o - 56. Let p(g) = -g + 1. Let i(q) = 4*k(q) + 28*p(q). Factor i(m).
-4*(m + 7)**2
Let s = 300/217 - 34/31. Factor -s*n**4 - 2/7*n**2 + 0 + 0*n + 4/7*n**3.
-2*n**2*(n - 1)**2/7
Suppose 0 - 15/2*c**3 + 2*c**4 + 2*c + 6*c**2 = 0. Calculate c.
-1/4, 0, 2
Let z be (0 - -1) + 0 - -1. Let c(o) be the first derivative of -2/3*o + 2 - 4/9*o**3 + o**z - 1/9*o**6 + 2/5*o**5 - 1/3*o**4. Determine n so that c(n) = 0.
-1, 1
Let d be 2/4 + 5/2. Suppose d*c + 2*c = 10. Factor p**c + 3 + 2*p**2 - 6.
3*(p - 1)*(p + 1)
Let z(v) be the second derivative of -v**5/5 + v**4/3 + 6*v. Suppose z(y) = 0. Calculate y.
0, 1
Let u(z) = -z - 5. Let y be u(-7). Solve 0*c + 4/9*c**y - 4/9*c**4 + 2/3*c**3 + 0 - 2/3*c**5 = 0 for c.
-1, -2/3, 0, 1
Let t(x) = -x + 9. Let f be t(6). Let o(g) be the third derivative of -g**2 + 2/45*g**5 - 1/9*g**f + 0*g + 1/12*g**4 + 0. Factor o(h).
2*(h + 1)*(4*h - 1)/3
Let t(v) be the second derivative of 0*v**2 + 0 + 1/21*v**3 - 1/35*v**5 - 1/42*v**4 + 6*v. Factor t(x).
-2*x*(x + 1)*(2*x - 1)/7
Let h(f) be the third derivative of f**7/630 - f**6/60 + f**5/15 - 5*f**4/36 + f**3/6 - 9*f**2. Factor h(c).
(c - 3)*(c - 1)**3/3
Suppose 0 = 10*q - 9*q. Let w(k) be the first derivative of -1/6*k**2 - 1/12*k**4 + 2/9*k**3 + 1 + q*k. Suppose w(p) = 0. Calculate p.
0, 1
Solve 6/7*b**3 + 0*b**2 + 0*b + 3/7*b**4 + 0 = 0.
-2, 0
Let z(w) be the third derivative of w**5/90 - 5*w**4/36 + 4*w**3/9 + 9*w**2. Solve z(y) = 0 for y.
1, 4
Let f(q) be the third derivative of -q**5/15 + q**4/6 + 4*q**3/3 - 11*q**2. Factor f(t).
-4*(t - 2)*(t + 1)
Suppose 5*f - 5 = 5. Factor -p**2 + 4*p + 3*p**2 - f*p.
2*p*(p + 1)
Factor 2*p**2 - 2/3*p - 4/3.
2*(p - 1)*(3*p + 2)/3
Let k(h) be the third derivative of -h**8/3360 + h**7/630 - h**6/360 - h**4/24 + h**2. Let m(j) be the second derivative of k(j). Find r, given that m(r) = 0.
0, 1
Solve 0*p - 3/7*p**3 + 1/7*p**5 + 0 - 2/7*p**2 + 0*p**4 = 0 for p.
-1, 0, 2
Let o(n) be the first derivative of -135*n**4/4 - 45*n**3 - 45*n**2/2 - 5*n + 4. Factor o(g).
-5*(3*g + 1)**3
Let g(q) = -2*q**5 + 4*q**4 + 6*q**3 - 6*q**2 - 2*q + 4. Let w(n) = -n**4 - n**3 + n**2 - 1. Let l(r) = -g(r) - 2*w(r). Determine t so that l(t) = 0.
-1, 1
Let n be (-5)/20 + 2/8*9. Suppose 3/5*y + 2/5 + 1/5*y**n = 0. Calculate y.
-2, -1
Let o(v) be the third derivative of -3*v**2 - 2/3*v**3 + 0*v - 1/240*v**5 + 0 + 1/12*v**4. Factor o(j).
-(j - 4)**2/4
Let m be 5 - (-4 + 3 + 1). Let y(q) = 4*q**2 - 2*q - 6. Let p(h) = -3*h**2 + 2*h + 5. Let r(j) = m*p(j) + 4*y(j). Determine b, given that r(b) = 0.
-1
Factor -17*z**4 - 2*z**5 - 2*z**5 + 37*z**4 - 32*z**3 + 16*z**2.
-4*z**2*(z - 2)**2*(z - 1)
Let i(p) be the second derivative of -3*p**5/20 + p**3/2 + 27*p. Factor i(g).
-3*g*(g - 1)*(g + 1)
Let f(p) be the first derivative of -p**2/2 + 2*p - 3. Let o be f(0). Factor 0*y**5 - 2*y**o + 2*y**5 - y**5 - y + 2*y**4.
y*(y - 1)*(y + 1)**3
Suppose 72 = -0*y - 4*y. Let l be 93/54 + 4/y. Factor -l*x**2 + 0 - 1/2*x + 2*x**3.
x*(x - 1)*(4*x + 1)/2
Determine i so that 2/9*i**3 + 0 - 4/3*i - 2/9*i**2 = 0.
-2, 0, 3
Solve 0*r**2 - 873*r**4 + 4*r**3 - 2 - 8*r**2 + 883*r**4 - 8*r + 4*r**5 = 0.
-1, -1/2, 1
Let i(l) be the first derivative of -l**4 + l**3/3 - 5*l**2/2 + 8*l - 3. Let x(m) = 3*m**3 - m**2 + 5*m - 7. Let r(n) = -4*i(n) - 5*x(n). Solve r(b) = 0.
-3, 1
Suppose -2*c + 7 + 21 = 0. Let u = 17 - c. Factor -1/5*p - 1/5*p**4 - 3/5*p**2 + 0 - 3/5*p**u.
-p*(p + 1)**3/5
Let l(n) be the third derivative of 1/420*n**6 + 0*n + 0 - 1/70*n**5 - 2*n**2 + 0*n**3 + 1/42*n**4. Let l(q) = 0. Calculate q.
0, 1, 2
Let u = 1 - 2. Let g(h) be the third derivative of h**6/30 + h**5/10 + h**4/8 - h**3/6 - 7*h**2. Let r(i) = i - 1. Let f(x) = u*r(x) + g(x). Factor f(d).
2*d*(d + 1)*(2*d + 1)
Factor -12*h + 0 - 4 + 4*h**3 - 4.
4*(h - 2)*(h + 1)**2
Let p = 7634 - 22678/3. Let y = -74 + p. Factor -2/3*z**2 + 4/3*z - y.
-2*(z - 1)**2/3
Suppose -z + y + 7 = z, 3*z + 3*y = -3. Let s(g) be the first derivative of -3*g**2 - z - 8/3*g**3 + 2*g. Factor s(f).
-2*(f + 1)*(4*f - 1)
Let y(s) = -s - 7. Suppose 0 = 4*t + r + 26, 2*r - 27 = 3*t - r. Let k be y(t). Factor -1/2*d**3 + k + d**2 - 1/2*d.
-d*(d - 1)**2/2
Let x(y) be the first derivative of 2*y**3/27 - 2*y**2/3 + 16*y/9 - 53. Suppose x(z) = 0. Calculate z.
2, 4
Let z = -90 + 90. Let l(d) be the second derivative of 0 + 1/6*d**4 + z*d**2 + 2/3*d**3 - 2*d. Let l(f) = 0. Calculate f.
-2, 0
Suppose 0 = -3*h - h. Suppose 0 = -h*a - 2*a + 6. Factor 2/3 + 2*s**2 - 2/3*s**a - 2*s.
-2*(s - 1)**3/3
Factor 0*r + 1/4*r**4 - 1/2*r**3 + 0 + 1/4*r**2.
r**2*(r - 1)**2/4
Let w be (4/6)/(3/(-9)). Let t = 5 + w. Determine z, given that 2*z**3 - z**4 - 4*z**t - z**4 = 0.
-1, 0
Let b(s) be the third derivative of -s**10/25200 + s**9/37800 + s**8/8400 - s**4/3 - 5*s**2. Let z(j) be the second derivative of b(j). Solve z(k) = 0.
-2/3, 0, 1
Factor -4/7*d**3 + 2/7*d + 0*d**2 + 0*d**4 + 0 + 2/7*d**5.
2*d*(d - 1)**2*(d + 1)**2/7
Let y(d) be the second derivative of 0*d**2 + 1/12*d**4 - 1/40*d**5 - 1/60*d**6 + 0*d**3 - 6*d + 0. Factor y(z).
-z**2*(z - 1)*(z + 2)/2
Let f(n) = -345*n**4 + 392*n**3 + 506*n**2 + 160*n + 14. Let u(c) = c**4 - c**2 + 1. Suppose 3*r + 0 = -3. Let a(b) = r*f(b) - 2*u(b). Factor a(l).
(l - 2)*(7*l + 2)**3
Suppose -g + 44 = 2*g + 5*b, -2*g + 5*b = 4. Determine s so that 22*s - 18*s**2 - 20*s**2 + 8*s**2 + g*s**3 - 4 + 4*s**2 = 0.
1/4, 1, 2
Let c(r) = -r**3 + 12*r**2 + r - 15. Let o be c(12). Let h be (2 - 6/o) + -1. Find b such that -2/3*b**2 - 4/3*b + 2/3*b**h + 0 = 0.
-1, 0, 2
Factor -5*d**2 - 489*d**3 - 120*d**4 - 242*d**5 + 3*d**2 + 64*d - 8 - 518*d**4 + 19*d**3.
-2*(d + 1)**3*(11*d - 2)**2
Determine j so that -j**3 - 2/9*j**2 + 2/9*j**4 + 0*j + 0 + j**5 = 0.
-1, -2/9, 0, 1
Factor 24*z**4 + 4*z**5 + 5*z**2 + 29*z**3 + 11*z**2 + 7*z**3.
4*z**2*(z + 1)**2*(z + 4)
Let w(p) be the second derivative of p**4/4 - 2*p**3 - 15*p**2/2 + 38*p. What is q in w(q) = 0?
-1, 5
Let m(g) be the third derivative of g**6/300 - g**5/75 + g**4/60 + 5*g**2. What is u in m(u) = 0?
0, 1
Let d(b) = b**2 + 4*b + 8. Let u(i) = i**2 + 4*i + 9. Suppose -24 = 10*y - 4*y. Let m(k) = y*u(k) + 5*d(k). Factor m(c).
(c + 2)**2
Let d(h) = -3*h. Let k be d(-2). Factor -2*z + 2 - 4 + k*z**3 - 4*z**3 + 2*z**2.
2*(z - 1)*(z + 1)**2
Let s be 4 - (8/28 - (-12)/7). Factor 90/7*q**3 + 8/7*q + 0 + 54/7*q**4 + 48/7*q**s.
2*q*(3*q + 1)*(3*q + 2)**2/7
Let 0*l - 2/3*l**4 - 4*l**2 - 14/3*l**3 + 0 = 0. Calculate l.
-6, -1, 0
Suppose 0 = 5*r + 5*z - 25, -4*r - 3*z - 4 + 23 = 0. Factor -3*w**4 - 3*w**5 + 2*w**5 + r*w**5.
3*w**4*(w - 1)
Let m be 4/10 - (-339)/(-360). Let a = 1/8 - m. Factor 0 + a*b + 2/3*b**2.
2*b*(b + 1)/3
Suppose -5*j = -2*j. Let k(t) be the first derivative of t**2 - 5/3*t**3 - 1/2*t**4 + 2 + j*t + t**5. Let k(d) = 0. Calculate d.
-1, 0, 2/5, 1
Let r = -12 + 14. Let z(k) be the first derivative of 2/3*k**r - 2/5*k**5 - 1/3*k**4 - 1 - 2/3*k + 8/9*k**3. Solve z(v) = 0.
-1, 1/3, 1
Suppose -3*u = -u. Suppose u = 2*d + 1 - 5. Factor 2 - d*i**2 + 3*i + 3*i - 6.
-2*(i - 2)*(i - 1)
Factor -15*v - 12 - 13*v - 20 + 4*v**2.
4*(v - 8)*(v + 1)
Let g(k) be the first derivative of -7*k**6/36 + 8*k**5/15 + k**4/8 - 8*k**3/9 + k**2/3 - 9. Find o, given that g(o) = 0.
-1, 0, 2/7, 1, 2
Let k be ((-92)/115)/((-28)/10). Factor -k*u**2 - 6/7*u - 4/7.
-2*(u + 1)*(u + 2)/7
What is n in 4/9 + 2/9*n - 2/9*n**2 = 0?
-1, 2
Let o(f) be the third derivative of f**7/840 + f**6/120 + f**5/48 + f**4/48 - 5*f**2. Find t, given that o(t) = 0.
-2, -1, 0
Let w be (-600)/(-336) + (-2)/7. Let -7/2*f**3 + w*f + 3/2*f**2 - 1 + 3/2*f**4 = 0. Calculate f.
-2/3, 1
Suppose 6*i - 3 = 9. Let c be 4/(-6) - i/(-3). What is k in 2/3*k**2 - 2/3*k**3 + 0 + c*k = 0?
0, 1
Let o(t) be the first derivative of -2*t**5/5 + 9*t**4/2 - 58*t**3/3 + 39*t**2 - 36*t + 