e the first derivative of s(d). Factor p(w).
3*(w - 1)*(4*w + 1)**2
Let s(v) = v**4 + v**2 - v. Let u(b) = -9*b**4 - 27*b**3 + 27*b**2 + 15*b + 6. Let d(q) = 12*s(q) - u(q). Factor d(w).
3*(w - 1)*(w + 1)**2*(7*w + 2)
Solve 6*z**4 - 3*z**4 - 3*z**3 - 6*z**4 = 0 for z.
-1, 0
Let z be (-4)/10 - (-176)/40. Let u(f) be the second derivative of 1/5*f**5 - 2/3*f**3 + 1/15*f**6 + 3*f + 0*f**z + 0 - f**2. Factor u(s).
2*(s - 1)*(s + 1)**3
Suppose 6/5*c**2 + 3/5*c**3 + 0*c + 0 = 0. Calculate c.
-2, 0
Let y = 2102/7 + -300. Determine i, given that y*i**2 + 4/7 - 6/7*i = 0.
1, 2
Suppose -4*c = 5*c - 36. Let j(b) be the third derivative of -4/3*b**3 + b**c + 7/30*b**5 + 3*b**2 + 0*b + 0. Factor j(k).
2*(k + 2)*(7*k - 2)
Factor -5*y**3 - 3*y**2 - 5*y**4 + 48*y**5 - 43*y**5 + 8*y**2.
5*y**2*(y - 1)**2*(y + 1)
Factor 3*j**2 + 0*j**2 + 27 - j**2 - 20*j + 23.
2*(j - 5)**2
Let o(m) = m - 4. Let l be o(6). Let r(u) be the first derivative of -2 + 2*u - 2/3*u**3 + 0*u**5 + u**4 - 3/2*u**l - 1/6*u**6. Find k, given that r(k) = 0.
-2, -1, 1
Let s(d) = d**4 + d**2 - d + 1. Let f(h) = -10*h**4 - 2*h**3 - 12*h**2 + 13*h - 11. Let r(a) = 4*f(a) + 44*s(a). Solve r(l) = 0 for l.
-1, 0, 1, 2
Let j(p) be the second derivative of p**4/8 + 5*p**3/2 + 75*p**2/4 + 12*p. Factor j(k).
3*(k + 5)**2/2
Find b, given that -7*b**3 + b**4 + b**3 + 3*b**4 + 3*b**5 - 6*b**4 + 4*b**2 - 2 + 3*b = 0.
-1, 2/3, 1
Let d(k) be the third derivative of k**5/330 + k**4/66 - k**3/11 + 21*k**2. Factor d(f).
2*(f - 1)*(f + 3)/11
Let w be ((-1)/4)/(4/(-40)). Let y = w + -9/4. Factor 1/2*k + y*k**2 + 0.
k*(k + 2)/4
Let r(q) be the third derivative of 4*q**2 - 1/84*q**4 + 0*q + 1/420*q**6 + 0 + 0*q**5 + 0*q**3. Find z such that r(z) = 0.
-1, 0, 1
Let k(q) be the second derivative of -q**4/16 + 3*q**2/2 - 7*q. Find r such that k(r) = 0.
-2, 2
Let i(k) be the third derivative of -k**5/60 - k**4/12 - k**3/6 - 2*k**2. Factor i(r).
-(r + 1)**2
Suppose 0 = -2*c + l + 38, 5*c - 3*l = 2*c + 54. Let t = c - 18. Suppose -20/11*k**3 + 20/11*k**t + 2/11 - 2/11*k**5 + 10/11*k**4 - 10/11*k = 0. What is k?
1
Let z be (-531)/12*(-4)/(-6). Let s = -29 - z. Factor -1/2*a**3 - s*a + 0 - a**2.
-a*(a + 1)**2/2
Determine a so that 4*a**3 + 2*a + a**2 - a**4 - 2*a**3 - 2*a**3 - 2*a**3 = 0.
-2, -1, 0, 1
Let r(j) be the second derivative of j**5/390 + j**4/156 - 2*j**3/39 - 3*j**2 - 4*j. Let y(o) be the first derivative of r(o). What is v in y(v) = 0?
-2, 1
Let w(n) be the third derivative of -n**8/672 + n**7/105 - n**6/48 + n**5/60 + 4*n**2. Determine k, given that w(k) = 0.
0, 1, 2
Let o(z) be the second derivative of z**6/90 - z**4/18 + z**2/6 + 6*z. Suppose o(u) = 0. What is u?
-1, 1
Let c(d) be the second derivative of d**7/21 - 8*d**6/15 + 9*d**5/5 - 8*d**4/3 + 5*d**3/3 - 10*d. Solve c(p) = 0.
0, 1, 5
Let o(v) be the second derivative of v**6/225 + 2*v**5/75 + v**4/18 + 2*v**3/45 - 5*v. Suppose o(n) = 0. Calculate n.
-2, -1, 0
Let p be 3 + 27 + 3/1. Let f(a) = -15*a**4 + 225*a**3 - 192*a**2 - 33*a. Let o(x) = x**4 - 14*x**3 + 12*x**2 + 2*x. Let g(u) = p*o(u) + 2*f(u). Factor g(i).
3*i**2*(i - 2)**2
Factor 0*i**2 + 0 + 0*i - 1/7*i**3 + 1/7*i**4.
i**3*(i - 1)/7
Let j(f) be the first derivative of f**3 - 3*f**2/2 - 6*f - 16. Let j(t) = 0. Calculate t.
-1, 2
Factor -4*b**3 - 8/3*b**2 + 0 + 0*b - 1/3*b**5 - 2*b**4.
-b**2*(b + 2)**3/3
Let y(j) = j**3 - 3*j**2 + 3*j + 3. Let c be y(3). Solve -36*h + c + 17*h**2 - 2*h**4 - 13*h**2 + 35*h**2 + 5*h**4 - 18*h**3 = 0.
1, 2
Let z be (4/(-10))/(10/(-25)). Suppose -3*n - z = -7. Factor -4*g**3 + g - 7*g**2 + 2*g**3 + g + 9*g**n - 2*g**4.
-2*g*(g - 1)*(g + 1)**2
Let q = 147 + -147. Find m, given that q*m**2 - 2/3*m**3 - 2/3*m**4 + 0 + 0*m = 0.
-1, 0
Let o(x) = x**4 - 2*x**2 + 2*x - 3. Let c be (5/(-3))/((-6)/18). Let w(z) = 2*z**4 + z**3 - 5*z**2 + 4*z - 7. Let i(m) = c*o(m) - 2*w(m). Factor i(l).
(l - 1)**3*(l + 1)
Let a = 76 - 72. Factor 1/5*q**a - 2/5*q**3 + 0 + 1/5*q**2 + 0*q.
q**2*(q - 1)**2/5
Let t(o) be the second derivative of o**5/10 - 2*o**4/5 + 3*o**3/5 - 2*o**2/5 - o. Let t(x) = 0. Calculate x.
2/5, 1
Let z(r) be the third derivative of -r**8/112 - r**7/70 + r**6/8 + r**5/20 - r**4 + 2*r**3 - 5*r**2. Let z(y) = 0. Calculate y.
-2, 1
Let x(i) = 4*i - 4. Let d be x(3). Let 16*z**2 - 16*z**3 + 28*z**2 + d + 2*z**4 + 24*z + 10 - 72*z = 0. Calculate z.
1, 3
Let d = 6 - 4. Let u = 2/39 - -146/195. Factor 2/5*c**3 + 0*c - u*c**d + 0.
2*c**2*(c - 2)/5
Determine s, given that 0 - 3/2*s**3 + 1/3*s + 13/6*s**4 - 5/6*s**5 - 1/6*s**2 = 0.
-2/5, 0, 1
Let u = 67 - 63. Let t(o) be the second derivative of -o + 1/12*o**3 - 1/24*o**u + 0*o**2 + 0. Factor t(w).
-w*(w - 1)/2
Let l(y) be the first derivative of -y**5/10 - y**4/4 - y**3/6 - 24. Factor l(q).
-q**2*(q + 1)**2/2
Let p(r) = r**2 - 1. Let s be p(2). Let x(k) = k**2 - 2*k. Let g be x(s). Factor 0*y**4 - 3*y**4 + y + y**4 + g*y**2 - 2*y**4.
-y*(y - 1)*(2*y + 1)**2
Find z such that -3/8*z**2 - 21/8*z + 0 = 0.
-7, 0
Suppose -a + 10 = 4*a. Let p be 2/(-16)*a*-2. Find v such that 1/4*v**2 + 1/4 + p*v = 0.
-1
Let l = 55/78 + -1/26. Suppose 2 = 5*m + 4*d - 6*d, 5*m + 6 = 4*d. Factor 2*q + m*q**2 + 2/3*q**3 + l.
2*(q + 1)**3/3
Solve 0 + 2/5*k**5 - 2/5*k**3 - 2/5*k**2 + 0*k + 2/5*k**4 = 0.
-1, 0, 1
Let u(k) be the second derivative of -k**6/45 - k**5/10 - k**4/18 + k**3/3 + 2*k**2/3 + 3*k. What is i in u(i) = 0?
-2, -1, 1
Let r(v) = -v**4 - 17*v**3 - 32*v**2 - 13*v - 3. Let s(n) = -2*n**4 - 18*n**3 - 32*n**2 - 14*n - 2. Let p(j) = -2*r(j) + 3*s(j). Factor p(y).
-4*y*(y + 1)*(y + 2)**2
Suppose -3*n + 40 = -5*u - 31, 3*n = -5*u + 31. Suppose -n - 3 = -4*s. Factor d**4 - 2*d**3 + 2*d**s + 4*d**4 + 2*d**2 - 7*d**4.
2*d**2*(d - 1)**2*(d + 1)
Let b(n) be the first derivative of -1/12*n**3 + 2 + 0*n + 1/4*n**2 - 1/16*n**4. Factor b(t).
-t*(t - 1)*(t + 2)/4
Determine u so that -2/5 + 68/5*u**3 - 42/5*u**4 + 18/5*u + 2*u**5 - 52/5*u**2 = 0.
1/5, 1
Solve 0*x - 2/13*x**3 + 0*x**2 + 0 = 0.
0
Determine g so that -48/5 + 33/5*g**3 + 24/5*g**2 - 6/5*g**4 - 3/5*g**5 - 12*g = 0.
-4, -1, 2
Let j(p) be the first derivative of 14*p**6 + 32*p**5/5 - 4*p**4 + 23. Factor j(b).
4*b**3*(3*b + 2)*(7*b - 2)
Find q such that -2/5*q**3 + 0 - 2/5*q**5 + 0*q - 4/5*q**4 + 0*q**2 = 0.
-1, 0
Suppose 5*k + 80 = -5*b, -60 + 16 = 4*b - k. Let i be (-6)/9*9/b. Let i + 1/4*d**2 - 3/4*d = 0. What is d?
1, 2
Find o, given that 0 - 9/2*o**2 - 3/2*o**3 + 0*o = 0.
-3, 0
Let j(t) be the third derivative of t**9/75600 + t**8/16800 + t**7/12600 + t**4/6 + 2*t**2. Let m(k) be the second derivative of j(k). Factor m(c).
c**2*(c + 1)**2/5
Factor -2/9*p**2 - 8/9 - 8/9*p.
-2*(p + 2)**2/9
Let f(y) be the third derivative of -1/8*y**6 + 5/8*y**4 + 0*y + 1/10*y**5 - y**2 + 0 - y**3. Solve f(v) = 0 for v.
-1, 2/5, 1
Let z(x) be the first derivative of x**3/6 - 4. Factor z(a).
a**2/2
Let g(q) = -10*q**4 + 25*q**3 + 5*q**2 - 25*q - 5. Let u(f) = -5*f**4 + 13*f**3 + 2*f**2 - 13*f - 3. Let a(z) = -3*g(z) + 5*u(z). Factor a(t).
5*t*(t - 2)*(t - 1)*(t + 1)
Let s(i) be the first derivative of -2*i**5/35 + 5*i**4/14 - 6*i**3/7 + i**2 - 4*i/7 + 2. Let s(p) = 0. What is p?
1, 2
Let m = 3273/5 - 653. Find v, given that 2/5*v**5 + 8/5*v**3 + 0*v + 0*v**2 + 0 - m*v**4 = 0.
0, 2
Suppose 42*o - 15*o + 64 - 11*o + o**2 = 0. Calculate o.
-8
Let k(b) be the second derivative of b**4/36 - 2*b**2/3 + 14*b. What is o in k(o) = 0?
-2, 2
Factor -9/5 - 3/5*q**2 - 12/5*q.
-3*(q + 1)*(q + 3)/5
Suppose r + 1 - 20 = -4*d, -3*r = 4*d - 25. Let f = 136/3 - 45. Factor 1/3*s - f*s**r - 1/3*s**2 + 1/3.
-(s - 1)*(s + 1)**2/3
Let g be 1 + -1 + 232/40 + -5. Solve 0 - 1/5*y - 6/5*y**3 + 4/5*y**2 + g*y**4 - 1/5*y**5 = 0 for y.
0, 1
Suppose -4*s - 10 = 3*l + 15, -5*s = -4*l + 8. Let p be (l/(-12))/((-1)/(-1)). Solve -5/4*z**4 - 7/4*z**3 + 2*z + 1 + 1/4*z**2 - p*z**5 = 0.
-2, -1, 1
Let p(n) be the first derivative of n**6/12 - 7*n**5/2 + 161*n**4/4 - 127*n**3/3 - 323*n**2/4 + 289*n/2 - 22. Find j such that p(j) = 0.
-1, 1, 17
Let u be (16/6 - 3)/(-1). Find k such that -u + 1/3*k**2 + 1/3*k**3 - 1/3*k = 0.
-1, 1
Let c(n) be the third derivative of n**5/150 - n**3/15 - 52*n**2. Suppose c(k) = 0. Calculate k.
-1, 1
Let l(d) be the second derivative of d**5/5 - 5*d**4/3 + 16*d**3/3 - 8*d**2 - 20*d. Solve l(f) = 0.
1, 2
Let v(k) be the fi