24*x**3 + 0 + d*x**5 - 3/8*x**4 + 4*x - 1/4*x**2. Factor o(r).
(r - 1)*(3*r - 2)*(3*r - 1)/4
Suppose -2*v - 7 = 7. Let d be (7/(-2))/v*1. What is o in 1/4*o**2 + 1/4 - d*o = 0?
1
Let m = -82 + 124. Let i be 6*9/m - 1. Factor -i + 0*c**2 + 4/7*c + 2/7*c**4 - 4/7*c**3.
2*(c - 1)**3*(c + 1)/7
Let j(n) = 52*n**5 - 25*n**4 + 7*n**3 - 3. Let o(l) = -103*l**5 + 51*l**4 - 13*l**3 + 5. Let i(h) = -10*j(h) - 6*o(h). Factor i(z).
2*z**3*(7*z - 2)**2
Let s(y) be the third derivative of -1/30*y**5 + 1/105*y**7 + 1/60*y**6 - 1/12*y**4 + 0*y - 2*y**2 + 0 + 0*y**3. Factor s(z).
2*z*(z - 1)*(z + 1)**2
Let w(d) = 8*d + 32. Let i be w(18). Let r be 320/i - 4/(-22). Factor 1/6*x**r - 2/3*x + 2/3.
(x - 2)**2/6
Let n(i) = -3*i**4 + 8*i**3 + 13*i**2 - 4*i - 6. Let o(p) = -2*p**4 + 8*p**3 + 12*p**2 - 3*p - 5. Let c(s) = 5*n(s) - 6*o(s). Determine d, given that c(d) = 0.
-1, -2/3, 0
Let h be 114/36 + -3*1. Let x(j) be the first derivative of -h*j**3 - 1/4*j**2 - 3 + 0*j. Factor x(u).
-u*(u + 1)/2
Let r(h) be the second derivative of h**5/4 + 35*h**4/12 + 20*h**3/3 - 40*h**2 + 12*h. Factor r(l).
5*(l - 1)*(l + 4)**2
Suppose 3*v - 2 = 2*v. Determine j so that -2*j**3 + 22 - 38*j + 14*j**v + 8*j - 6 + 2 = 0.
1, 3
Let q(k) be the second derivative of -k**7/252 + k**6/60 - k**5/60 + 16*k. Factor q(n).
-n**3*(n - 2)*(n - 1)/6
Suppose -65*d**5 + 62*d**5 + 9*d**3 - d**4 - 5*d**4 = 0. What is d?
-3, 0, 1
Suppose 0*u**3 - 10*u**3 + 8*u**4 + 5*u**2 + 0*u - 4*u**2 + u = 0. What is u?
-1/4, 0, 1/2, 1
Let h be (4/(-6))/((-7)/315). Let j be (6 - 2) + h/(-8). Factor 0 + j*p**2 + 1/4*p**3 - 1/2*p.
p*(p - 1)*(p + 2)/4
Let y(c) = 9*c**3 - 93*c**2 - 165*c - 75. Let d(m) = -2*m**3 + 23*m**2 + 41*m + 19. Let a(i) = -21*d(i) - 5*y(i). Determine k so that a(k) = 0.
-2
Let t = -2 + 2. Let c be t/(-2) + (14 - 12). Determine i so that 1/4*i - 1/4*i**3 + 0*i**c + 0 = 0.
-1, 0, 1
Let c(x) be the first derivative of -3*x**5/5 + 15*x**4/4 - 7*x**3 + 9*x**2/2 + 37. Factor c(n).
-3*n*(n - 3)*(n - 1)**2
Factor -5 - 2 + 3*c**2 - 8*c**2 + 10*c + 2.
-5*(c - 1)**2
Let w(u) = -7*u - 5*u**2 + u**2 - u**2 + 4. Let n(y) = y**2 - y + 1. Let a(m) = -m - 4. Let l be a(0). Let b(f) = l*n(f) + 2*w(f). Factor b(h).
-2*(h + 1)*(7*h - 2)
Let c(p) be the second derivative of -p**4/12 + p**3/6 + 3*p**2 + 3*p. Factor c(d).
-(d - 3)*(d + 2)
Let p(o) = -2*o**2 + 2*o - 3. Let d = 22 - 19. Let n(u) = -10*u**2 + 10*u - 14. Let z(w) = d*n(w) - 14*p(w). Factor z(a).
-2*a*(a - 1)
Let t = 344/105 - -2/35. Let p be ((-2)/(-1))/(4/6). Find g, given that -8/3*g**4 + t*g**2 - 2*g**p + 2*g - 2/3 = 0.
-1, 1/4, 1
Let o be (3/9)/(1/9). Suppose -5*z = o*j - 12, 0 = -6*z + z. Determine p, given that -j*p**2 - 8*p**3 + 2 + 3*p**2 + 13*p**2 + 2*p**4 - 8*p = 0.
1
Let p be (2/(-24))/(-3 + 40/15). Let n(c) be the first derivative of 1 + p*c**4 + 1/3*c**3 - c - 1/2*c**2. Find j, given that n(j) = 0.
-1, 1
Let p(b) be the first derivative of -b**5/10 + b**3/2 + b**2/2 - 7. Solve p(d) = 0.
-1, 0, 2
Let h(v) = 8*v**2 + 3*v. Let s(y) = -4*y**2 - 2*y. Let c(f) = -6*h(f) - 11*s(f). Factor c(w).
-4*w*(w - 1)
Let i(r) = -18*r**2 + 36*r - 18. Let q(u) = -2*u**2 + 4*u - 2. Let h(l) = 6*i(l) - 52*q(l). Solve h(m) = 0 for m.
1
Let p(y) = y - 8. Let g be p(13). Let k(h) be the second derivative of 1/2*h**3 + 0*h**2 + 0 - h - 3/20*h**g + 0*h**4. Factor k(t).
-3*t*(t - 1)*(t + 1)
Let 1/7*p**2 + 4/7 + 4/7*p = 0. What is p?
-2
Let s(c) be the third derivative of 0 + 1/7*c**8 + 0*c**4 + 0*c - 7/40*c**6 - 1/20*c**5 - 4/35*c**7 - 3*c**2 + 0*c**3. Solve s(t) = 0.
-1/4, 0, 1
Let o(q) = q**2 + q - 1. Let x(y) = -4 + 11 + 11*y**4 - 15*y**3 + 2*y**2 - 3*y - 3*y**5 - 6*y. Let i(m) = 14*o(m) + 2*x(m). Factor i(p).
-2*p*(p - 1)**3*(3*p - 2)
Let k(w) = -w**3 + 4*w**2 + 7*w - 6. Let i be k(5). What is l in 3*l**i + l**3 - 3*l**4 - l**4 = 0?
0, 1
Let l(q) be the second derivative of 3*q**4/14 - 2*q**3/21 + 12*q. Find c, given that l(c) = 0.
0, 2/9
Let d(c) be the third derivative of c**6/720 + c**5/60 + c**4/12 - c**3/2 + 2*c**2. Let i(q) be the first derivative of d(q). Solve i(h) = 0 for h.
-2
Let 5/4*s**5 + 1/2*s - 3/4*s**2 + 3/4*s**4 - 7/4*s**3 + 0 = 0. What is s?
-1, 0, 2/5, 1
Suppose -2*z + 0*z = -4. Let x = -571/3 - -193. Factor 2/3 + b - x*b**z + b**3.
(b - 2)*(b - 1)*(3*b + 1)/3
Let i(w) be the first derivative of 2*w**6/3 - 4*w**5/5 - 3*w**4 + 4*w**3/3 + 4*w**2 - 1. Factor i(q).
4*q*(q - 2)*(q - 1)*(q + 1)**2
Let i(a) = 6*a**2 - 2*a + 1. Let f be i(1). Suppose -4*y + 3*n + 25 = 0, -f*n - 19 = y - 2*y. What is b in -b**2 - 4*b**2 + y*b**2 = 0?
0
Suppose 2/5*o**3 + 2/5*o**2 + 0*o + 0 = 0. What is o?
-1, 0
Let m(n) be the first derivative of n**6/15 + n**5/10 - n**4/6 - n**3/3 - 4*n - 3. Let r(p) be the first derivative of m(p). Factor r(y).
2*y*(y - 1)*(y + 1)**2
Let l(k) be the second derivative of -k**5/4 - 5*k**4/3 + 7*k. Factor l(u).
-5*u**2*(u + 4)
Suppose 0 = 4*g - 3*g. Let u(k) be the third derivative of g*k**4 + 0*k + 1/30*k**5 - k**2 - 1/3*k**3 + 0. Factor u(v).
2*(v - 1)*(v + 1)
Let k = 4 - 0. Let o(s) be the third derivative of 0*s**5 + 0 - 1/6*s**3 - 1/12*s**k + 1/210*s**7 + 0*s + 1/60*s**6 - s**2. Factor o(q).
(q - 1)*(q + 1)**3
Let w = 58 - 28. Let y be 6/(-15)*w/(-78). Solve -y*p**2 - 4/13*p - 2/13 = 0 for p.
-1
Solve -7*z**2 + 6*z**2 + 2*z**2 - z**3 + 0*z**2 + z - 1 = 0 for z.
-1, 1
Determine k, given that k**4 + 0 + 2*k - 4*k**2 + 3/2*k**3 - 1/2*k**5 = 0.
-2, 0, 1, 2
Let s = -11 + 9. Let c be 4/(-10) + s/(-5). Suppose c - 1/4*b**3 + 1/4*b**2 + 0*b = 0. Calculate b.
0, 1
Let h(i) = -2*i - 2. Let z be h(-3). Let x(d) be the first derivative of -2/3*d**3 - 1/2*d**2 - 1 - 1/4*d**z + 0*d. What is b in x(b) = 0?
-1, 0
Let x be (-5)/(-2)*(-42)/(-15). Suppose 1 + x = 4*t. Factor 0*a**2 - 13*a**4 + 15*a**4 - 4*a**3 + t*a**2.
2*a**2*(a - 1)**2
Let p(f) = 2*f. Let m(n) = -n**2 - n. Let z = 9 - 6. Let a(c) = z*p(c) + 4*m(c). Determine w, given that a(w) = 0.
0, 1/2
Let g(v) be the third derivative of 0 + 4/21*v**3 - 5*v**2 + 121/210*v**5 + 0*v + 11/21*v**4. Solve g(f) = 0.
-2/11
Let f(i) be the first derivative of -i**6/3 - 14*i**5/5 - 5*i**4 + 12*i**3 + 27*i**2 - 54*i + 6. Factor f(w).
-2*(w - 1)**2*(w + 3)**3
Let i(z) be the second derivative of -4*z + 1/16*z**4 + 1/8*z**3 + 0 + 1/80*z**5 + 1/8*z**2. Determine q so that i(q) = 0.
-1
Let r(q) = 1. Let v(z) = z**3 + 18*z**2 + 108*z + 214. Let n(m) = -2*r(m) - v(m). Factor n(k).
-(k + 6)**3
Let f(v) be the third derivative of v**8/10080 + v**7/1260 - v**5/60 - 2*v**2. Let p(s) be the third derivative of f(s). Find t such that p(t) = 0.
-2, 0
Let h(d) be the third derivative of 175*d**6/24 - 10*d**5 + 45*d**4/8 - 5*d**3/3 - 7*d**2. Factor h(o).
5*(5*o - 1)**2*(7*o - 2)
Let c(m) be the third derivative of -m**6/480 + m**5/80 - m**4/48 - 4*m**2. Factor c(n).
-n*(n - 2)*(n - 1)/4
Let v(y) be the first derivative of -1/3*y**4 + 1/5*y**5 + 1/21*y**7 - 3 - y**3 - y - y**2 + 1/5*y**6. Let p(f) be the first derivative of v(f). Factor p(l).
2*(l - 1)*(l + 1)**4
Let z(n) = 6*n**3 - 7*n**2 + 7*n - 7. Let k(m) = m**3 - m**2 + m - 1. Let l(o) = -14*k(o) + 2*z(o). Let l(i) = 0. Calculate i.
0
Let x(r) = r**2 - 8*r - 128. Let a be x(16). Determine d so that 3/2*d**3 - d**2 + 5/2*d**4 + a*d + 0 = 0.
-1, 0, 2/5
Let b(q) be the second derivative of q**5/4 + 5*q**4/6 - 4*q. Factor b(m).
5*m**2*(m + 2)
Factor 5/3*k**2 - 5*k - 20/3.
5*(k - 4)*(k + 1)/3
Let s(u) = -u**2 + 5*u - 2. Let q = -2 - -6. Let i be s(q). Let 0 + 2/5*t**i - 2/5*t = 0. Calculate t.
0, 1
Let w = 21 + -16. Factor -8*s**2 + 2*s**4 + 4*s + w*s**2 + 0*s - 3*s**2.
2*s*(s - 1)**2*(s + 2)
Factor -2/3 - 5/6*g**2 - 1/6*g**3 - 4/3*g.
-(g + 1)*(g + 2)**2/6
Factor 7/10*h + 0 - 1/10*h**4 - 3/2*h**2 + 9/10*h**3.
-h*(h - 7)*(h - 1)**2/10
Let v(p) = 4*p**2 + 0 - 1 - 3*p**2 - p. Let j(q) = q**3 + 11*q**2 + 2*q - 2. Let c(o) = j(o) - 6*v(o). Factor c(z).
(z + 1)*(z + 2)**2
Let t = -4 - -6. Factor 0*r**t - 9*r**3 - 7*r**4 + 12*r**2 + 5*r - r.
-r*(r - 1)*(r + 2)*(7*r + 2)
Factor 2/3*s + 1/3*s**3 + s**2 + 0.
s*(s + 1)*(s + 2)/3
Suppose 9*j = 2*j - 0*j. Let t(i) be the second derivative of 3/20*i**5 + 0*i**2 - 2*i + 0*i**4 + j + 0*i**3. Determine l so that t(l) = 0.
0
Suppose 20 + 5 = -2*g + 5*v, 3*g + 6 = -3*v. Let z(a) = -2*a - 6. Let q be z(g). Factor -1/4*p**q - 1/4*p - 3/4*p*