**2
Suppose n + 1 = -5*u - 16, u + 13 = 3*n. Let k(t) be the third derivative of -1/3*t**4 + 0*t + 0 - 1/30*t**5 - 4/3*t**n - t**2. Factor k(v).
-2*(v + 2)**2
Let t = 6 + -8. Let j(a) = 3*a**4 + 12*a**3 + 11*a**2 - 10*a - 10. Let f(q) = 12*q**4 + 48*q**3 + 45*q**2 - 39*q - 39. Let s(w) = t*f(w) + 9*j(w). Factor s(g).
3*(g - 1)*(g + 1)*(g + 2)**2
Let n = -9 + 6. Let b(x) = 2*x**4 + 3*x**3 - 2*x**2 + 7*x + 5. Let y(p) = -p**4 - 2*p**3 + p**2 - 4*p - 3. Let g(d) = n*b(d) - 5*y(d). Factor g(k).
-k*(k - 1)**2*(k + 1)
Let l be ((-3)/2)/((-12)/16). Factor 4*v**l + v - v**3 + v**3 + 2*v**3 + v.
2*v*(v + 1)**2
Let p = 9 + -9. Let f(w) = p*w**2 + 1 + 0*w**2 + 0*w**2 + w**2. Let v(o) = -21*o**3 + 51*o**2 - 33*o + 9. Let t(m) = -3*f(m) + v(m). Factor t(c).
-3*(c - 1)**2*(7*c - 2)
Let b(n) be the third derivative of -7*n**2 - 1/30*n**5 + 0*n**4 + 1/60*n**6 + 0 + 0*n**3 + 0*n. Factor b(s).
2*s**2*(s - 1)
Let k(l) be the first derivative of 0*l + 1/60*l**4 + 1/3*l**3 - 1/150*l**5 + 0*l**2 + 1 + 1/900*l**6. Let g(h) be the third derivative of k(h). Factor g(j).
2*(j - 1)**2/5
Let s(t) be the second derivative of 2*t**6/15 + 2*t**5/5 - t**4 + 5*t. Factor s(a).
4*a**2*(a - 1)*(a + 3)
Let q(m) = 2*m**2 + m. Let k be q(-2). Suppose -k*n + 11*n = 0. Factor n + 5/2*o**2 - o.
o*(5*o - 2)/2
Let m(i) be the third derivative of -1/30*i**5 + 0 + 0*i + 2*i**2 + 1/12*i**4 + 0*i**3. Factor m(v).
-2*v*(v - 1)
Factor -32/3 - 3/2*b**2 - 8*b.
-(3*b + 8)**2/6
Let l(m) be the second derivative of -m**7/1785 - m**6/1020 + 5*m**2/2 + 5*m. Let n(h) be the first derivative of l(h). Determine f so that n(f) = 0.
-1, 0
Let r = -7 + 11. Let d(h) be the second derivative of -3/100*h**5 + 2/15*h**3 + 3*h + 0*h**r + 0 - 1/150*h**6 + 0*h**2. Factor d(a).
-a*(a - 1)*(a + 2)**2/5
Let v(m) be the second derivative of 3*m**5/20 + 5*m**4/16 + m**3/8 + 5*m. Factor v(l).
3*l*(l + 1)*(4*l + 1)/4
Let d(r) be the second derivative of -4*r**6/15 - 3*r**5/10 + 3*r**4/2 - 2*r**3/3 - 6*r. Find i, given that d(i) = 0.
-2, 0, 1/4, 1
Let k(p) be the third derivative of 3*p**5/160 + 5*p**4/48 + p**3/12 + 25*p**2. Factor k(t).
(t + 2)*(9*t + 2)/8
Let c(d) = d**2 - 4*d + 4. Suppose m = 3*t - 4, -m = 3*t + 4*m - 34. Let o be c(t). Suppose o + b**2 + 5*b - 2*b - 5*b = 0. What is b?
1
Let i be (-2)/7 - 62/(-364). Let z = i - -61/78. Find l, given that 0 - z*l**3 + 0*l**2 + 0*l = 0.
0
Suppose 5*u + 5 = 0, 0 = 2*i - u + 4*u - 3. Let -7/2*t**2 + 0 + 2*t**i - t = 0. Calculate t.
-1/4, 0, 2
Let p be 1 + (-9)/(-6) + -2. Factor 0 - p*s + s**2 - 1/2*s**3.
-s*(s - 1)**2/2
Let u(n) be the third derivative of 0 - 1/3*n**3 + 0*n - 5/24*n**4 + 4/15*n**5 - 2*n**2 - 3/40*n**6. Find j, given that u(j) = 0.
-2/9, 1
Let f(h) be the third derivative of 0*h**3 + 0*h + 0 + 1/160*h**6 - 1/40*h**5 + 1/32*h**4 + 4*h**2. Suppose f(k) = 0. Calculate k.
0, 1
Let l(w) be the first derivative of -w**4/4 - w**3/3 + 6. Let l(j) = 0. Calculate j.
-1, 0
Let j(d) be the third derivative of 0*d + 1/420*d**6 + 5/84*d**4 - 3*d**2 - 2/21*d**3 - 2/105*d**5 + 0. Factor j(z).
2*(z - 2)*(z - 1)**2/7
Suppose -5*d + 33 = 13. Let p = -1 + d. Factor 4 + 0*o**3 + 0*o**2 + 8*o + 8*o**2 - p*o**2 + o**3.
(o + 1)*(o + 2)**2
Let k(q) be the first derivative of -2*q**6/3 - 32*q**5/5 - 18*q**4 - 64*q**3/3 - 10*q**2 - 15. Find c, given that k(c) = 0.
-5, -1, 0
Suppose -23 = 8*g - 7. Let x be (g - 4)*(-2)/6. Factor 2/5*s**x + 6/5*s + 4/5.
2*(s + 1)*(s + 2)/5
What is d in 0*d + 3*d**3 + 2*d + 8*d**2 - 8*d - 5*d**3 = 0?
0, 1, 3
Let f(g) = g**2 + g + 1. Let y(j) = 7*j**2 + 7*j + 8. Let v(x) = -24*f(x) + 3*y(x). Factor v(s).
-3*s*(s + 1)
Let q be 4*(0 - (-15)/26). Let o = q - 124/65. What is a in -2/5*a**5 + 0*a + 2/5*a**2 - o*a**4 + 0 + 2/5*a**3 = 0?
-1, 0, 1
Let g(t) be the second derivative of 4*t + 0*t**2 - 1/24*t**4 + 0 + 1/6*t**3. Factor g(d).
-d*(d - 2)/2
Let n(m) = -4*m + 34. Let h be n(8). Let q(l) be the second derivative of -h*l + 1/70*l**5 + 0*l**2 + 0 + 0*l**4 - 1/21*l**3. Let q(u) = 0. Calculate u.
-1, 0, 1
Let h = 342 - 2390/7. Suppose -5 = -5*r + 10. What is m in 2/7*m + h*m**2 + 2/7*m**r + 0 = 0?
-1, 0
Let x(k) = k**4 + k**3 - k**2 - k + 1. Let w(r) = 22*r**4 - 10*r**3 - 2*r**2 - 10*r + 10. Let c(u) = -w(u) + 10*x(u). Factor c(y).
-4*y**2*(y - 1)*(3*y - 2)
Let f(g) = g + 10. Let h be f(-7). What is d in -h*d**2 - d**2 + 4*d**2 - 5*d**2 + 2*d = 0?
0, 2/5
Let l = 319/3 + -106. Let v(m) be the second derivative of 0 - 3*m - 1/6*m**4 + 2*m**2 + l*m**3. Factor v(z).
-2*(z - 2)*(z + 1)
Factor 6*i - 7*i**2 - 1 + 29*i - 3*i**2 - 35*i**3 + 11.
-5*(i - 1)*(i + 1)*(7*i + 2)
Let g = 158 + -2369/15. Let b(x) be the second derivative of 0*x**2 + 0 + 0*x**3 + g*x**6 + 0*x**4 - 2*x + 1/10*x**5. Factor b(u).
2*u**3*(u + 1)
Let j(y) = y**4 + 4*y**3 - 3*y**2 - 2. Suppose -4*g - 16 - 188 = 0. Let r(n) = -9*n**4 - 33*n**3 + 25*n**2 + 17. Let v(b) = g*j(b) - 6*r(b). Factor v(m).
3*m**2*(m - 1)**2
Let p(w) = -8*w**4 + 7*w**3 + 45*w**2 + 37*w. Let t(h) = -5*h**4 + 5*h**3 + 30*h**2 + 25*h. Let z(l) = -5*p(l) + 7*t(l). What is u in z(u) = 0?
-1, 0, 2
Let d be 3/6 + 6/4. Let n(w) be the second derivative of 0*w**3 + 1/6*w**4 - d*w + 0 - 1/2*w**5 + 0*w**2 + 4/15*w**6. Factor n(m).
2*m**2*(m - 1)*(4*m - 1)
Let d = 3 + -3. Let v be (d + -1 + 1)/2. Factor v*z**2 - 2*z**2 + z - 1 + 2*z.
-(z - 1)*(2*z - 1)
Solve -49/4*v**2 - 9/4 + 21/2*v = 0 for v.
3/7
Let g(a) be the first derivative of 2/3*a**2 + 4/3*a - 2 + 1/9*a**3. Factor g(l).
(l + 2)**2/3
Let i be (0 + -1)*1*-15. Suppose 4*j = -3*w + 20, 5*w + 3*j = -0*w + i. Find c, given that -c**2 - 4*c**3 + c + w*c**3 + 1 + 3*c**3 = 0.
-1, 1
Let v(q) be the third derivative of -3*q**8/140 + 2*q**7/35 - 7*q**6/150 + q**5/75 + 7*q**2. Let v(y) = 0. What is y?
0, 1/3, 1
Let n = -23 + 27. Let z(v) be the third derivative of v**2 - 1/12*v**n + 0*v**3 + 1/30*v**5 + 0 + 0*v. Factor z(d).
2*d*(d - 1)
Suppose 2*w - 15 = -1. Factor -3*a**2 - w*a + 13*a**2 + 13*a.
2*a*(5*a + 3)
Let l(u) be the first derivative of u**5/120 - u**4/24 + u**3/12 - u**2/2 + 2. Let f(j) be the second derivative of l(j). Let f(b) = 0. What is b?
1
Let w(m) be the first derivative of 0*m - 3*m**4 - 4*m**3 - 2*m**2 + 1 - 4/5*m**5. Find f such that w(f) = 0.
-1, 0
Let n(l) = -l**2 - 31*l + 105. Let w be n(-34). Let -48/5*p**2 - 18/5*p**4 + 27/5*p - 6/5 + 42/5*p**w + 3/5*p**5 = 0. Calculate p.
1, 2
Let p(v) be the second derivative of -v**6/30 + 5*v**4/12 - 2*v**2 - 27*v. Let p(z) = 0. Calculate z.
-2, -1, 1, 2
Let j(c) be the third derivative of 0*c**3 + c**2 + 0 - 1/140*c**7 + 0*c + 0*c**4 + 1/40*c**6 - 1/40*c**5. Factor j(n).
-3*n**2*(n - 1)**2/2
Suppose k + 20 = -4*k. Let c = -1 - k. Factor -1 + x**3 + 3*x**2 + 0*x**2 - 6*x**2 + c*x.
(x - 1)**3
Let i be 7 - -3*(-2 + 1 - 0). Let p(s) be the first derivative of 0*s + 3/10*s**5 - 1/4*s**2 - 1/2*s**3 - 1 + 1/8*s**i. Let p(j) = 0. What is j?
-1, -1/3, 0, 1
Let g(b) be the third derivative of -b**6/24 + 5*b**4/24 - 44*b**2. Factor g(q).
-5*q*(q - 1)*(q + 1)
Let d(l) = 3*l**5 + 21*l**4 + 3*l**3 + 9*l**2 + 9. Let g(c) = 2*c**5 + 11*c**4 + 2*c**3 + 5*c**2 + 5. Let j(q) = 5*d(q) - 9*g(q). Suppose j(i) = 0. Calculate i.
0, 1
Let v be 6 - 1 - (13 + -12). Let 0 - 11/4*d**2 + 1/4*d + 35/4*d**3 - 25/4*d**v = 0. What is d?
0, 1/5, 1
Let s(z) be the first derivative of -1/4*z + 1/5*z**5 + 5/16*z**4 - 5/8*z**2 - 2 - 1/4*z**3. Factor s(r).
(r - 1)*(r + 1)**2*(4*r + 1)/4
Let j = -505/2 - -255. Suppose -2/3 - 2*x + 1/6*x**2 + j*x**3 = 0. What is x?
-2/3, -2/5, 1
Let z(f) = -f**3 + 18*f**2. Let h be z(18). Factor h*o + 1/2 - 1/2*o**2.
-(o - 1)*(o + 1)/2
Let r(p) be the first derivative of p**5/10 + p**4/4 - p**3/2 - p**2 + 2*p - 3. Factor r(y).
(y - 1)**2*(y + 2)**2/2
Let r(c) = c**5 + 5*c**4 + 5*c**3 - 5*c**2 - 6*c. Let i(u) = u**5 - u. Let m(w) = -6*i(w) + r(w). Factor m(n).
-5*n**2*(n - 1)**2*(n + 1)
Let n(x) = -x**2 - x + 1. Let s(q) = 4*q**2 + 4*q - 8. Let z(p) = 8*n(p) + s(p). Solve z(v) = 0.
-1, 0
Let q(y) be the first derivative of -y**5/120 + y**4/48 - y**2 + 1. Let w(a) be the second derivative of q(a). Factor w(p).
-p*(p - 1)/2
Suppose 0 = 2*t - 3*t. Factor 10*l**4 + 2*l**5 + 4*l**2 + 8*l**3 + 2*l**5 + t*l**2 - 2*l**2.
2*l**2*(l + 1)**2*(2*l + 1)
Let y = 2/9 - -1/36. Factor 1/2 - y*m**4 - 1/4*m**2 - 3/4*m + 3/4*m**3.
-(m - 2)*(m - 1