4/3*k**w + 1/3*k.
k*(k + 1)**4/3
Let n be (-96)/12*(-1)/2. Let b(h) be the first derivative of 3/4*h**n - 2/5*h**5 - 2 - 1/3*h**3 + 0*h + 0*h**2. Factor b(s).
-s**2*(s - 1)*(2*s - 1)
Factor 2/3 - 2/9*i**5 + 22/9*i + 4/3*i**3 + 28/9*i**2 - 2/9*i**4.
-2*(i - 3)*(i + 1)**4/9
Let o(b) be the third derivative of -7*b**6/15 - 41*b**5/30 + 7*b**4/3 - 4*b**3/3 - 25*b**2. Solve o(x) = 0 for x.
-2, 1/4, 2/7
Let y(s) be the third derivative of s**8/10080 + s**7/1890 + s**6/1080 + s**4/4 - 2*s**2. Let u(r) be the second derivative of y(r). Factor u(x).
2*x*(x + 1)**2/3
Let w be 1/(-2)*(-1 - 1). Let t be w/(-1) - (2 + -5). Let -2*v**t - v + 3*v + 2*v = 0. What is v?
0, 2
Let a be (-1)/(6/24*-10). Solve -a*u**2 + 2/5*u - 2/5*u**3 + 2/5 = 0 for u.
-1, 1
Let f(z) = -z**3 + z**2 - z. Let y(j) = 2*j**4 + 8*j**3 + 2*j - 1. Let k = -5 + 6. Let x(d) = k*y(d) + 3*f(d). Factor x(h).
(h + 1)**3*(2*h - 1)
Let w(z) be the first derivative of -7*z**4 + 64*z**3/3 - 8*z**2 + 23. Factor w(o).
-4*o*(o - 2)*(7*o - 2)
Let t(w) be the third derivative of -w**8/5880 + w**6/420 + w**5/210 - w**3/6 + 2*w**2. Let z(l) be the first derivative of t(l). Factor z(r).
-2*r*(r - 2)*(r + 1)**2/7
Let z(x) be the first derivative of -x**4/16 - x**3/12 + x**2/8 + x/4 + 1. What is a in z(a) = 0?
-1, 1
Suppose 20*d = -64*d. Factor 0 + 7/5*o**5 + 2/5*o**2 - 12/5*o**4 + 3/5*o**3 + d*o.
o**2*(o - 1)**2*(7*o + 2)/5
Let 16/5*s - 4/5 - 12/5*s**2 = 0. Calculate s.
1/3, 1
Let o(n) be the third derivative of -n**6/120 - n**5/60 + n**4/4 - 7*n**2. Let h be o(-3). Let -1/2*r + 1/2*r**3 + h*r**2 + 1/4*r**4 - 1/4 = 0. What is r?
-1, 1
Let s(l) be the first derivative of -3*l**5/10 + 9*l**4/8 - l**3 - 6. Factor s(x).
-3*x**2*(x - 2)*(x - 1)/2
Let m(f) = -f**3 + 6*f**2 + 7*f. Let u be m(7). Factor -2*z**2 + 2*z - 4 - z**3 + 6 - z**3 + u*z**3.
-2*(z - 1)*(z + 1)**2
Let m be (-15 + 17)/((45/4)/9). Factor -m*t - 36/5*t**3 + 0 + 44/5*t**2.
-4*t*(t - 1)*(9*t - 2)/5
Suppose 0 = -0*g - 6*g. Let l(v) be the second derivative of 1/120*v**6 + 1/12*v**3 + 0*v**5 + 0*v**2 - 1/16*v**4 + g + 2*v. Solve l(m) = 0 for m.
-2, 0, 1
Find j, given that 6/5 + 9/5*j - 3*j**2 = 0.
-2/5, 1
Let t(n) be the second derivative of -n**6/135 + n**4/27 - n**2/9 + 2*n. Solve t(u) = 0.
-1, 1
Factor -u**2 + u + 2*u - 2*u.
-u*(u - 1)
Let y = -29 - -41. Suppose -4*d = 5*v - 9 - 9, -v = 5*d - y. Factor 3*n - n**2 - 3*n + 2*n + 0*n**v.
-n*(n - 2)
Factor 1 + 1 + t**2 + 4*t - 3*t + 2*t.
(t + 1)*(t + 2)
Let m(g) be the second derivative of g**2 + 0 - 2*g + 2/3*g**3 + 1/6*g**4. Factor m(s).
2*(s + 1)**2
Find y such that 1/2*y**2 - 1/2*y**3 + 0*y + 0 = 0.
0, 1
Let j(g) be the first derivative of -1/2*g**3 + 3/4*g**2 - 3/8*g**4 - 4 + 3/2*g. Let j(w) = 0. What is w?
-1, 1
Suppose -2*m + 34 = 2*d + 14, -36 = -3*m - 5*d. Let j(u) = -3*u + 13. Let a be j(3). Factor -2*l**4 + 3*l - m*l - 5*l**3 - 8*l**2 + l**a.
-l*(l + 1)*(l + 2)**2
What is c in 0*c**3 - 1/3*c - 1/6*c**4 + 0 + 1/2*c**2 = 0?
-2, 0, 1
Let p be 54/10 + 1 + -25 + 23. Factor -6/5*f**5 + 18/5*f**2 - 6*f**3 + p*f**4 + 0 - 4/5*f.
-2*f*(f - 1)**3*(3*f - 2)/5
Let p(b) = -b**5 + b**4 + b**3 - b**2 - 7. Let y(n) be the second derivative of -n**2/2 - 4*n. Let z(c) = -2*p(c) + 14*y(c). Factor z(h).
2*h**2*(h - 1)**2*(h + 1)
Let o(m) be the first derivative of -5*m**3 - 3/5*m**5 + 0*m + 3*m**2 + 3*m**4 + 1. Factor o(b).
-3*b*(b - 2)*(b - 1)**2
Let a(j) = 7*j**3 - 5*j**2 - 4*j. Let f = -23 + 16. Let z(b) = 13*b**3 - 9*b**2 - 7*b. Let p(t) = f*a(t) + 4*z(t). Factor p(k).
k**2*(3*k - 1)
Let h(t) be the second derivative of 3*t**5/20 - t**4/2 - t**3/2 + 3*t**2 - 3*t. Find d such that h(d) = 0.
-1, 1, 2
Factor -4 - 2 - r**2 + 2 + 3*r**2 - 2*r.
2*(r - 2)*(r + 1)
Suppose 2*m + 4*u = 14, -3*m + 2*u = -5*m + 10. Let i(x) be the second derivative of 1/18*x**4 - 1/60*x**5 + 0*x**2 + 0 - 4*x - 1/18*x**m. Factor i(c).
-c*(c - 1)**2/3
Let u be ((-36)/8 + 5)/2. Factor 1/4*l**3 + 0*l**2 - u*l + 0.
l*(l - 1)*(l + 1)/4
Let p be 4*(388/(-56) + 5 - -2). Factor -2/7*z**2 + 0 + p*z.
-2*z*(z - 1)/7
Suppose 18*h - 19*h + 2 = 0. Determine z, given that -27/2*z**h - 81/2 + 81/2*z + 3/2*z**3 = 0.
3
Let k(x) = -5*x**4 + 15*x**3 - 23*x + 3. Let z(o) = -35*o**4 + 105*o**3 - 160*o + 20. Let h(c) = 20*k(c) - 3*z(c). What is s in h(s) = 0?
-1, 0, 2
Let h(t) = -t**2 - 4*t - 2. Let y be h(-3). Let a be (-35)/(-25) + y*-1. Factor -a*c**2 + 4/5 + 2/5*c.
-2*(c - 2)*(c + 1)/5
Let p(a) be the first derivative of -3*a**4/4 - 6*a**3 + 96*a - 48. Solve p(u) = 0 for u.
-4, 2
Let y(o) be the third derivative of -o**5/180 + 6*o**2. Factor y(s).
-s**2/3
Let p(x) be the third derivative of -x**7/525 + x**6/150 - x**4/30 + x**3/15 - 10*x**2. Factor p(a).
-2*(a - 1)**3*(a + 1)/5
Let i(z) = z**2 - 3*z + 2. Let a be i(3). Factor -6*m - 5*m - m**a + 12*m.
-m*(m - 1)
Let d(o) = -3*o**2 - 7*o - 9. Let l(y) = y**2 + 3*y + 4. Let m = 11 - 16. Let p(r) = m*l(r) - 2*d(r). Factor p(f).
(f - 2)*(f + 1)
Let s(p) be the third derivative of -p**5/15 - p**4/4 - p**3 - 4*p**2. Let r(o) = 3*o**2 + 6*o + 7. Let y(d) = -5*r(d) - 6*s(d). Suppose y(v) = 0. What is v?
-1/3
Find x, given that 2/7*x**4 - 10/7*x**2 + 6/7*x + 2/7*x**3 + 0 = 0.
-3, 0, 1
Suppose 0 = k + 2*u + 6, -16 = 3*u - 4. Let x be (-6)/(-1)*(-6)/(-60). Factor -3/5*f**k + 0 + 3/5*f**4 - 3/5*f + x*f**3.
3*f*(f - 1)*(f + 1)**2/5
Let n(b) be the third derivative of -5*b**8/336 + b**7/21 - b**6/24 + b**2. Factor n(j).
-5*j**3*(j - 1)**2
Let j be ((-6)/(-4))/((-3)/(-6)). Let g(a) = 5*a**3 + a**2 - 6*a - 8. Let m(z) = -2*z**3 + 2*z + 3. Let d(f) = j*g(f) + 8*m(f). Determine p so that d(p) = 0.
0, 1, 2
Suppose -122 = -5*m + 2*k, 2*m + 5*k = -2*m + 91. Solve -4*d + 22*d**4 - m*d**4 + 2 + 2*d**3 + 2*d**3 = 0 for d.
-1, 1
Let t be 2/(-12) + 38/12. Factor 0*w**2 + 6*w**2 + w**3 - 3*w + 0*w**2 - 4*w**t.
-3*w*(w - 1)**2
Let u be 4/28 - (-137)/21. Factor -2*r**5 - 2/3*r + 0 - 8*r**3 - 4*r**2 - u*r**4.
-2*r*(r + 1)**3*(3*r + 1)/3
Let x = -791/4 - -198. Solve 0 - 1/4*o**3 + x*o + 0*o**2 = 0.
-1, 0, 1
Let q(b) = -b**3 + b**2 + b + 1. Let g(h) = -2*h**3 + 10*h**2 + 18*h + 12. Let x(l) = -g(l) + 3*q(l). Factor x(s).
-(s + 1)*(s + 3)**2
Let f = 4 - -10. Suppose f = 5*n - 1. Factor -o**3 - 2*o**n + 2*o**3 + 0*o**4 + o**2 - 2*o**4.
-o**2*(o + 1)*(2*o - 1)
Let q(y) be the second derivative of -169*y**5/50 + 221*y**4/30 - 56*y**3/15 + 4*y**2/5 - 14*y. Determine t, given that q(t) = 0.
2/13, 1
Let c be (14/8 - 2)*9/(-2). Let d(f) be the first derivative of 1/4*f**4 + 3 - 3/5*f**5 + 5/24*f**6 + 5/6*f**3 - c*f**2 + 1/2*f. Find u, given that d(u) = 0.
-1, 2/5, 1
Let u(p) be the second derivative of p**7/1050 + p**6/200 + p**5/150 - 3*p**2/2 - 5*p. Let m(z) be the first derivative of u(z). Factor m(f).
f**2*(f + 1)*(f + 2)/5
Factor 0*z**3 + 0 + 0*z + 0*z**2 - 1/4*z**5 - 1/4*z**4.
-z**4*(z + 1)/4
Let t(o) = -8*o**4 - 16*o**3 + 13*o**2 + 21*o - 5. Let v(z) = 4*z**4 + 8*z**3 - 7*z**2 - 11*z + 3. Let f(m) = 3*t(m) + 5*v(m). Solve f(h) = 0 for h.
-2, -1, 0, 1
Let d(o) be the second derivative of 0 - 1/3*o**3 + 3*o + 0*o**4 + 0*o**2 + 1/10*o**5. Factor d(h).
2*h*(h - 1)*(h + 1)
Let y = -855 - -4282/5. Let h be (-32)/(-14) + 2/(-7). Let 2/5*j + 0 - y*j**5 - 19/5*j**4 - 1/5*j**h - 3*j**3 = 0. What is j?
-1, 0, 2/7
Factor 1/5*c**3 - 2/5*c**2 + 0 + 0*c.
c**2*(c - 2)/5
Let o(i) = -9*i**2 + 4*i - 7. Let h(l) be the first derivative of 5*l**3/3 - l**2 + 4*l - 3. Let f(a) = 7*h(a) + 4*o(a). Factor f(w).
-w*(w - 2)
Let q = -61 + 306/5. Let v(t) be the first derivative of -3 - 2/15*t**3 + 1/10*t**2 + q*t. Determine j, given that v(j) = 0.
-1/2, 1
Let r(w) be the second derivative of -w**4/60 - 7*w**3/30 - w**2 - 14*w. Factor r(p).
-(p + 2)*(p + 5)/5
Let h be 22/(-6) + (-5)/15. Let w(l) = l + 8. Let g be w(h). Factor -8*f + g*f**2 + 2*f + 2 - 3*f.
(f - 2)*(4*f - 1)
Let t be 2 - 2/(-1 + -1). Factor 0*w**2 + 2*w**2 - t*w**2 + 1.
-(w - 1)*(w + 1)
Let g(c) = -4*c**2 + 3 + 0*c**3 - c**3 + 0*c**3. Let i be g(-4). Solve -m**2 - 3/2*m + m**i - 1/2 + 3/2*m**4 + 1/2*m**5 = 0.
-1, 1
Let i(m) = -m**2 + 11*m - 8. Let o be i(10). Suppose -o*g = 2*q - 32, 4*q - 78 = -5*g - 16. Factor 3*j - 12*j**3 + j - 3 - q*j**2 - 3*j**4 - 16*j.
-3*(j + 1)**4
Let b(j) be the second derivative of j**6/660 + j**5/110 + j**4/66 - j**2/2 - 3*j. Let r(d) be the first derivative of b(d