*f. Let b(l) = 9*h(l) + 4*x(l). Determine t so that b(t) = 0.
-1, 0
Let h(y) be the first derivative of y**7/42 - y**5/10 + y**3/6 + 2*y - 2. Let w(v) be the first derivative of h(v). Factor w(g).
g*(g - 1)**2*(g + 1)**2
Let y be -1 - 1/(10/(-14)). Factor 0 - 2/5*h + y*h**2.
2*h*(h - 1)/5
Let m be 38/(-10) + (-28)/(-7). Factor -2/5 - 1/5*u**3 + m*u + 2/5*u**2.
-(u - 2)*(u - 1)*(u + 1)/5
Let f(r) be the third derivative of 0*r + 1/20*r**5 - 4*r**2 + 1/40*r**6 + 0*r**3 + 0 + 0*r**4. Factor f(t).
3*t**2*(t + 1)
Let z(l) = -l**3 - 8*l**2 + 1. Let n be z(-8). Factor 3 - 2*c**2 - 2*c**3 + 2*c + 0*c**2 - n.
-2*(c - 1)*(c + 1)**2
Let k(l) be the first derivative of -l**4/4 - 3*l**3 - 27*l**2/2 + l + 3. Let a(f) be the first derivative of k(f). Factor a(d).
-3*(d + 3)**2
Let c(i) be the first derivative of 2*i**3/9 + 19. Factor c(k).
2*k**2/3
Let v(d) = 4*d + 2. Let s(c) = 9*c + 5. Let l(k) = -3*s(k) + 7*v(k). Let a be l(5). Solve a*j**4 - 4*j**2 - j - j + 3*j**5 - j**5 = 0.
-1, 0, 1
Let b = -2 - -3. Solve 0*o**2 + 3*o**2 - o - o**2 + b - 2*o = 0 for o.
1/2, 1
Let s(k) = -3*k**5 + 10*k**3 - 16*k**2 - 16*k + 32. Let r(a) = 7*a**5 + a**4 - 21*a**3 + 32*a**2 + 32*a - 64. Let b(h) = -6*r(h) - 15*s(h). Factor b(z).
3*(z - 2)**3*(z + 2)**2
Suppose 4*b - 27 = -15. Factor b*s - 3/2*s**2 + 0 - 3/2*s**3.
-3*s*(s - 1)*(s + 2)/2
Let w(a) be the second derivative of 4*a**6/75 + a**5/10 - a**4/2 - 4*a**3/3 - 4*a**2/5 + a + 6. Let w(y) = 0. Calculate y.
-2, -1, -1/4, 2
Let i(t) be the second derivative of t**7/840 - t**6/144 + t**5/60 + t**4/12 + t. Let c(s) be the third derivative of i(s). Factor c(o).
(o - 1)*(3*o - 2)
Let j be (-2 - 8/(-16))/(21/(-52)). Factor -12/7*z**3 - 2/7*z**4 - 8/7 - 24/7*z - j*z**2.
-2*(z + 1)**2*(z + 2)**2/7
Let i = -29 + 31. Suppose -l = 5*m + 12, 0 = -4*l - 5*m - i - 1. Solve 0 + 2/3*n**l + 2/3*n**2 + 0*n = 0 for n.
-1, 0
Factor 19*z**3 + 5*z**5 - 2*z**3 - 11*z**3 + 15*z**4 - 15*z**2 - 11*z**3.
5*z**2*(z - 1)*(z + 1)*(z + 3)
Let g = 69/20 - 13/4. Find z such that 0 + 2/5*z**3 + 0*z**2 - g*z**5 - 1/5*z + 0*z**4 = 0.
-1, 0, 1
Let b(q) be the second derivative of q**5/50 - q**4/30 - q**3/3 - 3*q**2/5 - 57*q. Factor b(w).
2*(w - 3)*(w + 1)**2/5
Let s(w) = w**2 - 3*w - 6. Let n be s(5). Suppose -3*y + n - 2*y**2 + 5*y + 0*y = 0. Calculate y.
-1, 2
Let b(x) = -x**3 + 3*x**2 + 3. Let w be b(3). Factor 4*k**w - 2 - 5*k**2 + 6*k + 2*k - 5*k**2.
2*(k - 1)**2*(2*k - 1)
Let t(v) = -v**2 + 4*v - 3. Let r(m) = m - 3. Let y be r(6). Let l be t(y). Factor 0*q + l + 0*q**2 + 2/3*q**3 + 0*q**4 - 2/3*q**5.
-2*q**3*(q - 1)*(q + 1)/3
Let h = 11/15 + -8/15. Determine u so that 0*u**2 - h*u**3 + 1/5*u + 0 = 0.
-1, 0, 1
Let j(w) be the first derivative of -5*w**3/3 + 30*w**2 - 180*w + 19. Factor j(c).
-5*(c - 6)**2
Let m(p) = -p**5 + 2*p**4 - 7*p**3 - 4*p**2 + 5*p + 5. Let i(a) = 4*a**5 - 10*a**4 + 34*a**3 + 20*a**2 - 24*a - 24. Let n(r) = 3*i(r) + 14*m(r). Factor n(x).
-2*(x - 1)**2*(x + 1)**3
Let c(r) = -2*r**2 - 9*r + 1. Let f be (-7)/14 + 21/(-6). Let l be c(f). Factor 1/4*a**4 + 0 - 1/4*a**2 + 1/4*a**l + 0*a - 1/4*a**3.
a**2*(a - 1)*(a + 1)**2/4
Let s(f) = -11*f - 2. Let v be s(3). Let r be (-21)/v + (-12)/(-5). Determine l, given that -2/3*l**2 + 0*l + 0*l**r + 0 + 2/3*l**4 = 0.
-1, 0, 1
Let v(o) be the second derivative of o**5/60 - 4*o**2 + 8*o. Let q(w) be the first derivative of v(w). Solve q(a) = 0.
0
Let j(w) = -w**3 - 7*w**2 - 9*w + 7. Let a be j(-5). Find s, given that -1/3 + 1/6*s**a + 1/6*s = 0.
-2, 1
Suppose -2*y = i - 2*i + 6, 3*i - y = 13. Suppose -5*w - 6*w**2 - 4*w + i*w**3 - w**3 = 0. What is w?
-1, 0, 3
Let d be (1 - 0) + 8 + -4. Suppose -1/2*t**d - 1/4 + 5/4*t**4 - t**2 + t - 1/2*t**3 = 0. What is t?
-1, 1/2, 1
Let x be ((-1)/30)/(40/(-5)). Let h(o) be the third derivative of 0*o + 0 - 1/96*o**4 - 2*o**2 + 0*o**3 + x*o**5. Factor h(a).
a*(a - 1)/4
Let j = 227/20 + -53/5. Factor -3*y + 3*y**2 + 0 - j*y**3.
-3*y*(y - 2)**2/4
Let f = 1251 + -8688/7. Let j = -9 + f. Find h, given that 0 - j*h**3 - 6/7*h**2 - 2/7*h**4 - 2/7*h = 0.
-1, 0
Let t = -88 - -620/7. Find f, given that t*f + 2/7 - 2*f**2 + 8/7*f**3 = 0.
-1/4, 1
Suppose 0*s - 3*s + 312 = 0. Let t = 319/3 - s. Let 0*h + 0 - 8/3*h**4 - t*h**3 - 2/3*h**2 - h**5 = 0. What is h?
-1, -2/3, 0
Suppose 4/11*g**3 + 0 + 0*g + 2/11*g**2 + 2/11*g**4 = 0. What is g?
-1, 0
Let z(l) be the first derivative of -l**6/40 - l**5/10 - l**4/8 - 11*l**2/2 - 11. Let u(x) be the second derivative of z(x). Suppose u(b) = 0. Calculate b.
-1, 0
Let y(k) be the first derivative of -k**6/30 + 4*k**5/25 - k**4/5 - 2*k**3/15 + k**2/2 - 2*k/5 + 3. Factor y(p).
-(p - 2)*(p - 1)**3*(p + 1)/5
Suppose -2*n - 2 = -8. Let x = 0 + 0. Solve -w**n + 0*w**2 + x*w**2 + w**2 = 0.
0, 1
Let o = 13 + -13. Let h(r) be the second derivative of 1/30*r**6 + r + 0*r**2 + 1/6*r**3 - 1/20*r**5 + o - 1/12*r**4. Factor h(k).
k*(k - 1)**2*(k + 1)
Let f(u) be the third derivative of 7*u**6/300 + 23*u**5/450 + u**4/90 + 23*u**2. Solve f(h) = 0.
-1, -2/21, 0
What is v in v + 2*v**2 - 4*v - v**3 + 0*v**3 + 2*v = 0?
0, 1
Suppose 51 = 28*y - 11*y. Let k(s) = s**2 - 2*s + 2. Let u be k(2). Factor 3/2*r**u + 0 - y*r.
3*r*(r - 2)/2
Suppose 24 = -5*v - 1. Let o = -3 - v. Let b(p) = -2*p**5 - 6*p**4 + 2. Let a(g) = -g**4 + g**3 + 1. Let x(l) = o*a(l) - b(l). Factor x(s).
2*s**3*(s + 1)**2
Factor -1/5*q**2 + 0*q + 0.
-q**2/5
Let a(l) = 9*l**4 - 14*l**3 + 4*l + 4. Let y(t) = -t**4 + t**3 - t - 1. Let u(z) = a(z) + 4*y(z). Factor u(i).
5*i**3*(i - 2)
Let s = 23 + -20. Let q(v) be the third derivative of -1/24*v**3 + 0 + 0*v + 1/48*v**4 + s*v**2 - 1/240*v**5. Factor q(f).
-(f - 1)**2/4
Determine r, given that 1/3 + r**2 + r + 1/3*r**3 = 0.
-1
Suppose 0 = -5*m + m + 16. Find n, given that -2 + 3 - 2*n**2 + 5*n**m + 0 - 4*n**4 = 0.
-1, 1
Suppose 14 = 3*a - 2*o, -2*o + 6 = o. Let b(x) be the third derivative of 1/60*x**a + 0*x**3 + 3*x**2 + 0*x + 0*x**4 + 0 - 1/15*x**5 + 1/105*x**7. Factor b(z).
2*z**2*(z - 1)*(z + 2)
Suppose -5*d - 48 = -63. Let i(v) be the third derivative of 0*v**4 + 0 + 2*v**2 + 0*v + 0*v**d + 1/150*v**5. Factor i(n).
2*n**2/5
Let z = -113/4 + 29. Let d = -19/36 + z. What is b in -2/9*b**3 - 2/9*b**2 + 0 + d*b + 2/9*b**4 = 0?
-1, 0, 1
Let o = -492 + 29521/60. Let q(k) be the second derivative of 1/18*k**3 + 0 + 0*k**2 - 3*k + o*k**5 + 1/18*k**4. Factor q(n).
n*(n + 1)**2/3
Let z be (-18)/15*(-50)/40. Factor 1/2*c**3 - z*c**4 + 0 + 3/2*c**2 - 1/2*c.
-c*(c - 1)*(c + 1)*(3*c - 1)/2
Let x(u) = -u + 1. Let s be x(-1). Solve -5*w**5 - s*w**3 - 2*w**2 - 2*w**5 + 3*w**3 + 2*w**4 + 6*w**3 = 0.
-1, 0, 2/7, 1
Let d(r) = -r - 1. Let o(b) = -b**4 + b**3 + 3*b**2 - 11*b - 4. Let z(f) = -6*d(f) + o(f). Let z(y) = 0. What is y?
-2, 1
Let d(q) be the second derivative of 1/7*q**2 + 1/35*q**5 + q - 2/21*q**3 + 0 - 1/105*q**6 + 0*q**4. Suppose d(l) = 0. What is l?
-1, 1
Let y(j) = -j**2 + 12*j - 31. Let s be y(5). Suppose -1/2*v**s + 0*v + 3/2*v**3 - v**2 + 0 = 0. Calculate v.
0, 1, 2
Let m be 1/(-1) - (-3)/1. Let p = 1 + m. Factor -2/5*a - 4/5*a**2 - 2/5*a**p + 0.
-2*a*(a + 1)**2/5
Factor -6/13*p**2 + 0 + 2/13*p - 2/13*p**4 + 6/13*p**3.
-2*p*(p - 1)**3/13
Let i be ((-1)/7)/(6/42 + -1). Let b(h) be the first derivative of 0*h + i*h**2 - 1/9*h**3 + 1. Factor b(c).
-c*(c - 1)/3
Let s(o) = -o**2 + 9*o + 3. Let u be s(9). Let x(r) be the first derivative of 2*r**5 + 0*r + 2 + 2*r**4 + 2/3*r**u + 0*r**2 + 2/3*r**6. Factor x(z).
2*z**2*(z + 1)**2*(2*z + 1)
Let z = 21 - 33. Let h(x) = x**3 + 11*x**2 - 11*x + 15. Let u be h(z). Let 9/2*n + u - 15/2*n**2 = 0. Calculate n.
-2/5, 1
Factor -24*r + 2*r**2 + 24 + 7 + 44 - 3.
2*(r - 6)**2
Let j be (-5)/(-10) - 11/(-2). Let d(m) be the second derivative of -1/15*m**j + 1/6*m**4 + 0 + 0*m**2 + 1/3*m**3 - 2*m - 1/10*m**5. Solve d(i) = 0 for i.
-1, 0, 1
Suppose -3*r + 4*r = 5*k - 20, -5*k - 2*r = -5. What is p in -p**k - 6*p**2 + 0*p**3 - 4*p + 5*p**3 + 6*p**4 + 0*p**2 = 0?
-1, -2/3, 0, 1
Let d be ((-6)/((-12)/4))/1. Suppose d = -5*j + 7. Find v such that -v**2 + j - 1/2*v**3 + 1/2*v = 0.
-2, -1, 1
Factor -2/3*a**3 - 2/3*a**2 + 0 + 4/3*a.
-2*a*(a - 1)*(a + 2)/3
Let j = -3424/9 + 382. Let -8/9*x**3 + j*x**2 - 2/9 - 4/9*x = 0. What is x?
-1/4, 1
Let w = -9 - -13. Let u(v) = -v**2 - 3*v**2 + 4*v + 9*v**3 - 3*v**3 + w. Let i(