 k. Determine b, given that 1/5*b**v + 0 + 1/5*b = 0.
-1, 0
Let g(q) = 3*q**4 - 6*q**2 + 6*q. Let m(k) = 3*k**4 - 7*k**2 + 5*k. Let y(p) = -5*g(p) + 6*m(p). Suppose y(r) = 0. What is r?
-2, 0, 2
Let q(v) = 6*v**5 + 21*v**4 + 42*v**3 - 27*v**2. Let y(f) = f**5 + 3*f**4 + 6*f**3 - 4*f**2. Let o(l) = 4*q(l) - 27*y(l). What is c in o(c) = 0?
-1, 0, 2
Factor 1/4*h**2 + 9/4*h**4 - 3 + 7*h - 15/2*h**3.
(h - 3)*(h + 1)*(3*h - 2)**2/4
Let n(k) = -4*k**3 + 4*k**2 - 5. Let r be n(-1). Solve -5/3*w**3 + r*w**2 + 2/3 - 7/3*w + 1/3*w**4 = 0.
1, 2
Find d, given that 56/9*d**3 - 10/3*d**4 + 20/9*d**2 - 8/9*d**5 - 16/3*d + 10/9 = 0.
-5, -1, 1/4, 1
Suppose -4*c + 4/5*c**2 + 16/5 = 0. What is c?
1, 4
Suppose 2*b + 56 = b. Let d be b/(-16) - 3*1. Factor -3/2*n + n**2 + n**3 + d*n**5 - 3/2*n**4 + 1/2.
(n - 1)**4*(n + 1)/2
Solve -3/4*x**2 + 3/2 + 17/4*x = 0 for x.
-1/3, 6
Let n = 308/31 + -16229/1674. Let p(h) be the second derivative of 0*h**2 + n*h**4 + 23/135*h**6 + 2/27*h**3 + 0 + 1/27*h**7 + 3/10*h**5 - 2*h. Factor p(y).
2*y*(y + 1)**3*(7*y + 2)/9
Let b = -2 + 4. Suppose u + 3*a = 11, b*u + 2 = 6*a - 4*a. Factor 2/3*k**u + 0 + 0*k + 2/3*k**3.
2*k**2*(k + 1)/3
Find l such that 0 - 1/2*l**3 - l**2 - 1/2*l = 0.
-1, 0
Factor 41*v + v**3 + 16 + 9*v**2 - 65*v - 2*v**3.
-(v - 4)**2*(v - 1)
Let y be 5/(-32)*4/(-30). Let x(s) be the second derivative of -y*s**4 + 0*s**2 + 0*s**3 - 1/80*s**5 + 2*s + 0. Factor x(m).
-m**2*(m + 1)/4
Let d(x) = -x**2. Let m(y) = -9*y**3 + 10*y**2 - 16*y + 4. Let b(j) = 44*d(j) - 4*m(j). Find g, given that b(g) = 0.
2/3, 1
Suppose 15 = -g + 3*v, 12 = 3*v - 3. Let i be ((-9)/12)/(-1*12/8). Factor -j**2 + 1/2*j**5 + j**4 + g*j**3 + 0 - i*j.
j*(j - 1)*(j + 1)**3/2
Suppose -3*l = r + 6, -3*l - 2*r - 5 = 4. Let g(p) = p**4 + 4*p**3 - 7*p - 1. Let n(k) = -k**4 + k + 1. Let z(w) = l*g(w) - 3*n(w). Let z(o) = 0. What is o?
-1, 1
Let y = -6/5 + 23/15. Factor y*t**2 - 1/3 + 0*t.
(t - 1)*(t + 1)/3
Determine m so that 8/3*m**2 + 0 - 8/3*m**4 + 16/3*m**5 - 1/3*m - 5*m**3 = 0.
-1, 0, 1/4, 1
Let i(z) be the first derivative of z**3/9 - 2*z**2/3 + z - 34. Suppose i(g) = 0. Calculate g.
1, 3
Let l(f) be the second derivative of 1/27*f**3 + 0*f**4 - f + 0 - 1/270*f**5 + f**2. Let u(o) be the first derivative of l(o). Determine s, given that u(s) = 0.
-1, 1
Let r(s) be the first derivative of -7*s**6/39 + 4*s**5/65 + 7*s**4/26 - 4*s**3/39 - 17. Determine g, given that r(g) = 0.
-1, 0, 2/7, 1
Let f(t) be the second derivative of -4*t + 0 + 3/10*t**5 + t**2 + 1/6*t**4 - 2/15*t**6 - t**3. Suppose f(k) = 0. What is k?
-1, 1/2, 1
Let m(b) be the first derivative of 3/5*b**5 + 0*b - 3 - 3/2*b**2 - 9/4*b**4 + 3*b**3. Factor m(j).
3*j*(j - 1)**3
Let x be -1*(12/9 + (-8)/6). Factor 1/2*k - k**3 + x*k**4 + 1/2*k**5 + 0 + 0*k**2.
k*(k - 1)**2*(k + 1)**2/2
Let j(h) be the second derivative of h**4/6 - 2*h. Suppose j(d) = 0. What is d?
0
Let f(q) be the third derivative of q**6/540 - q**5/135 - q**4/108 + 2*q**3/27 - 7*q**2. Factor f(y).
2*(y - 2)*(y - 1)*(y + 1)/9
Let r be (14/(-35))/(4/(-125)). Let s = r + -12. Find f, given that 3/2*f + s*f**2 + 1 = 0.
-2, -1
Solve -2/9*j**2 - 8/9 - 8/9*j = 0.
-2
Let r(c) be the first derivative of -c**3/9 - c**2/3 - c/3 - 4. Suppose r(i) = 0. Calculate i.
-1
Let t(m) be the first derivative of -m**4/84 - 2*m**3/21 - 2*m**2/7 - 4*m + 2. Let a(s) be the first derivative of t(s). Factor a(r).
-(r + 2)**2/7
Let m(g) be the second derivative of -1/20*g**5 + 0*g**3 + 1/6*g**4 - 1/30*g**6 - 2*g + 0 + 0*g**2. Find f such that m(f) = 0.
-2, 0, 1
Let a(n) be the third derivative of n**7/1155 - n**6/660 - n**5/330 + n**4/132 + 2*n**2. Factor a(u).
2*u*(u - 1)**2*(u + 1)/11
Let c(b) = -15*b**3 + 21*b**2 + 15*b + 21. Let i(m) = 3*m**3 - 4*m**2 - 3*m - 4. Let p = 32 + -11. Let j(o) = p*i(o) + 4*c(o). What is w in j(w) = 0?
-1, 0, 1
Let n(q) be the second derivative of 0*q**2 - 1/6*q**4 + 0 - 1/15*q**6 + 1/84*q**7 - 3*q + 3/20*q**5 + 1/12*q**3. Let n(p) = 0. Calculate p.
0, 1
Let s(z) be the first derivative of -z**4/5 + 52*z**3/15 - 14*z**2 - 196*z/5 - 24. Factor s(x).
-4*(x - 7)**2*(x + 1)/5
Let w be 1/(2 + 4 + 1). Let v(p) be the first derivative of w*p**4 + 2/7*p - 1/7*p**2 - 1/21*p**6 + 2/35*p**5 - 4/21*p**3 + 2. Factor v(f).
-2*(f - 1)**3*(f + 1)**2/7
Let s be 2/3*(-3)/2. Let q be (-2 - s)*-4 - 2. Let -2 + 3*w**2 + 9*w**q + 4 - 9*w - 5*w**2 = 0. What is w?
2/7, 1
Suppose 0 = 5*i + g - 15, -i - 6*g + 27 = -g. What is u in -3/2*u**i - 3/2*u + 0 = 0?
-1, 0
Let c(k) be the second derivative of k**4/36 - 5*k**3/9 + 25*k**2/6 + 23*k. What is j in c(j) = 0?
5
Solve 4*q**4 + 13*q**2 + 5*q**3 - 19*q**2 - 13*q**3 + 10*q**2 = 0.
0, 1
Let r be (8/5)/((-8)/(-20)). Suppose -2*b + r = -0. Factor -4*i**3 + 0*i**4 - 4*i**b + 0*i**5 + 2 + 2*i**5 + 2*i**4 + 2*i.
2*(i - 1)**2*(i + 1)**3
Let z(v) = v**3 - 8*v**2 + 4. Let m be z(8). Let q be (-2)/((-3)/2*m). Find b such that q*b + 0 - 2/3*b**2 = 0.
0, 1/2
Factor -n + 1194*n**3 - 1195*n**3 + 4*n - 3 + 1.
-(n - 1)**2*(n + 2)
Let h be 6/(-33) + 112/1925*10. Let h*s**2 + 0 - 2/5*s**3 + 0*s = 0. Calculate s.
0, 1
Solve -14/5*l**2 + 6/5*l + 2*l**3 - 2/5*l**4 + 0 = 0 for l.
0, 1, 3
Let z(p) be the second derivative of p**6/15 + p**5/2 + 4*p**4/3 + 4*p**3/3 - p. Factor z(t).
2*t*(t + 1)*(t + 2)**2
Suppose 2*y = -a + 3, -4*y + 2*y = 5*a + 1. Factor -4/5*l**y + 3/5*l + 1/5.
-(l - 1)*(4*l + 1)/5
Let n(z) = z**4 - z**3 - z**2 - 1. Let y(u) = -20*u**4 - 30*u**3 - 8*u**2 + 4*u + 2. Let q(v) = -4*n(v) - 2*y(v). Factor q(x).
4*x*(x + 1)**2*(9*x - 2)
Let m(r) be the third derivative of r**6/100 - 4*r**5/75 + r**4/15 - 14*r**2. Factor m(u).
2*u*(u - 2)*(3*u - 2)/5
Let m = 38 - 35. Factor -7/2*q - 5/2*q**m + 1 + 9/2*q**2 + 1/2*q**4.
(q - 2)*(q - 1)**3/2
Let g(m) be the second derivative of -2*m**2 + 1/6*m**4 + 0 - 5*m + 1/3*m**3. Factor g(n).
2*(n - 1)*(n + 2)
Let w(a) = 12*a**3 + 10*a**2 - 4*a - 2. Let r(o) = -11*o**3 - 10*o**2 + 3*o + 2. Let t(d) = 6*r(d) + 5*w(d). Solve t(h) = 0.
-1, 1/3
Let h(n) = -2*n**3 + 2*n**2 + n + 3. Let c(p) = -p**3 + 2*p**2 + p + 2. Let w be (-1)/(1*(-2)/4). Let q(s) = w*h(s) - 3*c(s). Factor q(x).
-x*(x + 1)**2
Let f(o) be the third derivative of -o**8/420 + 4*o**7/525 - o**6/150 - 5*o**2. Factor f(u).
-4*u**3*(u - 1)**2/5
Let m(v) be the first derivative of -v**7/105 + v**5/30 - 2*v**2 - 2. Let y(p) be the second derivative of m(p). Factor y(c).
-2*c**2*(c - 1)*(c + 1)
Let v(g) be the second derivative of g + 4/5*g**2 + 0*g**3 + 0 - 1/15*g**6 - 17/30*g**4 + 9/25*g**5. What is x in v(x) = 0?
-2/5, 1, 2
Suppose 4*n + 2*c = -c + 31, -n - 11 = -3*c. Suppose -4/7*h + 2/7*h**n + 0*h**2 + 4/7*h**3 - 2/7 = 0. What is h?
-1, 1
Let 8/17*y - 12/17*y**2 - 2/17*y**4 - 2/17 + 8/17*y**3 = 0. What is y?
1
Let n(c) = c**2 - 7*c + 6. Let t be n(6). Let g be (-2)/(8/(-18)) - t. Factor -1/2 - g*s**2 - 3*s.
-(3*s + 1)**2/2
Suppose 8*h - 3*h + 150 = 5*i, -2*h = -i + 64. Let k = h - -103/3. Factor -k*x**2 - 1/3*x + 0.
-x*(x + 1)/3
Suppose 5*o - 9 = 16. Factor -o*a**4 - 5*a**4 - a**2 - a**2 - 14*a**3 - 2*a**2.
-2*a**2*(a + 1)*(5*a + 2)
Let r be (0 + 1 + -11)*(-4)/10. What is d in -8/5*d**2 - 24/5*d**3 - 18/5*d**r + 0*d + 0 = 0?
-2/3, 0
Factor 4/13*h**2 - 2/13*h**3 + 0 - 2/13*h.
-2*h*(h - 1)**2/13
Let f(k) be the first derivative of k**3/12 + k**2/2 + k + 2. Factor f(n).
(n + 2)**2/4
Let r(x) be the first derivative of -4*x**5/5 - 15*x**4 - 100*x**3 - 250*x**2 + 25. Suppose r(m) = 0. Calculate m.
-5, 0
Let t = 27/104 - 1/104. Solve 1/2 + 3/4*i + t*i**2 = 0 for i.
-2, -1
Let b(u) be the first derivative of u + 0*u**2 - 1 - 1/18*u**4 + 2/9*u**3. Let i(l) be the first derivative of b(l). Solve i(j) = 0 for j.
0, 2
Let s(d) be the third derivative of -d**5/15 + d**4/6 + 4*d**3/3 + 3*d**2. Suppose s(c) = 0. Calculate c.
-1, 2
Let x(o) = 3*o + 41. Let d be x(-12). Let j(l) be the third derivative of 1/20*l**4 + 0 + 0*l - 1/15*l**3 - 2*l**2 - 1/75*l**d. Find m such that j(m) = 0.
1/2, 1
Let r(w) = w**4 - w**3 + w**2 - w. Let h(p) = -5*p**4 + 2*p**3 - p**2 + 4*p. Let x(o) = h(o) + 6*r(o). Factor x(t).
t*(t - 2)*(t - 1)**2
Let q = 2 + 1. Let h = 13 + -8. Factor r - 2*r**q + r**h - 12 + 12.
r*(r - 1)**2*(r + 1)**2
Factor -3/2*k + 5 - 1/2*k**2.
-(k - 2)*(k + 5)/2
Let u = -7 - -6. Let a be 145/15 + (-3)/u. Factor -a*g**3 + 4/3 - 10*g*