). Let n(z) be the first derivative of -2/21*z**3 + 0*z**b + 2/7*z - 1. Find m such that n(m) = 0.
-1, 1
Factor p**5 - 64*p**2 - 3*p**3 + p**4 + 63*p**2 + p + p**5.
p*(p - 1)*(p + 1)**2*(2*p - 1)
What is f in 0*f + 0*f**2 + 2/5*f**4 + 16/5*f**3 + 0 = 0?
-8, 0
Factor 0*q + 8/3 - 2/3*q**2.
-2*(q - 2)*(q + 2)/3
Let c be (-4)/(4 - 8) + 1. Factor m**c + 4*m**2 - m + 5*m**2 + 5*m.
2*m*(5*m + 2)
Let f(l) be the first derivative of -4*l**5/5 + l**4 + 4*l**3/3 - 2*l**2 + 2. Determine m so that f(m) = 0.
-1, 0, 1
Let y(c) be the first derivative of -2*c**4/3 - 50*c**3/9 - 14*c**2 - 6*c - 8. Factor y(x).
-2*(x + 3)**2*(4*x + 1)/3
Find d, given that -d + 7*d - d**2 + d + 6 - 6*d = 0.
-2, 3
Let j(f) = 2*f**2 + 4*f**2 - 3*f**3 - f**3 - 2 + 2*f**3. Let u(r) = r**3 - 5*r**2 - r + 1. Let q(m) = -4*j(m) - 6*u(m). Let q(a) = 0. Calculate a.
-1
Let v(r) be the first derivative of 5*r**4/14 + 2*r**3/7 - 2*r**2/7 + 8. Determine g, given that v(g) = 0.
-1, 0, 2/5
Let q(z) be the second derivative of -z**4/18 + z**2/3 + 18*z. Let q(w) = 0. Calculate w.
-1, 1
Let h = -6 - -8. Let v be 0/h - 16/(-24). Solve 2/9*o**2 + 2/3*o**4 - 2/9*o**5 - v*o**3 + 0 + 0*o = 0.
0, 1
Let x(u) = -2*u + 8. Let k be x(4). Let p(g) be the first derivative of k*g + 1 + 1/2*g**2 - 4/3*g**3. Solve p(t) = 0 for t.
0, 1/4
Let d = 73494/5 - 14644. Let t = 55 - d. Factor 1/5*k**3 + 2/5*k**2 + 0 + t*k.
k*(k + 1)**2/5
Let n(v) = -6*v + 36. Let q be n(6). Suppose 2/11*y**3 + q*y**2 - 6/11*y - 4/11 = 0. What is y?
-1, 2
Let s(y) be the third derivative of -1/24*y**4 + y**2 + 1/120*y**6 + 1/6*y**3 + 0*y - 1/60*y**5 + 0. Factor s(p).
(p - 1)**2*(p + 1)
Suppose -9*g**2 - 2*g**3 + 8*g + 8 - 3*g**2 + 10*g**2 = 0. Calculate g.
-2, -1, 2
Let h = -9 + 12. What is n in 16*n**3 + 22*n**h - 30*n**5 - 2*n - 32*n**4 - 6*n**3 + 36*n**2 - 4 = 0?
-1, -2/5, 1/3, 1
Let f be (-10)/3 + 3/(-3). Let s = 5 + f. Determine p, given that 1/3 - s*p**2 + 1/3*p = 0.
-1/2, 1
Let y(t) = t - 1. Let z be y(3). Find v such that -3/4*v**z + 1/4*v**3 + 3/4*v - 1/4 = 0.
1
Let r(i) be the first derivative of -i**3/6 - i**2/12 - 6. Factor r(q).
-q*(3*q + 1)/6
Suppose 0*f = -3*f + 9. Factor -p**2 + p**3 - 8*p**5 + 6*p**5 + 5*p**f + 5*p**2.
-2*p**2*(p - 2)*(p + 1)**2
Let p = 32/33 - 7/11. Let s(z) be the third derivative of 0 - 3*z**2 - p*z**4 + 0*z + 4/3*z**3 + 1/30*z**5. Factor s(d).
2*(d - 2)**2
Let a(k) be the third derivative of 3*k**8/2240 + k**7/840 - k**6/144 + k**5/120 - k**4/12 + 2*k**2. Let t(g) be the second derivative of a(g). Factor t(u).
(u + 1)*(3*u - 1)**2
Suppose 4*i + 0*i - 8 = 0. Find c such that -2*c**3 + c**i + 5*c**4 - 4*c**4 + c**2 - 3*c**4 + 2*c = 0.
-1, 0, 1
What is x in 0*x**3 + 6*x**3 - x**3 - 10*x**3 - 5*x**4 = 0?
-1, 0
Factor -2/5*p**2 - 4/5*p**3 + 4/5*p - 1/5*p**4 + 3/5.
-(p - 1)*(p + 1)**2*(p + 3)/5
Let p be (3 - 945/3)/(-1). Solve -50*w**5 - 19*w**5 + 1 - 75*w**5 + 87*w**2 - 15*w - 241*w**3 + p*w**4 + 0*w = 0 for w.
1/4, 1/3, 1
Suppose j + 0 = 3. Suppose -4*f**2 + 2*f + 3*f**2 - 3*f + j*f = 0. What is f?
0, 2
Factor -1/2*s**2 + 1/4*s + 1/2 - 1/4*s**3.
-(s - 1)*(s + 1)*(s + 2)/4
Let s(f) be the third derivative of 1/120*f**5 - 1/360*f**6 + 0*f**4 - f**2 + 1/6*f**3 + 0 + 0*f. Let g(a) be the first derivative of s(a). Solve g(k) = 0.
0, 1
Let k(j) be the second derivative of -j**7/168 - j**6/60 + j**4/24 + j**3/24 - 6*j. Find a, given that k(a) = 0.
-1, 0, 1
Let n(v) = 2*v**2 - 2*v. Let t be n(2). Suppose 2*h**2 + t*h + h**2 - h**2 = 0. What is h?
-2, 0
Let f(m) be the third derivative of -7*m**6/600 + m**5/25 - m**4/40 - m**3/15 + 11*m**2. Factor f(t).
-(t - 1)**2*(7*t + 2)/5
Let i(t) be the third derivative of -1/420*t**7 + 0*t + 1/48*t**4 + 0 + 1/120*t**5 + 0*t**3 - 1/240*t**6 - 5*t**2. Factor i(r).
-r*(r - 1)*(r + 1)**2/2
Let h(x) = -x - 5. Let m be h(-7). Let p be (-92)/(-28) - m/7. What is s in 4*s + s**3 - p*s**2 + 2*s**3 - s**4 - 3*s = 0?
0, 1
Let o = 8/11 + -2/33. Let c be 11/(-66) + 3/2. Factor -o*h**2 - 2/3 + c*h.
-2*(h - 1)**2/3
Let s = 20 - 18. Let o(d) be the first derivative of 0*d**2 + 0*d**3 + 2/5*d**5 + 0*d + 1/4*d**4 + 1/6*d**6 - s. Let o(q) = 0. Calculate q.
-1, 0
Suppose -n = 8*n - 27. Factor 15/4*a - n*a**2 - 3/4.
-3*(a - 1)*(4*a - 1)/4
Let d(q) be the second derivative of q**7/210 + q**6/60 + q**5/60 + 4*q**2 + 8*q. Let g(m) be the first derivative of d(m). Suppose g(z) = 0. Calculate z.
-1, 0
Suppose -2 = -2*b - 14. Let c be ((-1)/4)/(3/b). Factor c*i**3 - 1/2*i - 1/4*i**2 + 1/4.
(i - 1)*(i + 1)*(2*i - 1)/4
Let h be ((-4)/6 - 0)/((-2)/9). Factor -5/3*r**h + 4/3*r - 4/3*r**2 + 0 + r**4.
r*(r - 2)*(r + 1)*(3*r - 2)/3
Let j(y) be the second derivative of -y**3/6 + y**2 - 6*y. Let a be j(0). Determine b so that 2/3*b - 1/3 - 1/3*b**a = 0.
1
Let u(w) be the second derivative of 0 + 1/8*w**2 - 1/12*w**3 + 4*w + 1/48*w**4. Factor u(h).
(h - 1)**2/4
Suppose 0*u + u = 3. Let d(h) = -2*h + 6. Let f be d(u). Factor 1/2*t**3 + 0 + f*t - 1/2*t**2.
t**2*(t - 1)/2
Solve -h**2 - 5*h**2 + 4*h**2 + 3*h**2 = 0 for h.
0
Suppose 0*k + 9 = -3*k. Let d = -1 - k. Factor 4*v**3 + v**d - 2*v**3 - v**3.
v**2*(v + 1)
Let u(m) be the second derivative of -m**7/84 + m**5/40 + 7*m. Factor u(f).
-f**3*(f - 1)*(f + 1)/2
Let u(v) be the first derivative of 10*v**6/3 + 17*v**5 + 30*v**4 + 65*v**3/3 + 5*v**2 - 33. Let u(k) = 0. What is k?
-2, -1, -1/4, 0
Suppose -26/3*g**2 - 8/3 + 25/3*g**4 + 12*g - 15*g**3 = 0. Calculate g.
-1, 2/5, 2
Let l(q) = q**2 + 5*q - 10. Let r be l(-7). Factor -3*u - 2 - u + 2*u**2 + r.
2*(u - 1)**2
Let c(s) be the second derivative of s**4/12 - 3*s**3/14 + s**2/7 + 6*s. Solve c(g) = 0 for g.
2/7, 1
Let f(s) be the second derivative of 5*s**7/14 - 3*s**6/10 - 21*s**5/20 + 3*s**4/4 + s**3 + 59*s. Determine r so that f(r) = 0.
-1, -2/5, 0, 1
Find a such that -9*a + 6*a**2 - 3/4*a**3 + 0 = 0.
0, 2, 6
Let t = -118 + 121. Let 0 - 3/5*r**t - 3/5*r**2 - 1/5*r - 1/5*r**4 = 0. Calculate r.
-1, 0
Let m = 23 - 13. Solve 4*q**5 - q**5 + m*q**4 - 11*q**4 - 2*q**3 + 0*q**3 = 0 for q.
-2/3, 0, 1
Let r(v) be the second derivative of -v**4/30 + 2*v**3/15 + 3*v**2/5 - 7*v. Factor r(h).
-2*(h - 3)*(h + 1)/5
Let q(n) = -n - 2. Suppose 4*g + 5*r + 28 = 0, 3*g + 4*r + 24 - 2 = 0. Let a be q(g). Factor 0*z**5 + a*z**3 - 2*z**3 + 3*z**5 - z**4.
z**3*(z - 1)*(3*z + 2)
Let k(n) be the second derivative of 0 - 2*n + 1/2*n**2 - 2/45*n**5 + 1/18*n**3 - 1/36*n**4. Let y(x) be the first derivative of k(x). Factor y(j).
-(2*j + 1)*(4*j - 1)/3
Let i(f) be the second derivative of 0 + 0*f**3 - 1/50*f**6 - 1/70*f**7 + 3/100*f**5 + 0*f**2 - 4*f + 1/20*f**4. Find p, given that i(p) = 0.
-1, 0, 1
Let b = -38 + 1027/27. Let g = 49/135 + b. Factor -2/5*h**4 - g - 4/5*h**3 + 4/5*h**2 + 2/5*h + 2/5*h**5.
2*(h - 1)**3*(h + 1)**2/5
Let p be (-70)/132*2/(-5). Let q = p + 1/3. Determine r so that 0 + 4/11*r**4 + 2/11*r - 8/11*r**3 + q*r**5 - 4/11*r**2 = 0.
-1, 0, 1/3, 1
Let b(d) be the third derivative of -1/12*d**4 + 0 - 2*d**2 + 0*d**3 + 1/15*d**5 - 1/60*d**6 + 0*d. Factor b(n).
-2*n*(n - 1)**2
Let y(k) = 7*k - 89. Let o be y(13). Factor -i**3 + 0*i + 0 + 1/2*i**4 + 1/2*i**o.
i**2*(i - 1)**2/2
Let k(t) be the third derivative of 2*t**2 + 0*t - 1/32*t**4 - 1/80*t**5 + 0*t**3 + 0. Factor k(p).
-3*p*(p + 1)/4
Let g(a) be the third derivative of -a**8/168 - a**7/105 + a**6/12 - a**5/10 - a**2. Find d, given that g(d) = 0.
-3, 0, 1
Factor 0*d**2 + 6/5*d**3 - 8/5*d - 2/5*d**4 + 0.
-2*d*(d - 2)**2*(d + 1)/5
Let k = 342 - 340. Factor -1/5*b**k + 0*b + 1/5.
-(b - 1)*(b + 1)/5
Let v(b) be the third derivative of 0*b**3 + 0*b + 1/105*b**7 + 4/75*b**6 + 0 + 2/75*b**5 - b**2 - 5/168*b**8 + 0*b**4. Suppose v(j) = 0. Calculate j.
-2/5, 0, 1
Let w be ((-3)/(43 - -2))/((-40)/6). Let a(k) be the second derivative of -1/60*k**4 + 1/30*k**3 + 0 - w*k**5 + 3*k + 1/10*k**2. Suppose a(s) = 0. What is s?
-1, 1
Let w(f) be the first derivative of f**5/20 - 5*f**4/16 + 3*f**3/4 - 7*f**2/8 + f/2 - 11. Factor w(n).
(n - 2)*(n - 1)**3/4
Let i(f) be the second derivative of f**7/12 - 11*f**6/15 + 12*f**5/5 - 10*f**4/3 + 4*f**3/3 + 9*f. Solve i(a) = 0 for a.
0, 2/7, 2
What is s in 8*s**3 - 3*s**4 + 6 + 9*s**2 + 4*s**3 + 15*s - 15*s**3 = 0?
-1, 2
Let u(m) be the second derivative of 8*m**7/63 - 16*m**6/45 - 11*m**5/15 + 31*m**4/9 - 40*m**3/9 + 8*m**2/3 - 13*m. Determi