d.
-2*(d - 1)**2*(d + 1)/3
Suppose 3/7*f**4 + 0*f + 1/7*f**5 + 0*f**2 + 0 + 2/7*f**3 = 0. What is f?
-2, -1, 0
Suppose 0 = 5*p - 3*p - 10. Suppose p + 5 = 5*s. Factor z**2 + z**s - 2*z**4 + 0*z**4 + 2*z**5 - 2*z**3.
2*z**2*(z - 1)**2*(z + 1)
Let p(i) = i**2 - 2*i + 3. Let q be p(2). Let t(a) be the first derivative of 0*a**q + 2 + 1/8*a**4 + 0*a + 0*a**2. Factor t(m).
m**3/2
Let g = 419/196 - -30/49. Determine c, given that 0*c + 0 - g*c**3 - 1/2*c**2 = 0.
-2/11, 0
Let 0 + 0*u + 2/9*u**3 + 2/9*u**2 = 0. What is u?
-1, 0
Let j(x) be the first derivative of -x**3/12 + 3*x**2/4 - 9*x/4 - 4. Factor j(u).
-(u - 3)**2/4
Suppose 0 = -4*l - 3*a - 40, -4*l + a - 26 = 30. Let j = l - -15. Find o, given that 0 + 2*o**4 - 8/9*o**5 + 2/9*o**j - 4/3*o**3 + 0*o = 0.
0, 1/4, 1
Let z be ((-20)/14)/5 + (-48)/(-21). Let k(u) be the first derivative of 0*u**4 + 0*u + 1/10*u**5 + 0*u**z - 1/12*u**6 - 3 + 0*u**3. Factor k(j).
-j**4*(j - 1)/2
Let l(r) be the second derivative of -r**4/8 - 3*r**3/4 - 3*r**2/2 - 22*r. Factor l(k).
-3*(k + 1)*(k + 2)/2
Let c(p) be the third derivative of 2*p**8/63 + 8*p**7/63 + 17*p**6/180 + p**5/45 - 3*p**2. Solve c(t) = 0.
-2, -1/4, 0
Suppose -6*q + 12 = -3*q. Suppose 0 = -x - q*m - 2, 2*x + m - 2 = -m. Factor -4*f - 2*f**2 + 2*f**2 + 4 + f**x + 0*f**2.
(f - 2)**2
Let g be (-6)/(-2) + 168/(-224). Let f be 3/4 - (-1 - -1). What is d in 3/2*d**3 + 0*d + f*d**5 + 0*d**2 + 0 + g*d**4 = 0?
-2, -1, 0
Solve 1/3*z**2 - 1/3*z - 2 = 0.
-2, 3
Let r be ((-2 - -2)/(-7))/(4/(-2)). Suppose 0 = -3*c - c. What is d in 2/7*d**2 + c + r*d = 0?
0
Let z(f) be the second derivative of f**6/60 + f**5/20 - 31*f. Factor z(h).
h**3*(h + 2)/2
Factor 6*t**4 - 6*t**3 + 0 + 3/2*t**2 + 0*t.
3*t**2*(2*t - 1)**2/2
Suppose -2*q + 12 = -0*q + 3*l, -20 = -2*q - 5*l. Let f = -25 - -51/2. What is p in q*p - 1/2*p**2 + f = 0?
-1, 1
Let x(u) be the third derivative of -u**8/448 + u**7/105 + u**6/60 + u**4/12 + 5*u**2. Let r(y) be the second derivative of x(y). Solve r(t) = 0.
-2/5, 0, 2
Suppose 2*o**5 - 3 + 6 - 3 - 2*o**4 = 0. What is o?
0, 1
Let q = 868/5 - 173. Factor -9/5*p**2 - q*p**3 + 0*p + 12/5.
-3*(p - 1)*(p + 2)**2/5
Let x(z) be the third derivative of z**5/60 + z**3/3 - 4*z**2. Let r be x(0). Factor 2*w + 0*w - 1 - 6*w + 2*w - w**r.
-(w + 1)**2
Factor 0*n**2 - 1/3*n**3 + 1/3*n - 1/6*n**4 + 1/6.
-(n - 1)*(n + 1)**3/6
Factor 8/21*v - 2/3*v**2 + 0.
-2*v*(7*v - 4)/21
Let m(z) be the second derivative of 1/14*z**4 + 0 + 4*z + 1/70*z**5 + 1/7*z**3 + 1/7*z**2. Factor m(g).
2*(g + 1)**3/7
Factor 6/11*q + 4/11 + 2/11*q**2.
2*(q + 1)*(q + 2)/11
Factor 0 + 2/7*x - 2/7*x**4 - 2/7*x**3 + 2/7*x**2.
-2*x*(x - 1)*(x + 1)**2/7
Let p be 0 - 1/(-2)*8. Let h(l) be the second derivative of 7/18*l**3 - 1/3*l**2 + 1/4*l**p - 2*l + 0. Factor h(a).
(a + 1)*(9*a - 2)/3
Let a be ((-3)/9)/(((-2)/2)/6). Suppose 1/3*v - 1/3*v**3 + v**a - 2/3 - 1/3*v**4 = 0. What is v?
-2, -1, 1
Let b(q) be the second derivative of -q**5/60 + q**4/18 - q**3/18 - 20*q. Find y such that b(y) = 0.
0, 1
Factor -2/5*t + 1/5*t**3 - 1/5*t**2 + 0.
t*(t - 2)*(t + 1)/5
Suppose z - 9 = -2*z. Factor -7*k**2 - k**2 + 0*k**3 - 4*k**z.
-4*k**2*(k + 2)
Factor 4/3*n + 8/3 - 4/3*n**2.
-4*(n - 2)*(n + 1)/3
Let h(v) be the first derivative of -v**9/1008 + v**7/140 - v**5/40 - 2*v**3/3 + 4. Let g(f) be the third derivative of h(f). Factor g(p).
-3*p*(p - 1)**2*(p + 1)**2
Factor -6*a + 0 + 14*a**2 + 2*a**4 + 0 - 10*a**3.
2*a*(a - 3)*(a - 1)**2
Suppose 5*m = p - 15, -m - 3*p = -2*p + 9. Let v(h) = h**2 + 5*h + 6. Let z be v(m). What is n in -2*n**z + 2*n**4 + 5*n**2 - 5*n**2 = 0?
-1, 0, 1
Let r(x) = -2*x**3 - 5*x**2 - 7*x - 7. Let z(s) = 2*s**3 + 4*s**2 + 6*s + 8. Let k(g) = 4*r(g) + 3*z(g). Factor k(v).
-2*(v + 1)**2*(v + 2)
Let t(q) = -2. Let v(o) be the third derivative of -o**5/60 + 11*o**3/3 - 2*o**2. Let d(j) = -22*t(j) - 2*v(j). What is x in d(x) = 0?
0
Let t(a) = -a**3 - 2*a**2 - 4*a - 1. Let l be t(-3). Suppose 5*k + l = 5*g, -2*g + 2 = 3*k - 6. Factor k*r + 2/5*r**4 - 1/5*r**3 + 0 + 0*r**2 - 1/5*r**5.
-r**3*(r - 1)**2/5
Suppose r + 5*j - 23 + 2 = 0, -5*r - 4*j = -42. Suppose 3*x + 0*x - r = 0. Factor 2/9*v**3 + 0 + 2/9*v - 4/9*v**x.
2*v*(v - 1)**2/9
Let h(b) be the first derivative of b**9/10584 - b**8/1960 + b**7/980 - b**6/1260 + b**3/3 - 1. Let j(m) be the third derivative of h(m). Factor j(n).
2*n**2*(n - 1)**3/7
Let r(x) be the third derivative of x**5/150 - x**4/20 + 2*x**3/15 - 6*x**2. Solve r(k) = 0.
1, 2
Suppose 6/17*k**4 - 4/17*k**2 + 0 + 10/17*k**3 + 0*k = 0. What is k?
-2, 0, 1/3
Let i(d) be the second derivative of -d**5/130 - d**4/78 + 4*d**3/39 + 4*d**2/13 - 22*d. Factor i(q).
-2*(q - 2)*(q + 1)*(q + 2)/13
Let v(f) be the first derivative of 0*f**3 + 2 - 2/75*f**6 + 2*f + 0*f**5 + 0*f**4 - 1/105*f**7 + 0*f**2. Let h(n) be the first derivative of v(n). Factor h(k).
-2*k**4*(k + 2)/5
Let a be -4 + ((-768)/20)/(-8). Factor -a*j + 2/5 + 2/5*j**2.
2*(j - 1)**2/5
Let m(t) be the second derivative of -t**6/360 - t**5/120 - t**3/3 - t. Let b(a) be the second derivative of m(a). Factor b(i).
-i*(i + 1)
Let h = -6/25 + 92/175. What is s in -h*s + 2/7*s**2 + 2/7*s**3 - 2/7 = 0?
-1, 1
Let p(t) = 19*t + 118. Let k be p(-6). Factor 0*n**2 + 0 + 0*n - 1/6*n**5 - 1/6*n**k + 0*n**3.
-n**4*(n + 1)/6
Factor 15*l**2 - 89 + 2*l**3 + 24*l + 101 - l**3 + 2*l**3.
3*(l + 1)*(l + 2)**2
Let b be 2 - ((-8)/28)/((-2)/14). Let s(n) be the first derivative of -5/3*n**3 - 7/5*n**5 + b*n + 2 + 1/2*n**2 + 9/4*n**4 + 1/3*n**6. Solve s(v) = 0.
0, 1/2, 1
Let t = -493/5 - -99. Factor 0 + 0*p + t*p**2 - 2/5*p**4 + 0*p**3.
-2*p**2*(p - 1)*(p + 1)/5
Let x(u) = u - 5. Let c be x(7). Let g(l) be the third derivative of 0*l + 1/60*l**6 + 0*l**4 + l**c + 0 + 1/210*l**7 + 0*l**3 + 1/60*l**5. Factor g(y).
y**2*(y + 1)**2
Let t(a) be the first derivative of -2*a**5 - a**4 + 10*a**3/3 + 2*a**2 + 6. Factor t(x).
-2*x*(x - 1)*(x + 1)*(5*x + 2)
Let r(p) be the first derivative of -2*p**5/11 - 4*p**4/11 + 38*p**3/33 - 6*p**2/11 - 4. Find l such that r(l) = 0.
-3, 0, 2/5, 1
Let t = -16 - -21. Let f = -5 + t. Factor -1/2*w + 3/4*w**2 + 3*w**3 + f + 7/4*w**4.
w*(w + 1)**2*(7*w - 2)/4
Factor -t**3 + 0*t + 3/2*t**4 + 0 - 1/2*t**5 + 0*t**2.
-t**3*(t - 2)*(t - 1)/2
Let w(y) be the third derivative of -1/60*y**5 + 0 - 1/3*y**3 + 3*y**2 - 1/8*y**4 + 0*y. Factor w(f).
-(f + 1)*(f + 2)
Let b(t) be the first derivative of t**6/120 - t**4/24 + 2*t**2 + 2. Let h(g) be the second derivative of b(g). Factor h(u).
u*(u - 1)*(u + 1)
Let d(o) = -30*o**5 + 25*o**4 - 15*o**3. Let v(n) = n**5 + n**3. Let b(c) = -d(c) - 10*v(c). Determine k, given that b(k) = 0.
0, 1/4, 1
Suppose -2*a = -4*a + 6. Let l(d) be the second derivative of 0*d**2 + 0 + 1/30*d**4 - 3*d + 1/15*d**a. Let l(j) = 0. What is j?
-1, 0
Suppose -q + u + 3 = 0, 4*q - 4*u - 14 = -2*u. Suppose q*j = -4*o, j + 4*o + 10 = -2. Factor -3*w + 1 + j*w**2 - 5*w**2 + 2*w + w**3.
(w - 1)**2*(w + 1)
Let s(w) = w**2 - w - 2. Let z(c) = -5*c**2 + 6*c + 11. Let i(u) = -u**3 + 6*u**2 + u - 2. Let x be i(6). Let v(r) = x*z(r) + 22*s(r). Solve v(n) = 0 for n.
-1, 0
Let l(w) = -w**3 - 3*w**2 + 4. Let u be l(-3). Suppose u*v - 10 = 2*v, -v - 5 = -5*f. Determine d, given that 2*d + 2*d**3 - 1/2 - 1/2*d**4 - 3*d**f = 0.
1
Let p(r) be the first derivative of r**5/15 - r**4/12 - r**3/9 + r**2/6 - 1. Factor p(g).
g*(g - 1)**2*(g + 1)/3
Let z(p) be the first derivative of p**6/27 - p**4/9 + p**2/9 + 10. Factor z(o).
2*o*(o - 1)**2*(o + 1)**2/9
Let q(u) be the third derivative of 1/630*u**7 - 1/72*u**4 + 0*u**3 + 5*u**2 + 0*u + 1/60*u**5 - 1/120*u**6 + 0. Determine h, given that q(h) = 0.
0, 1
Let t(g) be the third derivative of g**7/630 - g**6/180 + g**5/180 + 16*g**2. What is x in t(x) = 0?
0, 1
Let y(h) be the second derivative of h**7/1260 - h**6/90 + h**5/15 - h**4/6 - 3*h. Let f(w) be the third derivative of y(w). Factor f(o).
2*(o - 2)**2
Suppose 2*o = -3*o + 10. Find x, given that o*x + 6*x**2 - 3*x**2 - 8*x = 0.
0, 2
Let u(h) be the first derivative of -h**4/8 - h**3/6 + 12. Factor u(v).
-v**2*(v + 1)/2
Let f(t) be the first derivative of t**6/10 - 3*t**5/20 - t**4/4 + t**3/2 - 2*t - 6. Let y(c) be the first derivative of f(c). Factor y(n).
3*n*(n - 1)**2*(n + 1)
Let d(f) be the first derivative of -f**6/21 - 8*f**5/35 - 2*f**4/