*p = 0. Factor m*i**5 + 0*i**5 + 3*i**2 + 2*i**4 - 5*i**2 - 4*i**5 + 2*i**3.
-2*i**2*(i - 1)**2*(i + 1)
Suppose 4 = 4*x - 0. Suppose -w - 4*o = -x + 2, w - o - 4 = 0. Suppose 2*d**4 - d - 5*d**w - 7*d + 12*d**2 + 2 - 3*d**3 = 0. What is d?
1
Let x(w) be the third derivative of w**4/8 - 2*w**2. Let p be x(1). Factor -2*z**p - z**4 - 3*z**4 - 2*z**5 + 0*z**3.
-2*z**3*(z + 1)**2
Determine p so that 0*p**2 + 0*p**4 + 0*p + 1/3*p**5 + 0 - 1/3*p**3 = 0.
-1, 0, 1
Solve 37/2*q**2 + 10*q + 15*q**3 + 9/2*q**4 + 2 = 0.
-1, -2/3
Let h(c) = c**3 - 5*c**2 - 5*c - 6. Let i be h(6). Suppose o + 3*o - 8 = i. Factor 18*y**o + 3*y**2 - 16*y + y - 6.
3*(y - 1)*(7*y + 2)
Suppose 0 = -33*v + 82 + 17. Factor 0 - 1/4*t**v + 0*t + 1/4*t**2.
-t**2*(t - 1)/4
Let l(x) be the second derivative of -x - 1/30*x**4 + 0*x**2 - 1/15*x**3 + 0. Factor l(u).
-2*u*(u + 1)/5
Suppose y = -m + 3*m - 73, 0 = 3*m - 2*y - 111. Let t = -33 + m. Factor -2/7 - 20/7*v**t - 2/7*v**5 - 10/7*v**4 - 10/7*v - 20/7*v**3.
-2*(v + 1)**5/7
Let s(o) be the second derivative of 1/45*o**5 + 1/9*o**2 + 1/135*o**6 - 5*o - 1/27*o**4 - 1/27*o**3 + 0 - 1/189*o**7. Suppose s(a) = 0. What is a?
-1, 1
Suppose 4*g = 3*b - 26, -5*b + 10*b + 4*g = -10. Factor -2*j + 0*j**2 - j**b + 4*j - 3*j.
-j*(j + 1)
Let b = -721/4 + 181. Suppose 0*s - 9/4*s**3 - 3/4*s**5 + 0 - 9/4*s**4 - b*s**2 = 0. Calculate s.
-1, 0
Suppose -3*w + p = w - 18, 2 = w + p. Factor 1 - 7*y**3 + w*y + 3*y**3 - 96*y**4 + 1 + 94*y**4.
-2*(y - 1)*(y + 1)**3
Let a(t) be the first derivative of -4*t**5/5 - 2*t**4 + 4*t**2 + 4*t - 9. Factor a(r).
-4*(r - 1)*(r + 1)**3
Let r(g) = 7*g - 58. Let c be r(9). Let 32/5*m**4 + 0 + 0*m - 14/5*m**c + 4/5*m**2 - 22/5*m**3 = 0. Calculate m.
0, 2/7, 1
Let z be (-1001)/4*(-32)/(-40). Let c = z + 201. Factor 0 - c*g**2 + 2/5*g**3 + 0*g.
2*g**2*(g - 2)/5
Let p(b) = 4*b**2 + 8*b - 2. Let i(s) = 4*s**2 + s + 2. Let k(u) = -3*u**2 - u - 1. Let d(a) = -2*i(a) - 3*k(a). Let r(m) = 2*d(m) - p(m). Factor r(f).
-2*f*(f + 3)
Suppose -v**4 - 6*v**2 + 7*v**3 + v**5 - 4*v**4 + 3*v**2 = 0. Calculate v.
0, 1, 3
Let c(n) be the first derivative of -2*n**3/27 + 2. Solve c(b) = 0 for b.
0
Factor 4/5*b**3 + 3/5 - 4/5*b - 1/5*b**4 - 2/5*b**2.
-(b - 3)*(b - 1)**2*(b + 1)/5
Let u(y) be the first derivative of -y**5/30 + y**4/36 + y**3/18 - 2*y - 2. Let m(l) be the first derivative of u(l). Find w, given that m(w) = 0.
-1/2, 0, 1
Let k = -20 - -15. Let o = k - -8. Factor -1/5*l**5 + 2/5 + 2/5*l**o - 2/5*l**4 + 8/5*l**2 + 7/5*l.
-(l - 2)*(l + 1)**4/5
Let q(k) be the second derivative of k**4/42 + 2*k**3/21 - 7*k. Factor q(s).
2*s*(s + 2)/7
Let q = 4019/1506 - 1/502. Find b such that 8/3 + q*b + 2/3*b**2 = 0.
-2
Let w(g) be the third derivative of g**5/80 + 3*g**4/16 + 9*g**3/8 + 25*g**2. Factor w(x).
3*(x + 3)**2/4
Let c(b) be the first derivative of 4/3*b**3 + 3 + 5/2*b**2 + 2*b + 1/4*b**4. What is v in c(v) = 0?
-2, -1
Let q(r) be the first derivative of -r**5/5 + 3*r**4/4 - r**3 + r**2/2 - 6. Factor q(u).
-u*(u - 1)**3
Suppose -n - 5*p = -10, n + 2*n = -3*p + 6. Factor -4/5*m + n - 2/5*m**2.
-2*m*(m + 2)/5
Let n be (-10 - -11)*0/1. Factor 2/11*q**4 + 2/11*q**2 + 0 + n*q - 4/11*q**3.
2*q**2*(q - 1)**2/11
Let t = 187 - 185. Let k(m) be the second derivative of -1/12*m**4 + 0 - 1/6*m**3 - 2*m - 1/80*m**5 + 0*m**t. Factor k(u).
-u*(u + 2)**2/4
Let p be (-1 + (-24)/(-21))/(360/84). Let d(j) be the second derivative of -1/18*j**7 + 0*j**4 - 2*j + 0 + 0*j**2 - p*j**5 + 1/10*j**6 + 0*j**3. Factor d(z).
-z**3*(z - 1)*(7*z - 2)/3
Let g(o) be the first derivative of 3*o**4/4 + 4*o**3 + 15*o**2/2 + 6*o - 6. Factor g(p).
3*(p + 1)**2*(p + 2)
Let n = 11/367 - 6998/25323. Let p = 2/23 - n. Factor -1/3*y**3 - 1/3*y**2 + p + 1/3*y.
-(y - 1)*(y + 1)**2/3
Let d(z) be the first derivative of z**3 + 15*z**2/2 - 18*z - 12. Find c such that d(c) = 0.
-6, 1
Let k(a) be the third derivative of a**6/15 - 19*a**5/30 + 11*a**4/12 + 4*a**3/3 - 6*a**2 + 2. Factor k(x).
2*(x - 4)*(x - 1)*(4*x + 1)
Let v be (1/(6/4))/(26/117). Let l(h) be the first derivative of 2/35*h**5 - 2/7*h + 0*h**3 - 1/7*h**4 + 2/7*h**2 + v. Solve l(n) = 0 for n.
-1, 1
Let n(p) be the first derivative of 8/3*p + 2/3*p**3 - 1/12*p**4 + 2 - 2*p**2. Factor n(o).
-(o - 2)**3/3
Let f be (-3 + (-8)/(-1))/7. Let l = f - 3/14. Factor -1/2 - b - l*b**2.
-(b + 1)**2/2
Let h(k) = 6*k**4 - 7*k**3 + 11*k**2 + 5*k + 5. Let q(i) = -3*i**4 + 4*i**3 - 5*i**2 - 2*i - 2. Let g(x) = 2*h(x) + 5*q(x). Solve g(o) = 0 for o.
0, 1
Let a(h) = -h**3 - 7*h**2 - 3*h - 9. Let q be a(-7). Suppose -2*u = 2*u - q. Find g such that -g**2 + g + u*g**3 + 3*g**2 + g**2 + g**4 = 0.
-1, 0
Let z(r) be the second derivative of r**7/168 - r**6/30 + r**5/16 - r**4/24 - r. Factor z(q).
q**2*(q - 2)*(q - 1)**2/4
Let g(i) be the first derivative of 5*i**6/33 - 46*i**5/55 + 35*i**4/22 - 34*i**3/33 - 4*i**2/11 + 8*i/11 + 51. Let g(b) = 0. Calculate b.
-2/5, 1, 2
Let n(s) be the first derivative of -2 - 3/2*s**2 - 3*s**3 - 9/4*s**4 + 0*s - 3/5*s**5. Solve n(h) = 0.
-1, 0
Let f(g) = g**2 - 7*g - 4. Let c be f(8). Suppose 6*z + 3*o = 3*z - 6, 2*z - c*o = 20. Find m, given that -m**z - m + 6 - 6 = 0.
-1, 0
Factor 46*z + 16*z**4 + 10 + 95*z**3 + 10 + 5*z**5 + 125*z**2 + 34*z + 19*z**4.
5*(z + 1)**3*(z + 2)**2
Let c(m) be the third derivative of -m**6/60 + m**5/10 - 4*m**3/3 + 10*m**2. Factor c(a).
-2*(a - 2)**2*(a + 1)
Let i = -30 - -33. Let n(a) be the third derivative of a**2 + 0*a**i + 0*a**4 - 1/210*a**7 + 0*a + 0*a**5 + 1/120*a**6 + 0. Determine k so that n(k) = 0.
0, 1
Suppose -6 = 5*p - 16. Factor -15*c**2 + 7*c**3 + 4*c + p*c - 3*c**3 + 5*c**3.
3*c*(c - 1)*(3*c - 2)
Let t be ((-2)/(-4))/((-7)/70). Let k = t - -9. Suppose 0*a + 0 + 0*a**2 - 1/2*a**k + 0*a**3 - 1/2*a**5 = 0. Calculate a.
-1, 0
Let x(t) be the second derivative of -50*t**7/21 + 77*t**6/6 - 43*t**5/2 + 85*t**4/12 + 40*t**3/3 - 10*t**2 - 17*t. What is p in x(p) = 0?
-2/5, 1/4, 1, 2
Let l be 30/9 - 9/((-9)/(-2)). Factor -2/3*j**5 + 0*j**3 + 0 + 4/3*j**4 + 2/3*j - l*j**2.
-2*j*(j - 1)**3*(j + 1)/3
Let j(d) be the first derivative of -d**6/2 + 21*d**5/5 - 12*d**4 + 8*d**3 + 24*d**2 - 48*d + 10. Factor j(k).
-3*(k - 2)**4*(k + 1)
Suppose 0 = -0*j + 2*j. Let o be j + (2 - 0/1). Factor -4*q**o + 3*q**3 + 2*q**2 - 2*q**3.
q**2*(q - 2)
Let n be 2/5 + (-28)/245. Let b be 333/252 - (-3)/(-4). Factor b*u + 2/7*u**2 + n.
2*(u + 1)**2/7
Let v(m) be the third derivative of -m**9/24192 + m**7/672 + m**6/144 + m**5/30 - 6*m**2. Let x(c) be the third derivative of v(c). Factor x(k).
-5*(k - 2)*(k + 1)**2/2
Factor -1/3*n**3 + 7/3*n**2 - 7/3 + 1/3*n.
-(n - 7)*(n - 1)*(n + 1)/3
Let 2/7*h**2 - 6/7*h + 0 = 0. What is h?
0, 3
Let q(d) = 6*d - 4. Let b be q(1). Factor -1/4*l + 1/2 - 1/4*l**b.
-(l - 1)*(l + 2)/4
Let a be (1/3)/((-2)/(-8)). Suppose -a*z**2 + 0 + 4/3*z + 1/3*z**3 = 0. Calculate z.
0, 2
Let n(o) be the first derivative of -o**3 - 6*o**2 + 5. Factor n(i).
-3*i*(i + 4)
Let s(m) be the third derivative of -m**5/120 + m**3/12 + 6*m**2. Determine q, given that s(q) = 0.
-1, 1
Let b(c) be the first derivative of 0*c - 1/4*c**4 - 1/3*c**2 + 5/9*c**3 + 1/18*c**6 - 3 - 1/15*c**5. Solve b(s) = 0 for s.
-2, 0, 1
Let v(j) be the second derivative of -10/3*j**3 - 7/20*j**5 + 2*j**2 + 2*j + 23/12*j**4 + 0. Suppose v(h) = 0. What is h?
2/7, 1, 2
Let i(t) be the first derivative of -t**6/6 + 3*t**5/5 - 3*t**4/4 + t**3/3 + 5. What is r in i(r) = 0?
0, 1
Let c(a) be the first derivative of a**5/15 + 5*a**4/12 - 13*a**3/9 + 7*a**2/6 + 17. Factor c(k).
k*(k - 1)**2*(k + 7)/3
Let v(t) be the first derivative of 4*t**2 + 4*t - 5 + 4/3*t**3. Solve v(l) = 0.
-1
Let k(w) be the first derivative of w**3 - 3*w**2/2 + 4. Factor k(l).
3*l*(l - 1)
Factor -2/3 - 4/3*k - 2/3*k**2.
-2*(k + 1)**2/3
Let q(y) be the second derivative of -y**7/70 + y**6/60 + y**5/20 - y**4/12 + y**2/2 - y. Let o(r) be the first derivative of q(r). Factor o(x).
-x*(x - 1)*(x + 1)*(3*x - 2)
Factor 32/7*w**3 - 144/7*w**2 - 10/7 - 78/7*w.
2*(w - 5)*(4*w + 1)**2/7
Let j(w) be the third derivative of w**6/180 - w**5/30 - w**4/9 + 23*w**2. Determine z so that j(z) = 0.
-1, 0, 4
What is u in 4/11*u**2 + 0 - 2/11*u - 2/11*u**3 = 0?
0, 1
What is f in -6*f - 4 + 10 - 3 - 3*f**4 + 6*f**3 = 0?
-1, 1
Let l = 111 + -775/7. Let d be 3 - (2/2 - 1). Facto