Let p(v) be the second derivative of w(v). Factor p(u).
-u*(u - 1)*(u + 1)/2
Suppose -j = 3*w - 10, -2*w + 75 = 5*j + 64. Determine d, given that 9/4*d**2 - 3/4*d**w - 9/4*d + 3/4 = 0.
1
Let o(k) be the first derivative of k**8/8400 - k**7/4200 - 2*k**3 - 1. Let b(m) be the third derivative of o(m). Find n such that b(n) = 0.
0, 1
Let g(x) = x - 2. Let r be g(7). Suppose -q**3 - 9*q - r*q - 2*q + 8*q**2 = 0. Calculate q.
0, 4
Factor 8*f**2 - f - 3*f + 325*f**3 - 327*f**3 - 4*f.
-2*f*(f - 2)**2
Let z be -1*(-9)/(3 + 0). Suppose 3*o + 33 = 5*c + 11, -14 = -c + z*o. Factor -2/11*s**4 - 4/11*s**3 + 0 + 0*s - 2/11*s**c.
-2*s**2*(s + 1)**2/11
Suppose -8*m = 9*m + m. What is t in 0*t - 6/5*t**3 + m + 4/5*t**2 + 2/5*t**4 = 0?
0, 1, 2
Let s = 106 - 106. Let m(g) be the first derivative of -3 + s*g - 1/3*g**3 + 0*g**2. Factor m(a).
-a**2
Let t(l) = -l - 6. Let k be t(-12). Suppose k*i**3 + 5*i**3 + 0*i**5 - 4*i**3 - 2*i**2 + 2*i**5 - 7*i**4 = 0. Calculate i.
0, 1/2, 1, 2
Let n(b) = -9*b**2 - 11*b - 8. Let h(p) = 8*p**2 + 10*p + 7. Let o(a) = 6*h(a) + 5*n(a). Find r such that o(r) = 0.
-1, -2/3
Let v(d) = 5*d**2 + 75*d + 100. Let m(c) = c - 1. Let n(s) = 25*m(s) - v(s). Factor n(p).
-5*(p + 5)**2
Let t(c) = -c**3 + 8*c**2 + 5*c - 6. Let q(a) = -2*a**3 + 25*a**2 + 16*a - 18. Let m(d) = 2*q(d) - 7*t(d). Factor m(j).
3*(j - 2)*(j - 1)*(j + 1)
Let r be (6 - 2)*(-2)/(-4). Suppose -r*q = -q - 2. Factor -2*w**2 + 0*w**q + w - 3*w + 0*w**2.
-2*w*(w + 1)
Let c(w) be the third derivative of w**6/72 + w**5/3 + 10*w**4/3 + 160*w**3/9 - 7*w**2. Factor c(k).
5*(k + 4)**3/3
Suppose -3*z + 4*d = -23, 11 = 3*z + 2*d - 0. Let g be z/(-10) - (-2 - -1). What is p in 0*p + 0*p**2 - g*p**3 + 0 = 0?
0
Let d(g) = 13*g**5 - 6*g**4 - 12*g**3 + 7*g**2. Let b(o) = -6*o**5 + 3*o**4 + 6*o**3 - 3*o**2. Let k(a) = 7*b(a) + 3*d(a). Factor k(u).
-3*u**3*(u - 2)*(u + 1)
Let v(a) be the third derivative of 9/11*a**3 - 6*a**2 + 0*a + 0 + 3/110*a**5 + 1/660*a**6 + 9/44*a**4. Factor v(k).
2*(k + 3)**3/11
Let o(t) = -t**2 + 19*t - 13. Let c(f) = -f**2 + 39*f - 25. Let x(w) = -3*c(w) + 7*o(w). Factor x(h).
-4*(h - 2)**2
Let x = 244 + -2923/12. Let k(w) be the second derivative of x*w**3 - 1/2*w**2 + 0 + 7/24*w**4 - 3*w. Find m such that k(m) = 0.
-1, 2/7
Let c be (-38)/(-12) - 15/(5 - 0). Let a(y) be the second derivative of -1/120*y**6 + 0*y**2 + c*y**3 - y + 0*y**4 + 0 - 3/80*y**5. Let a(m) = 0. What is m?
-2, 0, 1
Let q(r) be the third derivative of r**5/30 + r**4/12 - 2*r**3/3 - 11*r**2. Factor q(d).
2*(d - 1)*(d + 2)
Factor 4/7*x**2 + 0 + 2/7*x**3 - 6/7*x.
2*x*(x - 1)*(x + 3)/7
Let h(j) be the third derivative of j**5/60 + j**4/24 - j**3/3 + 3*j**2. Solve h(q) = 0 for q.
-2, 1
Let o(c) be the first derivative of c**4/2 - 2*c**3 + 2*c**2 + 2. What is l in o(l) = 0?
0, 1, 2
Let j = 12 - 9. Suppose -j*i = -i. Factor 0 + i*w**4 + 0*w**2 - 2/3*w + 4/3*w**3 - 2/3*w**5.
-2*w*(w - 1)**2*(w + 1)**2/3
Let y(v) be the first derivative of 9*v**5/35 - 15*v**4/28 - 11*v**3/21 + 11*v**2/14 - 2*v/7 + 1. Factor y(t).
(t - 2)*(t + 1)*(3*t - 1)**2/7
Let a = 2/47 + 31/376. Let u(v) be the first derivative of -1/16*v**4 + 1/4*v**3 + 2 - 1/4*v - 1/10*v**5 + a*v**2. What is r in u(r) = 0?
-1, 1/2, 1
Let p(y) be the second derivative of 7*y**4/4 + 75*y**3/2 - 33*y**2 + 7*y - 4. Let p(d) = 0. Calculate d.
-11, 2/7
Let o(q) be the first derivative of 1/3*q**3 + 0*q**2 - 2 + 0*q. Find r, given that o(r) = 0.
0
Let f be (13 + -3)*1/2. Let -3*a + a**2 + 0*a + f*a + 0*a = 0. Calculate a.
-2, 0
Let d(w) be the first derivative of -w**4/2 + 4*w**3/3 + 3*w**2 + 14. Suppose d(x) = 0. Calculate x.
-1, 0, 3
Let d(b) be the first derivative of -b**4/5 + 2*b**2/5 - 3. Let d(s) = 0. Calculate s.
-1, 0, 1
Let u(r) be the second derivative of 1/6*r**4 + 0 + r**2 - 5/6*r**3 + r. Factor u(t).
(t - 2)*(2*t - 1)
Let u = 43 - 41. Determine z so that 10/3*z**4 + 0*z**u + 0*z + 8/3*z**5 + 0 + 2/3*z**3 = 0.
-1, -1/4, 0
Let z(p) be the first derivative of -2/15*p**3 + 1/5*p**2 + 2 + 0*p. Suppose z(k) = 0. Calculate k.
0, 1
Let c(v) be the third derivative of 0*v**4 + 0 + 0*v - 1/840*v**7 + 1/480*v**6 + 0*v**3 + 1/240*v**5 - 1/1344*v**8 - v**2. Factor c(b).
-b**2*(b - 1)*(b + 1)**2/4
Suppose 0*a**5 - 12*a**3 + 8*a**4 + 8*a**2 - 2*a**5 + a - 3*a = 0. Calculate a.
0, 1
Let x(g) be the third derivative of 0*g**4 + 0*g + 0 - 1/50*g**6 - 1/560*g**8 + 0*g**3 + 2/175*g**7 + 6*g**2 + 0*g**5. Find d, given that x(d) = 0.
0, 2
Let p(g) = g**2 - 14*g + 18. Let x be p(13). Let s be (-8)/6*(-12)/x. Let 6/5*n**3 - s*n + 2/5*n**2 + 8/5 = 0. Calculate n.
-2, 2/3, 1
Let d be (-16)/(-28) + 4/(-7). Let h(p) be the third derivative of -1/840*p**7 + d*p - 2*p**2 + 0*p**5 + 0*p**4 + 0 + 0*p**3 + 1/480*p**6. Factor h(a).
-a**3*(a - 1)/4
Suppose a - 5*y = -38, a + 4*y - 2*y = -3. Let f = a - -15. Factor -f*n + 2/3*n**2 + 4/3.
2*(n - 2)*(n - 1)/3
Let z(b) = 3*b + 18. Let h be z(-6). Factor 0*o + h - 2/5*o**3 + 2/5*o**2 + 2/5*o**5 - 2/5*o**4.
2*o**2*(o - 1)**2*(o + 1)/5
Let i(o) be the first derivative of o**5/5 + o**4/4 - o**3 - 5*o**2/2 - 2*o + 4. Factor i(t).
(t - 2)*(t + 1)**3
Let v be ((-11)/((-77)/(-4)))/(36/(-42)). Factor -1/3*z + v*z**2 - 2/3 + 1/3*z**3.
(z - 1)*(z + 1)*(z + 2)/3
Let w(v) be the first derivative of -2*v**6/3 + 4*v**5/5 + 3*v**4 - 4*v**3/3 - 4*v**2 - 12. Suppose w(t) = 0. What is t?
-1, 0, 1, 2
Let l(m) be the first derivative of -49*m**4/22 - 70*m**3/11 - 72*m**2/11 - 32*m/11 - 21. Factor l(t).
-2*(t + 1)*(7*t + 4)**2/11
Let d(l) = -2*l**2 + 6*l - 8. Suppose 2*n - 1 = n. Let r(k) = -3*k - 1. Let q be r(n). Let g(u) = -3*u**2 + 7*u - 7. Let y(o) = q*g(o) + 3*d(o). Factor y(i).
2*(i - 1)*(3*i - 2)
Let r(n) be the first derivative of -n**4/4 + n**3/2 + n**2/2 - 3*n/2 + 7. Factor r(k).
-(k - 1)*(k + 1)*(2*k - 3)/2
Factor -4/5*r**4 + 0*r + 12/5*r**3 + 0*r**2 + 0.
-4*r**3*(r - 3)/5
Suppose 0 = -2*y - g - 3*g - 12, -y + g = -6. Suppose 0 + 0*w**y - 10/3*w**5 - 14/3*w**4 - 4/3*w**3 + 0*w = 0. Calculate w.
-1, -2/5, 0
Let t(c) = -2*c. Let i be t(-2). Let -3*b**3 + 4*b**3 + i*b - 3*b**2 - b**2 = 0. What is b?
0, 2
Let g(u) = 3*u**3 - u**2 + 2*u - 1. Let s be g(1). Let z(b) = b**3 + 4*b**2 + 2*b. Let o be z(-2). Factor 0*l**o - 5*l**4 + s*l**4.
-2*l**4
Suppose -t - 3*j - 9 + 0 = 0, t = -2*j - 6. Factor c**3 + t*c**2 - c + c**2 - 1 + 0*c**2.
(c - 1)*(c + 1)**2
Let h(f) be the first derivative of f**7/42 + f**6/30 - f**5/20 - f**4/12 + f + 1. Let t(n) be the first derivative of h(n). Factor t(i).
i**2*(i - 1)*(i + 1)**2
Let y be (2 - 0)*3/2. Let i be y + 3/42*-38. Determine h so that 0 + 2/7*h**2 - i*h = 0.
0, 1
Let z be 3 + (-1 - 3) - -4. Suppose 4*l = -4*i + 28, 4*l - 4*i + z*i = 8. Suppose 0*r**2 + 0*r + 0 - 2/3*r**l = 0. Calculate r.
0
Let a(d) = -3*d**2 + 2*d - 2. Let t be a(2). Let u(q) = q + 14. Let r be u(t). Factor -i**5 - 4*i + 5*i + 4*i**r - 2*i**2 - 2*i**4.
-i*(i - 1)**3*(i + 1)
Let s = 275 + -119. Let p = 472/3 - s. Factor p*m**3 + 0*m + 0 + 2/3*m**4 + 0*m**2.
2*m**3*(m + 2)/3
Factor -4*a**2 + a - 4*a + 1 + 6*a + 0*a.
-(a - 1)*(4*a + 1)
Suppose 3*w - 2*o = o + 27, 0 = 2*w + 4*o + 12. Suppose 5*i**2 - w*i + 2*i - 3*i**2 - i**2 = 0. What is i?
0, 2
Let m(k) be the first derivative of -k**6/15 + 8*k**5/25 - 2*k**4/5 + 14. Factor m(i).
-2*i**3*(i - 2)**2/5
Let r be 10/14 - ((-24)/42 - -1). Factor -2/7*p**4 - r + 4/7*p**2 + 0*p**3 + 0*p.
-2*(p - 1)**2*(p + 1)**2/7
Let o(u) be the first derivative of 2*u**3/21 - 2*u**2/7 + 2*u/7 + 2. What is v in o(v) = 0?
1
Let k(m) be the second derivative of -2*m**7/21 - 4*m**6/15 - m**5/5 + 6*m. Let k(g) = 0. Calculate g.
-1, 0
Let q be 12/(-8)*2*-1. Find j such that 0*j**2 + 2*j**3 + 7*j**3 + q*j**4 + 6*j**2 + 0*j**3 = 0.
-2, -1, 0
Suppose 3*k**3 + 2 - 5 - 9*k + 1 - 4 = 0. What is k?
-1, 2
Factor -2/5*c**3 - 4/5*c + 0 + 6/5*c**2.
-2*c*(c - 2)*(c - 1)/5
Let z(c) = c + 5. Let g be z(-6). Let u be (3/(-6))/(g*2). Factor 1/2*o + 1/4*o**2 + u.
(o + 1)**2/4
Factor 100/9 - 28/9*r**4 + 4/9*r**5 + 184/9*r**2 + 260/9*r - 8/9*r**3.
4*(r - 5)**2*(r + 1)**3/9
Let i = -16/109 - -141/218. Find u such that 3/2*u - 1 - i*u**2 = 0.
1, 2
Suppose 0 = 2*c - 3 - 5. Solve h**c + 3*h**5 - 8*h**2 + 2*h**2 + 5*h**4 - 3*h = 0 for h.
-1, 0, 1
Factor 4/7*p + 1/7*p**3 + 4/7*p**2 + 0.
p*(p + 2)**2/7
Suppose 0 = -0*z - 2*z - 4*i, -z =