(-9). Let q(w) be the first derivative of -2 - 8/5*w**5 - 3/2*w**4 + 2/3*w**3 + 0*w**2 + t*w. Let q(m) = 0. What is m?
-1, 0, 1/4
Let m(v) be the first derivative of -v**4/6 + 5*v**3/3 - 4*v**2 - v + 6. Let i(r) be the first derivative of m(r). Factor i(u).
-2*(u - 4)*(u - 1)
Suppose -8 = h - 5*h. Factor -6*r + 4*r**2 + 0*r - 3*r**h + 9.
(r - 3)**2
Let l(f) be the third derivative of -f**6/480 - f**5/40 - 11*f**4/96 - f**3/4 - 6*f**2. Factor l(z).
-(z + 1)*(z + 2)*(z + 3)/4
Let f(d) be the third derivative of 1/112*d**8 + 0*d - 1/24*d**4 - 1/60*d**6 + 1/6*d**3 + 5*d**2 - 1/10*d**5 + 1/42*d**7 + 0. Find l, given that f(l) = 0.
-1, 1/3, 1
Let f(l) = -33*l**2 + 24*l - 3. Let y(j) = -j**2 + j. Let b(o) = o**2 + 7*o + 6. Let q be b(-7). Let z(a) = q*y(a) - f(a). Factor z(s).
3*(3*s - 1)**2
Let w(z) be the second derivative of -1/42*z**7 - 1/30*z**6 + 1/108*z**4 + 0*z**3 + 0*z**2 + 8*z + 1/180*z**5 + 0. Solve w(f) = 0 for f.
-1, -1/3, 0, 1/3
Suppose -7 - 18 = -5*i. Let x be (-23)/(-7) - 2/7. Let -26*y**4 + 12*y**3 + 18*y**3 - 14*y**2 + x*y**i + 2*y + 5*y**5 = 0. Calculate y.
0, 1/4, 1
Let n(d) = 4*d**3 - 1. Let z be n(1). Let y be 32/(-12)*z/(-2). Factor -y*j + 3*j + 3*j - 2 + 4*j + 2*j**3 - 6*j**2.
2*(j - 1)**3
Let v(c) be the third derivative of -1/21*c**3 + 0 + 0*c + 1/42*c**4 + c**2 + 1/210*c**6 - 1/294*c**8 + 4/105*c**5 - 1/105*c**7. Let v(z) = 0. Calculate z.
-1, 1/4, 1
Suppose 0*n - 11/5*n**2 + 4/5 + 7/5*n**4 - 3/5*n**3 + 3/5*n**5 = 0. What is n?
-2, -1, 2/3, 1
Let w(b) be the second derivative of -b**6/60 - b**5/20 - b**4/24 - 5*b. Find m such that w(m) = 0.
-1, 0
Let j(w) = 3*w - 9 + 0*w + 0*w**2 - 3*w**2. Let l(o) = o**2 - o + 4. Let s(c) = 4*j(c) + 9*l(c). Factor s(q).
-3*q*(q - 1)
Let t(v) be the second derivative of v**4/28 + 5*v**3/14 - v - 40. Factor t(m).
3*m*(m + 5)/7
Factor 11/4*l + 3/2 + l**2 - 1/4*l**3.
-(l - 6)*(l + 1)**2/4
Let g be (-1)/(-3 - (-32)/12). Suppose -11 = g*j - 17. Determine t, given that 0 + 3*t**j - 3*t - 3/4*t**3 = 0.
0, 2
Suppose 5*k = -3*f + 22, -16 = 4*k - 5*f - 4. Let y be (-6)/k + 20/6. Let -y - 1/3*h**2 - 2/3*h = 0. What is h?
-1
Factor 0*o - 27/4*o**3 + 0*o**2 + 3/4*o**4 + 0.
3*o**3*(o - 9)/4
Let p(k) be the third derivative of k**7/42 - k**6/6 + k**5/4 + 5*k**4/6 - 10*k**3/3 - 19*k**2. Let p(i) = 0. What is i?
-1, 1, 2
Suppose -2*r = -6*r + 4*z + 4, -z = -5. Suppose 3*q - r = -0. Suppose -6/7*u**q - 2/7 - 2/7*u**3 - 6/7*u = 0. What is u?
-1
Let r(h) = h**4 + h**3 + 7*h**2 + 7*h. Let g(z) = 3*z**2 + 3*z. Let y(s) = 7*g(s) - 3*r(s). Find b such that y(b) = 0.
-1, 0
Suppose -246*x**2 + 124*x**2 + 2*x - 4*x + 124*x**2 = 0. Calculate x.
0, 1
Suppose 5*s + 0*s = -15. Let g be 196/36 + s - 2. Find a, given that 0 + 0*a + 0*a**3 + 0*a**2 - 2/9*a**4 + g*a**5 = 0.
0, 1/2
Let i(c) = -57*c**4 + 15*c**3 - 9*c**2 - 48*c - 33. Let a(n) = -7*n**4 + 2*n**3 - n**2 - 6*n - 4. Let x(j) = 33*a(j) - 4*i(j). Let x(q) = 0. What is q?
-1, 0, 1, 2
Let s = 5/209 + 3/19. Let u(j) be the first derivative of -4/11*j**2 + 3 - 2/11*j**3 - s*j. Factor u(g).
-2*(g + 1)*(3*g + 1)/11
Let s(u) be the first derivative of -4/3*u**3 + u**2 + 6 + 1/2*u**4 + 0*u. Determine v, given that s(v) = 0.
0, 1
Let x(v) = -63*v**3 + 18*v**2 + 52*v - 29. Let o = -25 - -14. Let j(s) = -21*s**3 + 6*s**2 + 17*s - 10. Let n(t) = o*j(t) + 4*x(t). Let n(p) = 0. What is p?
-1, 2/7, 1
Let i(u) be the first derivative of -u**4/16 + 5*u**3/12 + 3*u**2/4 + 26. Determine l so that i(l) = 0.
-1, 0, 6
Suppose 25 - 31 = -2*v. Let j(d) be the second derivative of 1/60*d**5 - d + 1/36*d**4 - 1/18*d**v + 0 - 1/6*d**2. Factor j(l).
(l - 1)*(l + 1)**2/3
Suppose 2/17*y**5 - 4/17*y + 6/17*y**4 + 0 - 6/17*y**2 + 2/17*y**3 = 0. What is y?
-2, -1, 0, 1
Let q be (-5)/((-10)/12) + (-144)/36. Let r(h) be the first derivative of 4 - 4/3*h**3 + 0*h + 1/2*h**q. Let r(d) = 0. What is d?
0, 1/4
Let w(z) = z**2. Let c(k) = -47*k**2 - 40*k - 8. Let x(o) = c(o) - 3*w(o). Factor x(r).
-2*(5*r + 2)**2
Determine w, given that -1/2*w**3 - 2*w**2 + 0 - 2*w = 0.
-2, 0
Let r(q) = 2*q - 6. Let y be r(6). Factor -2*b**4 - 25*b - 27*b**2 - b**4 + 6*b - y - 15*b**3 - 2*b.
-3*(b + 1)**3*(b + 2)
Let d(w) be the second derivative of -w + 0*w**2 - 1/12*w**3 - 1/48*w**4 + 0. Factor d(b).
-b*(b + 2)/4
Let l be 2/5 - (-264)/(-710). Let c = 79/284 - l. Suppose 1/4*u**4 - 1/2*u**2 + c + 0*u + 0*u**3 = 0. Calculate u.
-1, 1
Let z be 14/4*(-32)/(-56). Factor 6/7*f + 2/7 + 4/7*f**z.
2*(f + 1)*(2*f + 1)/7
Factor 0*h - 11*h**2 + 12*h**2 + 0*h + 3*h.
h*(h + 3)
Let t be 1 + (-3)/3 - -3. Factor -3*m**3 + 2*m**2 + 6*m**t - m**2 + 2*m**2 - 6*m.
3*m*(m - 1)*(m + 2)
Let j(h) be the first derivative of h**7/21 - 2*h**6/15 + h**4/3 - h**3/3 + 2*h - 1. Let k(x) be the first derivative of j(x). Factor k(m).
2*m*(m - 1)**3*(m + 1)
Let g(i) = -i**3 - 4*i**2 - i. Let m be g(-4). Let h be m/(-1)*(1 + -2). Factor -1/5*a**5 - 1/5*a + 2/5*a**3 + 0 + 0*a**2 + 0*a**h.
-a*(a - 1)**2*(a + 1)**2/5
Determine o so that 4*o**5 + 0 + 68/5*o**4 + 0*o + 64/5*o**3 + 16/5*o**2 = 0.
-2, -1, -2/5, 0
Let n = -472 - -5200/11. Find p, given that 8/11*p + 2/11*p**2 + n = 0.
-2
Let m(j) be the second derivative of j**6/6 + j**5 + 5*j**4/4 - 30*j. Let m(k) = 0. What is k?
-3, -1, 0
Let j(p) be the third derivative of p**8/20160 + p**7/2520 + p**6/720 - p**5/20 - p**2. Let c(g) be the third derivative of j(g). Factor c(z).
(z + 1)**2
Let f be 22/6 + (-1)/(-3). Let c = 14 + -10. Suppose 20/3*r**3 + f*r + 8*r**2 + 2*r**c + 2/3 = 0. What is r?
-1, -1/3
Let h = 106 + -524/5. Factor 2/5*g**4 + 8/5*g**3 - 8/5 - 8/5*g + h*g**2.
2*(g - 1)*(g + 1)*(g + 2)**2/5
Let o = -2/229 - -468/1145. Let -o*k**2 - 2/5*k + 4/5 = 0. What is k?
-2, 1
Suppose 5 = 5*s + c, 2*s = -4*c + 20 - 0. What is k in 6/5*k**5 + s*k - 8/5*k**4 + 0 - 2/5*k**3 + 4/5*k**2 = 0?
-2/3, 0, 1
Let u(t) be the third derivative of 0*t**6 + 1/350*t**7 + 0*t**3 + 0*t + 0*t**4 + 0 - 2*t**2 + 0*t**5. Factor u(s).
3*s**4/5
Let l(o) be the second derivative of -1/15*o**3 - 1/30*o**4 - 9*o + 0*o**2 + 0. Factor l(d).
-2*d*(d + 1)/5
Let g = 14 - 12. Factor 8*b**2 - 8*b - 16*b**g - 2*b**3 + 0*b**3.
-2*b*(b + 2)**2
Let r be 12 + (1 - 0) + 0. Let g be 4/(-18) - r/(-18). Factor 1/2*h**2 + h + g.
(h + 1)**2/2
Let z be 3/12 + 1/(-4). Let c = z - -3. What is f in -4*f**3 + 6*f**c - 2*f**2 - 4*f**3 = 0?
-1, 0
Solve 0 - 9*m**2 + 14*m - 11*m + 9 - 3*m**3 = 0.
-3, -1, 1
Factor 3/7*d**4 + 0*d - 2/7*d**3 + 0*d**2 + 0.
d**3*(3*d - 2)/7
Let u(g) be the first derivative of 2/9*g**3 - 1 + 0*g + 2/3*g**2. Solve u(c) = 0 for c.
-2, 0
Suppose -4*o + 6 + 14 = 0. Find m such that -6*m**3 + 0*m**3 - 21*m + 3*m**o + 24*m = 0.
-1, 0, 1
Let o be (-5)/(-10)*8/1. Suppose 0 = -h + 3*h - 2*y, -o*h - 2*y = -12. Suppose -1/2*n**h + 0 + 1/2*n = 0. Calculate n.
0, 1
Factor 1/3*u**4 + 1/3 + 0*u - 2/3*u**2 + 0*u**3.
(u - 1)**2*(u + 1)**2/3
Let f(x) = -6*x**2 + 10. Let a(w) = 7*w**2 + w - 11. Let m(c) = 4*a(c) + 5*f(c). Solve m(h) = 0 for h.
-1, 3
Let h(j) be the second derivative of -1/18*j**4 - 1/30*j**5 + 0 + 1/45*j**6 + 0*j**2 + 1/9*j**3 + 2*j. Factor h(c).
2*c*(c - 1)**2*(c + 1)/3
Let z(g) be the third derivative of g**7/1680 - g**6/192 + 3*g**5/160 - 7*g**4/192 + g**3/24 - 13*g**2. Solve z(s) = 0.
1, 2
Suppose -20*a + 5*a = 0. Suppose 0*n + a + 0*n**2 + 2/9*n**3 - 2/9*n**4 = 0. What is n?
0, 1
Let d(u) be the first derivative of -6*u**5/5 + 3*u**4/4 + u**3 - 1. Factor d(c).
-3*c**2*(c - 1)*(2*c + 1)
Let u be (-14)/(-4) - 1/2. Let -3*k**u + 7*k**3 - 2*k**4 - 2*k**2 - 4*k + 4*k = 0. Calculate k.
0, 1
Let o(b) be the third derivative of -b**6/120 + b**4/24 - b**2. Let s(k) = 6*k**3 - 5*k. Let h(x) = -5*o(x) - s(x). Factor h(c).
-c**3
Let u = -8 - -6. Let t(r) = 7*r**2 - 3*r - 2. Let d(c) = 29*c**2 + 5*c - 3 - 10*c - 7*c - 5. Let l(j) = u*d(j) + 9*t(j). What is z in l(z) = 0?
-2/5, 1
Let t(d) be the first derivative of d**6/21 - 2*d**5/35 - d**4/7 + 4*d**3/21 + d**2/7 - 2*d/7 + 8. Factor t(p).
2*(p - 1)**3*(p + 1)**2/7
Let r(p) be the third derivative of p**5/180 + 5*p**4/36 + 25*p**3/18 - 5*p**2. Factor r(s).
(s + 5)**2/3
Solve 4*i**4 + 8*i**3 - 961*i**2 + 961*i**2 = 0 for i.
-2, 0
Let w(t) = 64*t**3 + 180*t**2 + 120*t - 94. Let d(j) = 13*j**3 + 36*j**2 + 24*j - 19. Let f(b) = -14*d(b) + 3*w(b). Find c, given that f(c) = 0.
-2, 2/5
Let t(n) b