-6
Let a(s) be the third derivative of s**8/1008 - s**7/315 + 29*s**2. Factor a(g).
g**4*(g - 2)/3
Factor -16*q**2 + 15*q + 2*q + 4*q**4 - 4*q**3 - q.
4*q*(q - 2)*(q - 1)*(q + 2)
Let x(t) be the third derivative of t**6/36 - t**5/20 - t**4/6 + t**3/3 + 2*t**2. Let q(g) be the first derivative of x(g). Suppose q(z) = 0. Calculate z.
-2/5, 1
Let m(g) = 3*g**3 - 11*g**2 - 11*g - 9. Let a(h) = h**3 - h**2 + h. Let x(r) = -4*a(r) + m(r). Factor x(z).
-(z + 1)*(z + 3)**2
Let u be 7*(3 + -3 + -1). Let y = 9 + u. Factor 1/2 + 1/4*g**3 + g**y + 5/4*g.
(g + 1)**2*(g + 2)/4
Factor -13 - 1 - 60*r**2 + 5 - 7 + 52*r + 28*r**3 - 4*r**4.
-4*(r - 4)*(r - 1)**3
Let f(w) = -w**2 - 3*w - 2. Let h be f(-1). Let u = -20/21 + 9/7. Solve -1/3*k**4 + 0*k + h + 2/3*k**3 + u*k**2 - 2/3*k**5 = 0.
-1, -1/2, 0, 1
Let a(p) be the second derivative of p**5/50 + p**4/15 + p**3/15 - p. Factor a(x).
2*x*(x + 1)**2/5
Solve -m - 1/3*m**3 - 1/3 - m**2 = 0.
-1
Let z(v) = -v**3 - 12*v**2 - 8*v + 17. Let r be z(-11). Let w(f) = -f**2 - 17*f - 14. Let d be w(r). Factor -1/4*o**3 - 1/4*o**4 + 1/4*o**d + 1/4*o + 0.
-o*(o - 1)*(o + 1)**2/4
Let h(x) be the second derivative of -1/70*x**5 + 1/21*x**3 - 1/14*x**4 + 0 + 2/7*x**2 + 1/105*x**6 + x. Solve h(k) = 0.
-1, 1, 2
Factor -18/13 + 6/13*y**4 - 2/13*y**5 - 20/13*y**2 + 12/13*y**3 - 42/13*y.
-2*(y - 3)**2*(y + 1)**3/13
Let m(z) be the first derivative of z**6/14 - 3*z**5/5 + 45*z**4/28 - 9*z**3/7 - 20. Factor m(d).
3*d**2*(d - 3)**2*(d - 1)/7
Let c be (-1 + (-7)/(-6))/2. Let t(z) be the second derivative of -1/8*z**4 + z + 0*z**2 + 0 - 1/20*z**5 - c*z**3. Factor t(k).
-k*(k + 1)*(2*k + 1)/2
Let v(p) be the second derivative of -p**5/20 + 2*p**3/3 + 6*p. What is x in v(x) = 0?
-2, 0, 2
Solve -64*d**3 - 768*d + d**4 + 116*d**2 + 377 + 199 + 236*d**2 + 3*d**4 = 0.
2, 6
Let a be (-160)/24 + (-4)/(-6). Let i be (6/(-75))/(a/30). Determine r, given that -2/5*r**2 - i*r + 2/5 + 2/5*r**3 = 0.
-1, 1
Let a(c) be the first derivative of c**3 + 4*c**2 - 1 + c - 4*c**2. Let p(f) = 2*f**2 + 1. Let o(t) = 3*a(t) - 4*p(t). Solve o(u) = 0 for u.
-1, 1
Find x, given that 1/5*x**4 + 2/5*x - 2/5*x**3 - 1/5 + 0*x**2 = 0.
-1, 1
Let s(k) = -60*k**5 + 45*k**4 + 39*k**3 - 24*k - 24. Let p(q) = -3 - 5*q + 3*q**3 + 5*q**3 - 12*q**5 - 2 + 9*q**4. Let j(m) = 24*p(m) - 5*s(m). Factor j(f).
3*f**3*(f - 1)*(4*f + 1)
Factor 4/5 - 4/5*t + 1/5*t**2.
(t - 2)**2/5
Suppose 0*n + 16 = 2*n. Suppose -4*t - n = 2*y, 20 = -4*t + 4*y - 9*y. Factor t - 2*u**3 + 0*u - 2/3*u**5 - 2/3*u**2 - 2*u**4.
-2*u**2*(u + 1)**3/3
Let u = -8 - -5. Let p = 5 + u. Find r, given that 0*r**3 - 3*r - p + 3*r**3 + 2 = 0.
-1, 0, 1
Let y(h) be the second derivative of h**7/70 - 7*h**6/50 + 57*h**5/100 - 5*h**4/4 + 8*h**3/5 - 6*h**2/5 + 2*h - 4. Let y(b) = 0. What is b?
1, 2
Let a = -6 - -21. Factor 22*q + 12 + 2*q + a*q**2 + 21*q**3 - 18*q**3.
3*(q + 1)*(q + 2)**2
Let d(s) be the third derivative of s**7/280 + s**6/420 + s**3/6 + s**2. Let t(u) be the first derivative of d(u). What is h in t(h) = 0?
-2/7, 0
Let x be 5/14 - (-2)/28*2. Let x*z**3 - 1/2*z**2 + 0*z + 0 = 0. Calculate z.
0, 1
Factor -1/5*j**2 - 3/5 + 4/5*j.
-(j - 3)*(j - 1)/5
Let t(m) = m**2 - 2*m - 1. Let h be 2/(-8)*6*-2. Let k be t(h). Let 9*p - 15*p + 2*p**k - 5*p**2 = 0. What is p?
-2, 0
Let g(k) be the first derivative of -3/11*k**2 + 4/55*k**5 - 8/33*k**3 - 1/11*k**6 + 3/11*k**4 + 3 + 4/11*k. What is r in g(r) = 0?
-1, 2/3, 1
Let d(b) be the first derivative of -b**5/10 - b**4/8 + 8. Factor d(x).
-x**3*(x + 1)/2
Let f(a) be the third derivative of a**5/180 + a**4/18 + a**3/6 + 17*a**2. Factor f(i).
(i + 1)*(i + 3)/3
Let i(p) be the third derivative of p**5/20 - p**4/4 + p**3/2 + 6*p**2. Factor i(b).
3*(b - 1)**2
Let t(r) = 2*r**2 - 2*r + 2. Let x(n) = n**2 + 1. Let q(b) = 5*t(b) - 15*x(b). Find c such that q(c) = 0.
-1
Let d(s) be the second derivative of -s**5/160 + s**4/32 + 22*s. Let d(g) = 0. Calculate g.
0, 3
Let d = 112/305 + 2/61. Factor 0 - 2/5*b**2 + d*b.
-2*b*(b - 1)/5
Let y be 3*(-2)/(-2) + 16/(-6). Let t(u) be the first derivative of y*u**3 + 1/2*u**2 + 0*u - 1. Suppose t(n) = 0. Calculate n.
-1, 0
Let c(u) be the second derivative of u**5/50 + u**4/15 + u**3/15 - u. Factor c(z).
2*z*(z + 1)**2/5
Let g be 4/(-6)*-3 + -2. Let x(o) be the second derivative of 1/60*o**5 + 0*o**2 + g - 2*o + 0*o**3 + 1/45*o**6 + 0*o**4 + 1/126*o**7. Factor x(k).
k**3*(k + 1)**2/3
Suppose -11*f = -5*f - 12. Factor 2/3*n + 2/3 + 1/6*n**f.
(n + 2)**2/6
Let o = 69/4 - 17. Factor 1/2*c + 1/4 + o*c**2.
(c + 1)**2/4
Let t(z) be the second derivative of -2/5*z**5 + 0 - 5*z - 4/3*z**3 - z**2 - z**4 - 1/15*z**6. Factor t(q).
-2*(q + 1)**4
Let w(x) = 9*x**2 + 11*x. Let a(m) = 4*m**2 + 5*m. Let s(n) = -7*a(n) + 3*w(n). Factor s(c).
-c*(c + 2)
Let w = -4 + 6. Let y(q) be the third derivative of 0 - w*q**2 - 1/15*q**3 + 0*q - 1/30*q**4 - 1/150*q**5. Factor y(j).
-2*(j + 1)**2/5
Let i = 61/52 - 12/13. Let q(t) be the first derivative of -1/16*t**4 - 1/12*t**3 + 1 + 0*t + i*t**2. Find r, given that q(r) = 0.
-2, 0, 1
Let h = -72 - -506/7. Factor 2/7*a + h - 4/7*a**2 + 2/7*a**4 - 4/7*a**3 + 2/7*a**5.
2*(a - 1)**2*(a + 1)**3/7
Let v(d) = d**3 - 11. Let t be v(0). Let w = 41 + t. Factor 3 - 1 + 8*f**4 + 16*f - 2*f + w*f**2 + 10*f**3 + 16*f**3.
2*(f + 1)**3*(4*f + 1)
Let w(y) be the first derivative of y**6/360 + y**5/60 + y**4/24 + y**3/18 - 9*y**2/2 + 5. Let u(q) be the second derivative of w(q). Solve u(m) = 0 for m.
-1
Factor 3*g - 9 - 3*g**2 - 7 + 9*g + 4.
-3*(g - 2)**2
Suppose 0 - 4/5*p**2 + 1/5*p**4 + 0*p + 3/5*p**3 = 0. Calculate p.
-4, 0, 1
Let q(r) = -12*r**4 + 13*r**3 + 47*r**2 + 11*r + 11. Let a(j) = -4*j**4 + 4*j**3 + 16*j**2 + 4*j + 4. Let l(o) = -11*a(o) + 4*q(o). Let l(s) = 0. Calculate s.
-1, 0, 3
Let k = -8 + 14. Suppose -5*g = -k*g + 98. Factor 16 + 110*t + 436*t**4 - 691*t**4 + 420*t**2 + 42*t - 431*t**4 + g*t**3.
-2*(t - 1)*(7*t + 2)**3
Suppose 3*u = 2*j, 3*u - 8 = -u. Suppose -5*z = -j*z. Factor 4/3*m**2 + 2/3*m**3 + 0 + z*m.
2*m**2*(m + 2)/3
Let k(s) be the third derivative of s**8/1680 - s**7/840 - s**3/6 + 2*s**2. Let p(h) be the first derivative of k(h). Find u, given that p(u) = 0.
0, 1
Let c(q) be the second derivative of q**6/10 + 3*q**5/20 - 3*q**4/4 - 5*q**3/2 - 3*q**2 + 4*q. Factor c(z).
3*(z - 2)*(z + 1)**3
Let g = -2459/6 - -410. Find s, given that -g*s + 1/6*s**2 + 0 = 0.
0, 1
Let r(q) be the second derivative of q**4/6 + 4*q**3/3 + 3*q**2 - 47*q. Factor r(i).
2*(i + 1)*(i + 3)
Let y(l) = -l - 4. Let z be y(-5). Suppose t - z - 2 = 0. Factor v**2 - 2*v**2 - 2*v**4 + t*v**2.
-2*v**2*(v - 1)*(v + 1)
Let c(l) be the first derivative of l**5/10 - l**3 - 2*l**2 + 4*l + 2. Let k(d) be the first derivative of c(d). Factor k(r).
2*(r - 2)*(r + 1)**2
Let p = -125/16 + 16883/2160. Let h(z) be the third derivative of 0 + 1/36*z**4 + 0*z - p*z**5 - 2/27*z**3 - z**2. What is o in h(o) = 0?
1, 2
Let q be (10/100)/((-5)/(-2) - 2). Factor -2/5 + q*w - 1/5*w**3 + 2/5*w**2.
-(w - 2)*(w - 1)*(w + 1)/5
Let a(u) be the second derivative of 0*u**2 + 0 + 1/3*u**3 - 6*u - 7/12*u**4 + 13/30*u**6 + 2/7*u**7 - 2/5*u**5. Suppose a(t) = 0. What is t?
-1, 0, 1/4, 2/3
Let j(k) be the first derivative of -k**7/280 - k**6/120 + k**5/20 + 7*k**3/3 + 4. Let r(q) be the third derivative of j(q). Factor r(n).
-3*n*(n - 1)*(n + 2)
Let h(r) = r**3 - 8*r**2 + 8*r - 5. Let n be h(7). Find j, given that -7 - 3*j + j**2 - 2*j**n - 2 - 3*j = 0.
-3
Let k be 3*1 - (-10)/(-6). Let b(u) be the first derivative of k*u**3 - 2*u - 1 - u**2. What is j in b(j) = 0?
-1/2, 1
Let j(n) be the third derivative of -3*n**2 - 1/10*n**7 + 3*n**4 - 43/20*n**5 + 0 + 3/4*n**6 + 0*n - 2*n**3. Find q, given that j(q) = 0.
2/7, 1, 2
Let y(c) be the first derivative of -2*c**3/39 + 2*c**2/13 + 6*c/13 - 2. Factor y(w).
-2*(w - 3)*(w + 1)/13
Let d(a) be the second derivative of -a**4/3 - 2*a**3 + 3*a - 9. Factor d(i).
-4*i*(i + 3)
Suppose -15 = d + 4*d. Let k(t) = -6*t**3 + 9*t**2 - 6*t. Let p(r) = -11*r**3 + 17*r**2 - 11*r. Let s(w) = d*p(w) + 5*k(w). Factor s(f).
3*f*(f - 1)**2
Let h be -3*(-3 - 10/(-6)). Factor -6*w**2 + h*w**2 + 0*w**2 + 2.
-2*(w - 1)*(w + 1)
Let q be (-13 + 12)/(2/(-10)). Factor 2*o**3 - 98/3*o**q + 140/3*o**4 + 0 - 40/3*o**2 - 8/3*o.
-2*o*(o - 1)**2*(7*o + 2)**2/3
Suppose