t(a) = -a - 4. Let u be t(-8). Let -2*j**3 - u*j**5 - 20*j**3 + 2*j**3 + 1 + 0*j**2 - 10*j**2 - 15*j**4 = 0. What is j?
-1, 1/4
Let t(j) be the second derivative of 0 - 1/8*j**4 + 6*j + 0*j**2 + j**3. What is z in t(z) = 0?
0, 4
Let u(x) be the third derivative of -x**5/150 - 23*x**4/120 + 2*x**3/5 + 24*x**2. Find n, given that u(n) = 0.
-12, 1/2
Suppose 4*d = 2*d + 10. Let f(j) be the first derivative of -4/35*j**d + 0*j**2 + 0*j + 1/21*j**6 + 1/14*j**4 - 3 + 0*j**3. Factor f(l).
2*l**3*(l - 1)**2/7
Let v = -8 - -11. Let a = -1 + v. Factor -9 + 1 + 12*h + h**3 - 5*h**2 - h**a.
(h - 2)**3
Let k be ((-12)/105)/(3/(-6)). Let t(a) be the second derivative of -a + 0 - 1/21*a**3 - 4/21*a**4 + 0*a**2 - k*a**5. Suppose t(d) = 0. Calculate d.
-1/4, 0
Suppose -5 + 17 = r. Let d be 2/(-3) - (-32)/r. Factor -2/7*s - 2/7*s**3 + 0 + 4/7*s**d.
-2*s*(s - 1)**2/7
Let d be (-6 - -3) + (4 - 1). Factor d + 0*s**2 - 1/5*s + 1/5*s**3.
s*(s - 1)*(s + 1)/5
Suppose 5*k + i - 23 = 0, 3*i = 4*k + 4*i - 19. Let f(n) = n**4 - n**3 - 3*n**2 + n. Let y(q) = -q**4 - q**3 - q. Let w(x) = k*y(x) + 2*f(x). Factor w(s).
-2*s*(s + 1)**3
Let h(q) be the third derivative of 2*q**7/35 + 11*q**6/60 - q**5/10 - q**4/6 - 8*q**2. Solve h(l) = 0 for l.
-2, -1/3, 0, 1/2
Suppose -1/2*w**3 - 1/6*w**2 + 1/3 - 1/6*w**4 + 1/2*w = 0. What is w?
-2, -1, 1
Let i(h) be the first derivative of -7*h**5/20 + h**4/8 + 7*h**3/12 - h**2/4 - 18. Determine g, given that i(g) = 0.
-1, 0, 2/7, 1
Let r(n) be the second derivative of -n**9/15120 - n**8/3360 + n**7/840 + n**4/3 - n. Let u(j) be the third derivative of r(j). Factor u(t).
-t**2*(t - 1)*(t + 3)
Suppose 0 = a - 4*a + 12. Let t be (2/15)/(a/40). Factor 1/3*h + 1/3*h**5 + 2*h**3 + t*h**4 + 4/3*h**2 + 0.
h*(h + 1)**4/3
Let j(k) = 4*k**2 - 13*k + 5. Let y = -27 - -22. Let d(x) = -6*x**2 + 19*x - 7. Let l(g) = y*d(g) - 7*j(g). Factor l(o).
2*o*(o - 2)
Suppose 15 = 5*l, 3*b + 2*l + 0*l - 15 = 0. Suppose -b*c = -f + 4, -3*f = c + c - 23. Factor -f - i**4 + 7.
-i**4
Let a be (6*(-8)/252)/(-6). Let o = a + 116/315. Factor -6/5*r**2 - o - 8/5*r.
-2*(r + 1)*(3*r + 1)/5
Let g(u) be the first derivative of u**3/4 + 9*u**2 + 108*u - 59. Factor g(l).
3*(l + 12)**2/4
Let g be -2*(1 - 21/6). Let z(w) = w**4 - w**3 + 11*w**2 - w + 1. Let y(s) = -s**3 + s**2 - s. Let t(n) = g*y(n) - z(n). Factor t(v).
-(v + 1)**4
Let y(p) be the first derivative of p**3 - 3*p**2/2 - 6*p - 12. Factor y(b).
3*(b - 2)*(b + 1)
Let q(w) be the third derivative of 4*w**5/15 + 2*w**4 + 6*w**3 + 2*w**2. Factor q(j).
4*(2*j + 3)**2
Let l(c) be the third derivative of 7*c**5/120 + 23*c**4/48 + c**3/2 + c**2. Find x, given that l(x) = 0.
-3, -2/7
Let y(v) be the third derivative of v**11/1663200 - v**10/378000 + v**9/302400 + v**5/30 - 2*v**2. Let l(q) be the third derivative of y(q). Factor l(f).
f**3*(f - 1)**2/5
Let m(l) be the third derivative of l**5/60 - l**4/8 - 2*l**3/3 - 10*l**2. Let m(p) = 0. Calculate p.
-1, 4
Let q(j) be the first derivative of j**4/18 + 2*j**3/27 - 5*j**2/9 + 2*j/3 - 12. Factor q(h).
2*(h - 1)**2*(h + 3)/9
Suppose 4*f = 2*c - 24 + 2, 4*f + 4*c = 8. Let v = f + 5. Suppose 1 - d**2 - 4*d + 6*d - v = 0. Calculate d.
1
Let l(r) be the third derivative of r**6/30 - r**5/15 - 7*r**2. Factor l(k).
4*k**2*(k - 1)
Let g(h) be the third derivative of 1/840*h**7 + 0*h**3 + 0*h**4 + 6*h**2 + 0*h**5 + 0*h + 0*h**6 + 0. Solve g(b) = 0 for b.
0
Suppose -2*r = 2*k + 6, 8*r = -3*k + 4*r - 12. Let -3/5*g**3 + 0*g**2 + k + 0*g = 0. What is g?
0
Let s = 3 - -1. Let z = 8 + -3. Solve -11*r**3 + 2*r**3 + 2*r + 3*r**2 + z*r**3 - 42*r**s - 19*r**3 = 0 for r.
-1/2, -1/3, 0, 2/7
Suppose -3*i + 3*i = -3*i. Let n(m) be the third derivative of -1/60*m**6 + i*m**3 + 0*m**5 + 2*m**2 + 0*m + 0*m**4 + 0 + 1/105*m**7. Factor n(f).
2*f**3*(f - 1)
Let x be 1/3*(4 - 4). Let p(j) be the third derivative of -3*j**2 + x*j + 3/25*j**5 + 0 + 1/75*j**6 + 9/10*j**3 + 9/20*j**4. Factor p(d).
(2*d + 3)**3/5
Let x(z) be the first derivative of z**4/42 + 2*z**3/63 - 4*z**2/21 - 8*z/21 + 1. Factor x(b).
2*(b - 2)*(b + 1)*(b + 2)/21
Let j(l) be the second derivative of l**7/210 - 2*l**6/25 + 9*l**5/25 - 10*l. Solve j(m) = 0.
0, 6
Let b(r) be the second derivative of -1/10*r**6 + 0*r**2 + 0 + 1/2*r**4 - 2*r - 3/20*r**5 + 0*r**3. Factor b(v).
-3*v**2*(v - 1)*(v + 2)
Let x(a) = -1 + a**3 - 2*a**3 - 2*a + a. Let l(y) = 3*y**3 - 2*y**2 + y + 1. Suppose 0 = 4*w - 3 + 7. Let b(n) = w*l(n) - x(n). Factor b(v).
-2*v**2*(v - 1)
Let c(n) = n - 3. Let s = 3 + 2. Let o be c(s). Factor -m**4 + 6*m**2 - 4*m**o + 4*m**5 - m**2 - 4*m**3.
m**2*(m - 1)*(m + 1)*(4*m - 1)
Let b(d) be the second derivative of -1/21*d**4 - d**2 - 4/21*d**3 - 1/210*d**5 + 0 - 2*d. Let r(l) be the first derivative of b(l). Factor r(x).
-2*(x + 2)**2/7
Let j be ((-4)/3)/((-4)/6). Let y be 408/595 + (-2)/7. Factor 2/5*z + 0 + y*z**j.
2*z*(z + 1)/5
Let n(g) be the second derivative of 5*g**4/12 - 5*g**3/6 + 18*g. Factor n(v).
5*v*(v - 1)
Suppose -3/4*f**3 - 1/4*f + 0 - 1/4*f**4 - 3/4*f**2 = 0. Calculate f.
-1, 0
Suppose 0 = -4*t + j + 3, 0 = -3*t + 2*t - 3*j + 17. Factor 3*x**t + 0 - 2 - x**2.
2*(x - 1)*(x + 1)
Let k(y) be the first derivative of -y**4/18 + 4*y**3/27 + y**2/9 - 4*y/9 + 1. Determine n so that k(n) = 0.
-1, 1, 2
Factor 0*v**2 + 1/2*v**3 + 1/2*v**4 + 0*v + 0.
v**3*(v + 1)/2
Suppose 3*j = -4*s + 37, 4*s - 17 = -4*j + 27. Let l(t) = -t**2 + 6*t + 10. Let m be l(j). Factor 0*k + 2/7*k**m + 0 - 2/7*k**5 - 2/7*k**2 + 2/7*k**4.
-2*k**2*(k - 1)**2*(k + 1)/7
Let s = -9 + 9. Let c(z) be the third derivative of -z**2 + 0*z**5 + 0 + 0*z**4 + s*z + 1/210*z**7 - 1/240*z**6 + 0*z**3. Find g such that c(g) = 0.
0, 1/2
Let g(d) be the third derivative of d**7/1260 - d**6/45 + 4*d**5/15 + d**4/4 + 8*d**2. Let m(k) be the second derivative of g(k). Determine l so that m(l) = 0.
4
Let l(y) be the first derivative of -2/3*y**5 + 2 + 2/9*y**6 + 1/3*y**4 + 2/3*y + 8/9*y**3 - 4/3*y**2. Find x such that l(x) = 0.
-1, 1/2, 1
Let r(a) be the first derivative of a**8/1176 + a**7/245 + a**6/140 + a**5/210 - a**2 - 5. Let z(p) be the second derivative of r(p). Factor z(q).
2*q**2*(q + 1)**3/7
Factor 0*d + 2/7*d**2 + 0.
2*d**2/7
Factor -4/3*w**2 + 7/3*w + 2/3.
-(w - 2)*(4*w + 1)/3
Let j(p) be the second derivative of -p**6/60 + p**4/12 - p**2/4 + 15*p. Suppose j(s) = 0. What is s?
-1, 1
Let v(r) be the first derivative of -3*r**5/20 + 3*r**3/2 + 3*r**2 + 9*r/4 - 1. Factor v(z).
-3*(z - 3)*(z + 1)**3/4
Solve 1/6*c - 1/2*c**2 + 1/6*c**4 + 1/3 - 1/6*c**3 = 0 for c.
-1, 1, 2
Let f(g) be the first derivative of -g**4/6 + 2*g**3/9 + 2*g**2/3 - 5. Factor f(x).
-2*x*(x - 2)*(x + 1)/3
Let i be (4/5)/(4/20). Factor n - 2*n**5 + 7*n + 0*n**5 - 8*n**i - 2*n**3 + 20*n**2 - 16.
-2*(n - 1)**2*(n + 2)**3
Let c(z) be the first derivative of 2/55*z**5 + 1 - 1/22*z**4 - 2/33*z**3 + 0*z**2 + 0*z + 1/33*z**6. Factor c(l).
2*l**2*(l - 1)*(l + 1)**2/11
Let k(o) = o**4 - o. Let g(y) = -6*y**4 - y**3 - y**2 + 8*y. Let m(s) = -2*g(s) - 14*k(s). Let m(t) = 0. Calculate t.
-1, 0, 1
Let w be (1 - 1)*6/6. Suppose w = -2*u + x + 5, x = -4*u - 4 + 11. Solve 0*f + 2/7*f**4 + 2/7*f**3 - 2/7*f**5 + 0 - 2/7*f**u = 0 for f.
-1, 0, 1
Let a(x) be the third derivative of x**8/896 + x**7/280 + x**6/320 + 4*x**2. Suppose a(p) = 0. What is p?
-1, 0
Let z(t) be the second derivative of 0*t**6 + 0*t**2 + 0*t**3 + 1/36*t**4 - 9*t - 1/252*t**7 + 1/40*t**5 + 0. Factor z(k).
-k**2*(k - 2)*(k + 1)**2/6
Let y(z) = 5*z**4 + 5*z**3 - z**2 - z. Let l(o) = -4*o**4 - 4*o**3 + o**2 + o. Let t(i) = 4*l(i) + 3*y(i). Factor t(m).
-m*(m - 1)*(m + 1)**2
Let x(v) = 10*v**2 - 55*v + 35. Let q(f) = 5*f**2 - 28*f + 17. Let u(g) = -5*q(g) + 3*x(g). Factor u(s).
5*(s - 4)*(s - 1)
Let f(s) be the first derivative of 3*s**4/2 + 50*s**3/3 - 18*s**2 - 68. Factor f(k).
2*k*(k + 9)*(3*k - 2)
Suppose -3*r + 3*k - 65 = -8*r, 4*r - 4*k = 20. Suppose 0 = 2*y + x - 22, 3*x = -y + r + 1. Find l, given that 11 - y + l**3 = 0.
0
Let t be 4 - (-376)/(-90) - 4/(-10). Suppose 2/3*m**2 - 2/9*m**3 - 2/3*m + t = 0. What is m?
1
Factor a**5 + 71*a**3 - 71*a**3 - a + 2*a**4 - 2*a**2.
a*(a - 1)*(a + 1)**3
Solve j**2 + 3/5 - 8/5*j = 0 for j.
3/5, 1
Let z = 1 - 1. Let s(a) be the third derivative of z*a**6 + 0*a - 2*a**2 + 0 + 1/240*a**5 + 0*a**3 + 0*a**4 - 