f 1/2*c**2 + c**3 + 1/5*c**5 + v*c**4 - 1 + 0*c. What is f in j(f) = 0?
-1, 0
Let t(o) be the third derivative of -o**5/240 - 3*o**4/32 - 10*o**2. Factor t(h).
-h*(h + 9)/4
Factor 0 - 1/6*n**2 + 0*n.
-n**2/6
Let r = 7 - 7. Suppose 2 = t - r*t. Find u such that 10*u - 10*u + u**3 + u**2 + u**t = 0.
-2, 0
Let c(u) = -4*u**2 - 2*u. Let w(f) = 3*f**2 + 2*f. Let k(z) = 4 - 4 + 7*z + 1. Let m be k(-1). Let p(o) = m*w(o) - 5*c(o). What is i in p(i) = 0?
0, 1
Let r(s) be the first derivative of 0*s**2 + 5 + 2/5*s**5 + 0*s - 1/2*s**4 - 4/3*s**3. Factor r(a).
2*a**2*(a - 2)*(a + 1)
Let o(j) = -4*j**2 + 15*j - 13. Let h(i) = -i**2 - 1. Let r(k) = h(k) - o(k). What is b in r(b) = 0?
1, 4
Let h(b) be the second derivative of 0*b**2 + 1/12*b**4 - 1/30*b**6 + 1/20*b**5 + 0*b**3 - b + 0 - 1/42*b**7. Factor h(j).
-j**2*(j - 1)*(j + 1)**2
Factor 3 - 3*x - 3*x**3 + 9*x**2 - 7*x - 2*x + 3*x.
-3*(x - 1)**3
Let k(g) be the first derivative of 2/9*g**3 - 1/6*g**4 + 4 + 0*g + 2/3*g**2. Factor k(o).
-2*o*(o - 2)*(o + 1)/3
Suppose 0 = -2*s - 5*i + 3, -5*i = 2 + 3. Let z(n) = 3*n - 6. Let d be z(s). Let -c**2 - d*c + 6*c + 1 = 0. Calculate c.
-1, 1
Let k(r) be the third derivative of -r**6/45 - 7*r**5/90 - r**4/18 + r**3/9 - 3*r**2. Solve k(p) = 0 for p.
-1, 1/4
Suppose 0*k + 0*k**3 + 1/9*k**5 + 0 + 2/9*k**4 + 0*k**2 = 0. What is k?
-2, 0
Suppose 0*x = -5*s - x, -4*s + 2*x = 0. Let c(q) be the second derivative of -2/3*q**4 + 2*q - 2/3*q**3 - 1/4*q**2 + s. Factor c(n).
-(4*n + 1)**2/2
Let i(l) be the second derivative of -l**6/60 - l**5/40 + l**4/12 - 23*l. Factor i(s).
-s**2*(s - 1)*(s + 2)/2
Let a(p) be the third derivative of -1/120*p**5 + 0*p**4 + 1/168*p**8 + 0*p**3 + 1/60*p**7 + 0*p + 0 - 6*p**2 + 1/120*p**6. Factor a(d).
d**2*(d + 1)**2*(4*d - 1)/2
Find b, given that -1/2*b**3 + 3/2*b**5 + 0 + 0*b**2 + 0*b - b**4 = 0.
-1/3, 0, 1
Suppose -9*g**4 - 12*g + 21*g**2 + 12*g**3 - 7 + 0*g**3 + 1 - 6 = 0. What is g?
-1, -2/3, 1, 2
Let h(b) be the first derivative of 3/5*b + 3 - 1/5*b**3 + 3/20*b**4 - 3/10*b**2. Factor h(o).
3*(o - 1)**2*(o + 1)/5
Factor -2/11*a**3 - 8/11 + 0*a + 6/11*a**2.
-2*(a - 2)**2*(a + 1)/11
Suppose -7/5*t**3 + 0*t + 0 + 7/5*t**5 - 2/5*t**2 + 2/5*t**4 = 0. Calculate t.
-1, -2/7, 0, 1
Factor 10/9*s**3 + 0 - 4/9*s**4 + 0*s + 2/3*s**2.
-2*s**2*(s - 3)*(2*s + 1)/9
Let t(d) be the third derivative of d**6/540 - d**5/90 + d**4/54 + 13*d**2. Let t(g) = 0. Calculate g.
0, 1, 2
Suppose 0 = 4*q - 9*q - 2*x + 10, 5*q = 2*x + 30. Factor 0*h**2 - 2/5*h**3 + 0 + 0*h - 2/5*h**q.
-2*h**3*(h + 1)/5
Let f(o) be the first derivative of 32/7*o - 3 - 8/7*o**2 + 2/21*o**3. Determine t, given that f(t) = 0.
4
Let f(v) be the second derivative of 1/3*v**3 - 6*v + 0 - 1/10*v**5 - 1/30*v**6 + 1/2*v**2 + 0*v**4. Let f(g) = 0. Calculate g.
-1, 1
Let m(x) be the second derivative of -x**6/45 - x**5/15 + 2*x**3/9 + x**2/3 - 7*x. Factor m(f).
-2*(f - 1)*(f + 1)**3/3
Suppose -l - 3*l + 20 = -2*d, 0 = -d + 5*l - 19. Let q = 6 + d. Let 0 + 1/2*p**q - 1/2*p = 0. Calculate p.
0, 1
Let i(m) be the second derivative of -m**5/50 - m**4/10 - 2*m**3/15 - m. Suppose i(t) = 0. Calculate t.
-2, -1, 0
Let d = 11 + -5. Let r(y) be the second derivative of 1/15*y**d - 1/6*y**4 + 0*y**2 + 0 + 2*y - 1/3*y**3 + 1/10*y**5. Factor r(j).
2*j*(j - 1)*(j + 1)**2
Let p(o) = -2*o**4 - 18*o**3 - 22*o**2 - 4*o + 2. Let d(y) = -y**3 - y**2. Let n(t) = 44*d(t) - 2*p(t). Let n(f) = 0. Calculate f.
-1, 1
Let m = 550 - 2749/5. Find d, given that 3/5*d**2 + 0 - 3/5*d**4 + 4/5*d**5 + m*d - d**3 = 0.
-1, -1/4, 0, 1
Let f(o) be the second derivative of -o**4/48 + 5*o**3/12 - 25*o**2/8 + 11*o. Solve f(u) = 0 for u.
5
Let p be (1 - (0 + -2))*1. Solve 5*o**p + o - 3*o - 10*o**2 - 3*o**3 + 6*o**4 + 4 = 0 for o.
-1, 2/3, 1
Factor 5/4*o - 1/2 + 3/4*o**2.
(o + 2)*(3*o - 1)/4
Let a be (-888)/(-42) - 1/7. Let o be (0 - 3)*(-14)/a. Factor 0 - 4/3*b**o - 2/3*b - 2/3*b**3.
-2*b*(b + 1)**2/3
Let g = 2401/20 + -120. Let y(h) be the second derivative of -g*h**5 + 0*h**2 + 0 - 2*h + 0*h**3 - 1/12*h**4. Let y(o) = 0. What is o?
-1, 0
Let i(k) be the first derivative of -k**8/1680 + k**7/420 + k**6/120 - k**5/30 - k**4/6 - k**3 + 1. Let w(u) be the third derivative of i(u). Factor w(n).
-(n - 2)**2*(n + 1)**2
Let 0*y**3 + 6/25*y**2 + 4/25*y + 0 - 2/25*y**4 = 0. Calculate y.
-1, 0, 2
Let s(j) be the third derivative of j**5/160 + 3*j**4/64 + j**3/8 + 4*j**2 + j. Factor s(l).
3*(l + 1)*(l + 2)/8
Suppose -7*v + 6*v - 36 = 0. Let r be (8/(-12))/(8/v). Factor 0 + 0*w**2 - 2/7*w - 2/7*w**5 + 4/7*w**r + 0*w**4.
-2*w*(w - 1)**2*(w + 1)**2/7
Let z(o) be the first derivative of o**6/120 - o**4/24 - o**2/2 + 1. Let n(q) be the second derivative of z(q). Determine l so that n(l) = 0.
-1, 0, 1
Let t(f) be the first derivative of f**6/36 - f**5/5 + 7*f**4/12 - 8*f**3/9 + 3*f**2/4 - f/3 + 22. Suppose t(w) = 0. What is w?
1, 2
Let c be (-3)/7 + 3582/126. Let m be 3*2*7/c. Factor -1/2*h**3 - 1/2 - m*h**2 - 3/2*h.
-(h + 1)**3/2
Let h(l) = -l**2 - l + 214. Let d be h(-15). Find g such that 1/2*g**3 + 0 - g + 3/2*g**d - 3/2*g**2 + 1/2*g**5 = 0.
-2, -1, 0, 1
Let w(f) be the third derivative of 0*f**7 - 1/360*f**6 + 0*f + 0*f**5 + 7*f**2 + 0*f**4 + 0*f**3 + 1/1008*f**8 + 0. Determine g, given that w(g) = 0.
-1, 0, 1
Let g(d) be the first derivative of -2*d**3/27 + 5*d**2/9 - 8*d/9 + 46. Factor g(m).
-2*(m - 4)*(m - 1)/9
Let u(h) = h - 6. Let k(c) = c + 13. Let r be k(-7). Let a be u(r). Suppose n**2 + a + 1/2*n = 0. Calculate n.
-1/2, 0
Let c(b) be the third derivative of -b**7/840 - b**6/360 + 2*b**3/3 - b**2. Let k(n) be the first derivative of c(n). Solve k(m) = 0.
-1, 0
Suppose 2*b + 3*b = 5, 3*b + 5 = 4*z. Factor 4/5*m**z - 2/5 + 0*m**3 - 2/5*m**4 + 0*m.
-2*(m - 1)**2*(m + 1)**2/5
Suppose l + 1995 = -y, -3*y + 2812 = -2*l - 1153. Let p be l/(-100) + 2/4. Find m such that 0 - 294/5*m**5 - 12*m**2 + 8/5*m + 119/5*m**4 + p*m**3 = 0.
-2/3, 0, 2/7, 1/2
Let b(c) be the second derivative of -c**9/5040 + c**8/3360 + c**7/840 - c**6/360 + c**4/4 - c. Let d(g) be the third derivative of b(g). Factor d(m).
-m*(m - 1)*(m + 1)*(3*m - 2)
Suppose -8*k**3 + 2*k + 6*k - 11 + 13 - 2*k**2 = 0. Calculate k.
-1, -1/4, 1
Let m(r) = -r - 1. Let n(p) = -4*p**2 + 3*p - 5. Let w(a) = 5*a**2 - 2*a + 5. Let b(u) = -3*n(u) - 2*w(u). Let o(v) = -b(v) - m(v). Factor o(f).
-2*(f - 2)*(f - 1)
Factor 0 + 0*z - 2/3*z**2 - 1/3*z**3 + z**5 + 4/3*z**4.
z**2*(z + 1)**2*(3*z - 2)/3
Let k be 6/(-5)*(-10)/3. Factor -2*d**k - 2*d - 12*d**2 + 14*d**2 + 4*d - 2*d**3.
-2*d*(d - 1)*(d + 1)**2
Let d(t) be the first derivative of t**6/2 - 3*t**5/5 - 3*t**4/4 + t**3 + 10. Solve d(u) = 0 for u.
-1, 0, 1
Let w(t) be the second derivative of -t**8/6720 - t**7/1260 + t**6/720 + t**5/60 - t**4/4 - 3*t. Let m(n) be the third derivative of w(n). Factor m(c).
-(c - 1)*(c + 1)*(c + 2)
Let a(l) be the third derivative of 2*l**7/105 - l**6/6 + 2*l**5/5 + 2*l**4/3 - 16*l**3/3 + 15*l**2. Factor a(o).
4*(o - 2)**3*(o + 1)
Let m(w) = w**2 - w - 3. Let p(c) = c**2 + 2*c - 5. Let j(q) = -q**2 - q + 5. Let d(f) = 3*j(f) + 2*p(f). Let h(r) = -3*d(r) - 5*m(r). Factor h(n).
-2*n*(n - 1)
Let u(i) = i**2 - 2. Let p(w) = 3*w**2 - 2*w - 5. Let l(y) = -2*p(y) + 5*u(y). Factor l(j).
-j*(j - 4)
Let c be 2/(-7) + (-18)/(-63). Let g(j) be the second derivative of -j + 1/3*j**3 + c*j**2 + 0*j**4 + 0 - 1/10*j**5. Find k, given that g(k) = 0.
-1, 0, 1
Suppose 6*p - 5*p = 4. Let c(x) be the first derivative of -1/2*x**p - 2 + 2*x + x**2 - 2/3*x**3. Factor c(m).
-2*(m - 1)*(m + 1)**2
Factor -2/7 - 1/7*s + 1/7*s**2.
(s - 2)*(s + 1)/7
Let k(j) = -7*j**3 + 23*j**2 + 23*j - 11. Let x(y) = -69*y**3 + 231*y**2 + 231*y - 111. Let t(u) = 21*k(u) - 2*x(u). Factor t(r).
-3*(r - 3)*(r + 1)*(3*r - 1)
Let p(c) = -3*c**2 - 3*c. Let k(l) = 4*l**2 + 3*l. Let j(y) = -2*k(y) - 3*p(y). Factor j(n).
n*(n + 3)
Suppose -4*r - 5*n = -29, 3*r - 2*n = n - 12. Suppose -u = -r - 1. Let s**4 - 4*s**4 + s**4 + u*s**3 = 0. Calculate s.
0, 1
Suppose 2*u - u - 4 = 0. Suppose -u*g + 23 - 7 = 0. Factor -x**5 + 4*x**g + 3*x**5 + 0*x**4 + 2*x**3.
2*x**3*(x + 1)**2
Solve 11 + 10 + 6 + 18*u + 3*u**2 = 0 for u.
-3
Let o(j) be the second derivative of j**8/3360 + j**7/1680 - j**6/720 - j**5/240 - j**3/6 - 2*j. Let q(r) be the second derivative of o(r). Solve q(n) = 0.