st derivative of b(f). Determine t, given that g(t) = 0.
2/3
Let x = 230 - 2068/9. Factor -2/9*v**2 - x*v + 4/9.
-2*(v - 1)*(v + 2)/9
Let j(y) = -6*y - 24. Let s be j(-4). Factor -2/9*b**2 - 2/9*b + s + 2/9*b**4 + 2/9*b**3.
2*b*(b - 1)*(b + 1)**2/9
Let y(p) be the third derivative of -p**10/151200 + p**8/20160 - p**5/30 - p**2. Let w(s) be the third derivative of y(s). Factor w(a).
-a**2*(a - 1)*(a + 1)
Suppose -4 = -3*i + 2. Factor -5*l**2 - 4*l - 2 + i + 3*l**2.
-2*l*(l + 2)
Let k(z) = 2*z + 3. Let u be k(5). Suppose 0*c = 3*c - 2*r - u, -2*c + r = -9. Suppose -2*t**2 + 2*t**5 - 34*t**c - 4*t**3 - 48*t**4 - 14*t**3 = 0. What is t?
-1, -1/4, 0
Let v = 54/3115 + 1/89. Let h(b) be the second derivative of -v*b**5 - 1/105*b**6 + 0*b**2 - 1/42*b**4 + 0*b**3 + 0 + b. Factor h(n).
-2*n**2*(n + 1)**2/7
Let i(r) be the first derivative of -r**5/90 - r**4/27 + r**3/27 + 2*r**2/9 - 6*r + 5. Let g(u) be the first derivative of i(u). Find p, given that g(p) = 0.
-2, -1, 1
Let u(l) = -13*l + 43. Let j be u(3). Let t(b) be the third derivative of 0*b - 1/24*b**j - 1/60*b**5 + 0 + 3*b**2 + 0*b**3. Factor t(f).
-f*(f + 1)
Let a(y) be the second derivative of -2*y**7/3 + 2*y**6/3 + 23*y**5/5 - 29*y**4/3 + 8*y**3/3 + 8*y**2 - 5*y. Solve a(h) = 0.
-2, -2/7, 1
Let u = 24 + -17. Suppose 0 = -r - 2*s - u, 0 = 3*r + 2*r - s - 20. Factor -3*i**3 + 2*i**r + 5*i**2 - 8*i + 6 - 2.
-(i - 2)**2*(i - 1)
Let i = 72 + -285/4. Factor 3/4*m**2 - i + 0*m.
3*(m - 1)*(m + 1)/4
Let q(v) be the second derivative of 1/60*v**5 - 1/2*v**2 - 1/12*v**3 + v + 0 + 1/48*v**4. Let s(n) be the first derivative of q(n). Find w such that s(w) = 0.
-1, 1/2
Let v be 5*(-3)/6*2. Let k be 3 + -1 - v/(-3). Find p such that -2/3*p**4 + 0*p**3 + 1/3*p - k*p**5 + 2/3*p**2 + 0 = 0.
-1, 0, 1
Let n(x) be the first derivative of 8/25*x**5 + 8/15*x**3 + 3/5*x**4 + 1/15*x**6 + 1/5*x**2 + 0*x - 3. Factor n(d).
2*d*(d + 1)**4/5
Let n(q) be the second derivative of -q**7/21 + 2*q**6/5 - 7*q**5/5 + 8*q**4/3 - 3*q**3 + 2*q**2 - 2*q. Suppose n(u) = 0. Calculate u.
1, 2
Let z be 1/(-1)*(-9 - -11). Let y be (-91)/(-147) + z/6. Let y*p - 4/7 + 2/7*p**2 = 0. Calculate p.
-2, 1
Let a(w) be the first derivative of 3*w**4/20 - 3*w**2/10 + 27. Determine i so that a(i) = 0.
-1, 0, 1
Let v(y) be the third derivative of 0*y - 1/9*y**3 + 0 + 7*y**2 - 1/18*y**4 - 1/90*y**5. Determine a, given that v(a) = 0.
-1
Suppose -28 = -5*d - 2*l, -4*d = -2*l + l - 25. Factor 6 + 4*p**2 - 6 - 6*p**2 - d + 2*p**3 - 10*p.
2*(p - 3)*(p + 1)**2
Suppose 7*b = 2*b + 25. Let r(j) be the third derivative of 0*j + 0*j**3 + 7/20*j**6 + 1/3*j**4 - 4/5*j**b + 7/15*j**7 + j**2 + 0. Factor r(p).
2*p*(p + 1)*(7*p - 2)**2
Suppose 17 = 4*m + 3*z, m = -0*m + 3*z - 7. Suppose -6*d**m + 9*d + 2 - 3 - 2 = 0. What is d?
1/2, 1
Let t be 14/5*(-15)/51. Let j = 76/51 + t. Let -j*s + s**5 - 5/3*s**2 + 5/3*s**4 + 0 - 1/3*s**3 = 0. Calculate s.
-1, -2/3, 0, 1
Let d(c) be the third derivative of -c**9/60480 - c**8/26880 - 3*c**4/8 + 3*c**2. Let q(s) be the second derivative of d(s). Suppose q(f) = 0. What is f?
-1, 0
Let d(l) be the first derivative of -l**5/5 - 7*l**4/4 - 6*l**3 - 10*l**2 - 8*l + 5. Factor d(f).
-(f + 1)*(f + 2)**3
Suppose w = 3*w. Let x be ((-2)/(-4))/(1/8). Factor 2*a**2 + 4*a + w*a - 2 - x*a**2.
-2*(a - 1)**2
Let t(s) be the third derivative of 3*s**8/784 + 4*s**7/245 + s**6/210 - 11*s**5/210 - 13*s**4/168 - s**3/21 + 24*s**2. Solve t(h) = 0 for h.
-2, -1, -1/3, 1
Let b(h) be the second derivative of 0 + 1/6*h**3 - 1/48*h**4 + h - 1/2*h**2. Factor b(f).
-(f - 2)**2/4
Let r be 4/(-16) + (-21)/(-4). Factor 2*n**5 + 2*n**r - 6*n**5.
-2*n**5
Factor h**2 - h**2 + 1 + h**2 + 19*h - 21*h.
(h - 1)**2
Let n(w) be the third derivative of 1/30*w**4 + 0*w - 7/150*w**5 + 0 + 0*w**3 + 2*w**2. Factor n(x).
-2*x*(7*x - 2)/5
Let k(h) be the first derivative of 4*h**3/3 + 4*h**2 + 4*h - 3. Factor k(p).
4*(p + 1)**2
Let h**2 + 34*h**4 + 33*h**3 - 20*h**3 + 19*h**3 + 10*h**5 + 7*h**2 = 0. Calculate h.
-2, -1, -2/5, 0
Let u be (8/5)/((-2)/(-5)). Suppose 0 = 5*d + 10, 3*l + 0 = -4*d + u. Let -1 - p**l + 2*p**2 + p**3 - p**3 + 0*p**4 = 0. What is p?
-1, 1
Let p be 0 + 0 + (4 - 1). Suppose 4*g - 2*g + 6 = -p*u, u = -g - 3. Determine s, given that 0 + 0 - s**3 + s + u = 0.
-1, 0, 1
Suppose -u - 2*x = -x - 2, 4*x + 24 = 4*u. Let n = u - 2. Suppose 0*z + 6*z**2 - 2*z + 2*z**n = 0. Calculate z.
0, 1/4
Let u(g) be the third derivative of -g**6/120 - g**5/20 + 2*g**3/3 + 3*g**2. Factor u(h).
-(h - 1)*(h + 2)**2
Let v(d) = 5*d**2 - d + 5. Let u(p) = -4*p**2 + 2*p - 4. Let m(x) = 3*u(x) + 2*v(x). Factor m(q).
-2*(q - 1)**2
Let s(n) = 2*n**3 + n**2 + 9*n. Let d(t) = -2*t**2 - 2*t**3 - 5*t + t - 5*t + t. Let m(k) = 5*d(k) + 4*s(k). Factor m(b).
-2*b*(b + 1)*(b + 2)
Let k be ((-31)/93)/(2/(-3)). Factor -1 - k*q + 1/2*q**2.
(q - 2)*(q + 1)/2
Let k(m) = m**2 + 3*m - 3. Let u be k(-5). Suppose 5*q + u = 22. Factor -q + 2*g**3 + 3 - 2*g**2.
2*g**2*(g - 1)
Let f(h) be the second derivative of 0*h**5 - 1/10*h**6 + 1/12*h**4 + 0*h**3 + 2*h + 1/21*h**7 + 0*h**2 + 0. Factor f(y).
y**2*(y - 1)**2*(2*y + 1)
Let l(t) be the third derivative of -5*t**6/24 - t**5/2 - 42*t**2. Factor l(f).
-5*f**2*(5*f + 6)
Let z(n) be the second derivative of -11*n + 0*n**2 + 0 - 1/75*n**6 + 2/25*n**5 + 0*n**3 - 2/15*n**4. Factor z(m).
-2*m**2*(m - 2)**2/5
Let z = -1 + 4. Suppose 0 = 5*f - 5*n - 15, 2*f + 5*n = 6*n + z. Solve f - 1/5*o**2 - 3/5*o**3 + 2/5*o = 0.
-1, 0, 2/3
Let n(a) be the second derivative of 5*a**4/12 - 37*a**3/6 + 7*a**2 - 30*a. Factor n(y).
(y - 7)*(5*y - 2)
Let g(n) be the third derivative of -n**5/80 + n**4/12 - n**3/6 - 5*n**2. Find r such that g(r) = 0.
2/3, 2
Solve 0 + 2/5*z**3 - 4/5*z - 2/5*z**2 = 0.
-1, 0, 2
Let z = 1/22 - -19/66. Determine l so that 0 + 1/3*l**4 + 0*l + 2/3*l**3 + z*l**2 = 0.
-1, 0
Let o(f) be the second derivative of 0*f**3 + 4*f - 1/6*f**2 + 1/36*f**4 + 0. Factor o(b).
(b - 1)*(b + 1)/3
Factor -2*b**2 + 3 + 8*b - 11 + 2*b.
-2*(b - 4)*(b - 1)
Let u be (-1)/4*-18 - 4. Factor -1/2*n**2 + 1 - u*n.
-(n - 1)*(n + 2)/2
Factor 2*g - 3 - 1/3*g**2.
-(g - 3)**2/3
Let y(i) be the first derivative of 1 - 1/5*i**2 + 4/15*i**3 + 1/30*i**4 - 2/25*i**5 - 2*i. Let d(g) be the first derivative of y(g). Let d(s) = 0. What is s?
-1, 1/4, 1
Suppose -1 + 3 = a. Determine i so that -i**3 + 2*i**2 + i**3 + a*i - 4*i**3 = 0.
-1/2, 0, 1
Let g(w) be the third derivative of w**5/60 + w**4/24 - w**3/3 - 2*w**2. Determine l so that g(l) = 0.
-2, 1
Let n(x) = -11*x**3 + 20*x**2 - 31*x + 10. Let r(v) = v**3 + v. Let f(y) = -n(y) - 6*r(y). Solve f(d) = 0 for d.
1, 2
Factor 5/2*f**4 + 0 + 0*f + 5/4*f**3 + 5/4*f**5 + 0*f**2.
5*f**3*(f + 1)**2/4
Let k(y) be the second derivative of y**4/66 + 2*y**3/33 + y**2/11 + 4*y. Factor k(p).
2*(p + 1)**2/11
Let i be 1*4*8/128. Factor 0*w - 1/4 + 0*w**3 - i*w**4 + 1/2*w**2.
-(w - 1)**2*(w + 1)**2/4
Factor -4/7 + 6/7*p - 2/7*p**2.
-2*(p - 2)*(p - 1)/7
Let n = -1092 - -2245/2. Let x = n + -29. Determine h, given that 1/2 + x*h**2 - 2*h = 0.
1/3, 1
Let i = 5 - 4. Let u be -4*i*1/(-10). Factor 0 - 1/5*q - u*q**2 - 1/5*q**3.
-q*(q + 1)**2/5
Let w(f) be the third derivative of -f**5/270 - f**4/36 - 2*f**3/27 - 12*f**2. Find k, given that w(k) = 0.
-2, -1
Let d(y) be the first derivative of -y**3/18 - y**2/3 - y/2 + 8. Find v such that d(v) = 0.
-3, -1
Let p(d) = -2*d. Let x be p(-2). Suppose -2*j + 8*j**5 + 10*j**2 + 2*j**3 - 2 + 0*j**3 + 4 - x - 16*j**4 = 0. What is j?
-1/2, 1
Solve 11/5*p**2 + 0 - 16/5*p**3 - 2/5*p + 7/5*p**4 = 0 for p.
0, 2/7, 1
Let l(u) be the second derivative of -u**5/80 - u**4/32 + u**2 - u. Let w(y) be the first derivative of l(y). Determine z so that w(z) = 0.
-1, 0
Suppose k + 6 = 3*k. Factor 0 - 2 + 4*y**k - 5*y**5 + 6*y**5 + 4*y**4 - 2*y**2 - 5*y.
(y - 1)*(y + 1)**3*(y + 2)
Let z(i) = 9*i**2 - 13*i. Let m(w) = 4*w**2 - 6*w. Let u(k) = 7*m(k) - 3*z(k). Solve u(n) = 0.
0, 3
Factor -4/5*r**4 + 36/5*r**3 + 108/5*r - 108/5*r**2 + 0.
-4*r*(r - 3)**3/5
Suppose 162/11*j**4 + 32/11*j - 108/11*j**2 + 20/11*j**5 + 2/11*j**3 + 0 = 0. What is j?
-8, -1, 0, 2/5, 1/2
Let z(n) be the third derivative of n**8/6720 + n**7/1260 + n**6/720 + n**4/24 - 4*n**2. Let a(t) be the second derivative of z(t). Let a(l) = 0. What is l?
-1, 0
Let q be ((-192)/(-56