t) be the third derivative of 0*t**5 + 0*t - 1/315*t**7 + 6*t**2 + 0 + 0*t**4 + 1/1512*t**8 + 1/270*t**6 + 0*t**3. Factor x(c).
2*c**3*(c - 2)*(c - 1)/9
Let w = -8 - -16. Let 2*m**3 + 8*m**3 - 2*m**2 + 5*m**2 + w*m**4 + m**2 + 2*m**5 = 0. What is m?
-2, -1, 0
Let a = -1/1879 - -1883/7516. Factor 3/4*p**4 + 0 + a*p**2 - 3/4*p**3 + 0*p - 1/4*p**5.
-p**2*(p - 1)**3/4
Let -16*s**2 + 2*s - 13*s**3 + 13*s**2 - 10*s**2 + 40*s**3 + 7*s**5 - 23*s**4 = 0. Calculate s.
0, 2/7, 1
Suppose 0*s + 3 = s. Suppose -5 = s*o - 4*o. Factor -5*t + 2 + o*t - 4*t + 2*t**2.
2*(t - 1)**2
Let j be (-3 - (-2602)/(-10)) + 1. Let v = j - -263. Factor -2/5 + 4/5*k**3 - 2/5*k**4 - 2/5*k + v*k**2 - 2/5*k**5.
-2*(k - 1)**2*(k + 1)**3/5
Let t(q) = -q**3 + q**2 - q + 1. Let p(x) = 6*x**3 - 7*x**2 + 8*x - 7. Let y(v) = 2*p(v) + 14*t(v). Suppose y(k) = 0. Calculate k.
-1, 0, 1
Let u be (-6)/(-10)*-1*(-125)/45. Factor 0*h - 4/3*h**4 - 1/3*h**2 - u*h**3 + 0.
-h**2*(h + 1)*(4*h + 1)/3
Let t = -25 + 25. Let r(g) be the second derivative of 1/6*g**2 + 1/18*g**4 + 1/120*g**5 + t + 3*g + 5/36*g**3. Solve r(h) = 0 for h.
-2, -1
Let h = 16 - 191/12. Let g(c) be the first derivative of 1/8*c**4 - 1/10*c**5 - 1 + 0*c + 0*c**2 + 1/6*c**3 - h*c**6. Let g(f) = 0. What is f?
-1, 0, 1
Let v(a) be the second derivative of -a**7/15120 - a**6/1440 - a**5/360 - 5*a**4/12 + 7*a. Let h(u) be the third derivative of v(u). Factor h(x).
-(x + 1)*(x + 2)/6
Let o(b) be the third derivative of b**6/60 + b**5/10 + b**4/6 + 7*b**2. Factor o(d).
2*d*(d + 1)*(d + 2)
Let g be 6/14 - (-18)/7. Let r(s) be the third derivative of 0 + 1/150*s**5 + 2*s**2 - 1/30*s**4 + 0*s + 1/15*s**g. Find w, given that r(w) = 0.
1
Let -8/5*p**3 + 0 + 4/15*p + 2/3*p**2 = 0. Calculate p.
-1/4, 0, 2/3
What is c in -4*c**3 - 2*c**4 + 0*c**4 + 2*c**3 + 4*c - 2*c + 2*c**2 = 0?
-1, 0, 1
Suppose 5*d - 17 = o, o + 9 = 3*d - 0*o. Factor -2*b**4 + 8*b**4 - 7*b**d - b**2 + 2*b**3.
-b**2*(b - 1)**2
Let a(g) be the second derivative of -g**6/30 + 3*g**5/80 + 5*g**4/48 - g**3/8 - g**2/8 - 5*g. Find y, given that a(y) = 0.
-1, -1/4, 1
Let x(s) be the first derivative of -s**4/18 + 2*s**3/27 - 42. Factor x(f).
-2*f**2*(f - 1)/9
Let s be (-4)/((-32)/(-30)) - -4. Let 1/4*q + 11/4*q**3 - s + 9/4*q**2 + q**4 = 0. Calculate q.
-1, 1/4
Let l(y) = -y**3 - 3*y**2 - 12*y + 3. Let d(p) = -p**3 - 2*p**2 - 13*p + 4. Let q(a) = 3*d(a) - 4*l(a). Factor q(z).
z*(z + 3)**2
Suppose -5*w = -10 - 5. Factor -9*r**3 + w*r**4 - 3*r - 9*r**2 - 14*r**4 + 8*r**4.
-3*r*(r + 1)**3
Let x(z) = -2*z**2 - 8*z - 9 + 4*z**2 - 3*z**2. Let b be x(-6). Suppose 4*i**3 - 3*i**b - 5*i + 4*i = 0. What is i?
-1, 0, 1
Let q(k) = 13*k**2 + 13*k + 13. Let r(l) = 3*l**2 + 3*l + 3. Let y(t) = -4*q(t) + 18*r(t). Let b be y(-2). Let -3 + 1 + b*z - z**2 - 3*z = 0. What is z?
1, 2
Let p(x) = x**2 - 4*x + 3. Let m be p(4). Determine b so that -b - 2*b**3 + 11 - 11 + 3*b**m = 0.
-1, 0, 1
Let m(s) be the third derivative of s**5/30 + 4*s**2. Suppose m(n) = 0. Calculate n.
0
Let i(a) = -3*a**2 + 56*a + 64. Let g(n) = 16*n**2 - 308*n - 352. Let k(x) = 5*g(x) + 28*i(x). Suppose k(f) = 0. Calculate f.
-1, 8
Suppose 2*r + 5 = 3*r. Let i(c) be the third derivative of 1/45*c**r - 1/9*c**3 + 0 + 0*c - 1/36*c**4 + c**2. Solve i(l) = 0 for l.
-1/2, 1
Let r(n) be the third derivative of -n**5/60 + n**4/24 + n**3/3 + 7*n**2. Solve r(g) = 0 for g.
-1, 2
Let v(u) be the second derivative of u**7/24 + 3*u**6/40 - 19*u**5/80 - 41*u**4/48 - u**3 - u**2/2 + 24*u. Factor v(a).
(a - 2)*(a + 1)**3*(7*a + 2)/4
Let z(m) be the second derivative of -m**6/6 - m**5/4 + 6*m. Suppose z(w) = 0. Calculate w.
-1, 0
Let h(z) be the first derivative of 28*z**5/45 + 16*z**4/9 + 44*z**3/27 + 4*z**2/9 + 56. Determine a so that h(a) = 0.
-1, -2/7, 0
Let v be (-1 + 4 - 1)/3. Let c(z) be the second derivative of v*z**3 + 2*z**2 + 0 + 1/12*z**4 - z. Find q, given that c(q) = 0.
-2
Let t(m) be the third derivative of 0*m**3 + 1/165*m**5 + 0*m + 0*m**4 + 1/1155*m**7 + 1/220*m**6 - 5*m**2 + 0. Factor t(y).
2*y**2*(y + 1)*(y + 2)/11
Let g(p) = 4*p**3 - 3*p**2 - 3*p + 4. Let y(r) = -2*r**3 + 5*r - 8 + 5*r**2 - 4*r**3 - r**3 + r**2. Let w(z) = 5*g(z) + 3*y(z). Suppose w(u) = 0. What is u?
-1, 2
Factor 2*x + 661*x**2 + x - 658*x**2.
3*x*(x + 1)
Let q(t) = -3*t**2 + 2*t + 1. Let l be q(-1). Let i be (-3 - -3)/(l - -2). Find v, given that -3/2*v**4 - 3/4*v**3 + 0*v + 0*v**2 + i - 3/4*v**5 = 0.
-1, 0
Let w(v) = 2*v**2 - 2*v. Let z be w(2). Let f = 6 - z. Suppose r - 4*r**3 - 3*r + 12*r**3 + 6*r**f = 0. What is r?
-1, 0, 1/4
Let r(b) = -2*b - 6. Let c be r(-5). Factor 6*a + 7*a**4 - a**4 - 8*a**3 - 2 - 2*a**5 - c*a**2 + 4*a**3.
-2*(a - 1)**4*(a + 1)
Let h(z) be the first derivative of -2*z**5/25 - z**4/30 + 15. Factor h(n).
-2*n**3*(3*n + 1)/15
Suppose -2*o + 14 = -0*z - 2*z, -8 = 2*z. Let k(w) be the third derivative of 1/60*w**4 + 0*w + 0*w**o + 2*w**2 + 1/75*w**5 + 0. Factor k(y).
2*y*(2*y + 1)/5
Factor -2*u**3 - 4*u**3 + 4*u**3 - 2*u**4.
-2*u**3*(u + 1)
Let u(n) be the second derivative of -n**7/98 - n**6/35 + n**4/14 + n**3/14 - 2*n. Let u(i) = 0. Calculate i.
-1, 0, 1
Let -2/9*r + 0 - 2/3*r**3 - 2/9*r**4 - 2/3*r**2 = 0. Calculate r.
-1, 0
Let k(l) be the second derivative of l**7/1680 - l**5/240 + l**3/2 + l. Let z(o) be the second derivative of k(o). Suppose z(j) = 0. Calculate j.
-1, 0, 1
Let h(x) = -7*x**3 + 4*x**2 + 11*x. Let n(v) = -4*v**3 + 2*v**2 + 6*v. Let k = -29 + 40. Let j(b) = k*n(b) - 6*h(b). Let j(w) = 0. What is w?
-1, 0
Suppose -3*y = -2*y - 3*g - 2, 0 = -y + 4*g + 2. Factor -y*l + 1/2*l**2 + 2.
(l - 2)**2/2
Let z = -358/5 - -376/5. Let h be (54/15)/(-3) - -4. Factor 4/5 + h*y**2 + z*y.
2*(y + 1)*(7*y + 2)/5
Factor 9/2*j**4 - 4*j + 37/2*j**2 - 2 - 17*j**3.
(j - 2)*(j - 1)**2*(9*j + 2)/2
Let u(v) be the third derivative of v**8/30240 - v**7/1890 + v**6/270 + v**5/12 - 4*v**2. Let h(q) be the third derivative of u(q). Solve h(r) = 0 for r.
2
Let v(g) = g**3 + 5*g**2 + 2*g - 5. Let h be v(-4). Determine i, given that 4*i - 3 - h*i**2 + 4*i + 5*i - 7*i = 0.
1
Suppose 9*b = -0*b. Let o = 31/84 + -1/28. Factor 2/3*w**4 - 1/3*w + 0*w**3 + b - 2/3*w**2 + o*w**5.
w*(w - 1)*(w + 1)**3/3
Suppose -s - g - 31 = 0, 3*s + 3*g = s - 63. Let u = s - -121/4. Let 0*w**3 + 0*w + 1/2*w**2 - 1/4*w**4 - u = 0. Calculate w.
-1, 1
Suppose -s - 7 = -3*o, -3*o + 3*s = -4 - 5. Find i such that 1/5*i**o - 2/5*i + 1/5 = 0.
1
Let l(s) be the second derivative of 1/21*s**3 + 1/42*s**4 + 0 + 0*s**2 - 2*s. Factor l(p).
2*p*(p + 1)/7
Let o**4 + 2*o - 6*o**2 + 6*o + 0 - 3 = 0. What is o?
-3, 1
Factor -12 - 4*i**3 - 5 + 17 + 24*i**2.
-4*i**2*(i - 6)
Let q = 77 - 77. Factor q*p - 2/7*p**2 + 0.
-2*p**2/7
Let q = 131 - 11003/84. Let a(d) be the third derivative of 0*d - 1/420*d**6 - 1/105*d**5 - q*d**4 + 0 + 0*d**3 + d**2. Factor a(u).
-2*u*(u + 1)**2/7
Let j(w) = w**2 + 3. Let n(o) = -2*o**2 + o - 7. Let b(s) = -10*j(s) - 4*n(s). Determine h so that b(h) = 0.
-1
Let d(f) = f**3 + 5*f**2 + 3*f + 5. Let c be d(-4). Suppose 0 = 4*g - c*g + 10. Let x**2 + 5*x + x**2 - g*x**4 - 5*x = 0. What is x?
-1, 0, 1
Let d(c) be the first derivative of -14*c**3/39 - 2*c**2/13 + 3. Find w such that d(w) = 0.
-2/7, 0
Factor 21*k**3 + 1 - 6*k**2 - 11*k**4 - 1 + 23*k**4.
3*k**2*(k + 2)*(4*k - 1)
Let y = -5 - -5. Let m = y + 2. Factor -r - r**5 + 3*r**4 + 2*r**5 + 2*r**3 - 1 - m*r - 2*r**2.
(r - 1)*(r + 1)**4
Let y(p) be the first derivative of -2 + 1/24*p**4 + 1/6*p**3 + 1/4*p**2 + 1/6*p. Find n such that y(n) = 0.
-1
Let l be 18/30 - 88/(-415). Let j = l + -1/83. Factor 0 - j*d + 2/5*d**2.
2*d*(d - 2)/5
Suppose -13 = -7*k + 22. Find n, given that 2/7*n**k - 2/7*n**4 + 2/7*n**2 - 6/7*n**3 + 0 + 4/7*n = 0.
-1, 0, 1, 2
Let f(c) be the second derivative of -c**6/30 + 3*c**5/20 - c**4/4 + c**3/6 - 7*c. Determine p so that f(p) = 0.
0, 1
Suppose -6 = 5*i + 4*t + 4, -5*i - 15 = 5*t. Suppose -4*r + 5*s + 5 = -3*r, -i*r + 3 = -3*s. Find x, given that x - x - x + x**3 + r*x**3 = 0.
-1, 0, 1
Let d(b) be the third derivative of -1/120*b**5 + 1/6*b**3 + 0*b + 0 - 1/48*b**4 - 1/720*b**6 + b**2. Let w(y) be the first derivative of d(y). Factor w(p).
-(p + 1)**2/2
Let n = 5/4 + -7/6. Let h(i) be the third derivative of 0*i**3 - 5/336*i**8 - 7/40*i**6 + 2*i**2 + 0*i - n*i**4 + 11/60*i**5 + 17/210*i