
Let j be 1/(-6) - (-481)/78. Let a(n) be the third derivative of 0*n**3 + n**2 + 1/150*n**5 + 0*n - 1/525*n**7 + 0 + 0*n**4 + 0*n**j. Factor a(f).
-2*f**2*(f - 1)*(f + 1)/5
Let p(c) be the first derivative of 1/24*c**3 + 1/12*c**4 + 4 + 3/80*c**5 + 0*c**2 + 2*c. Let n(r) be the first derivative of p(r). Suppose n(l) = 0. What is l?
-1, -1/3, 0
Let h be (-7)/(-315)*(2 - -1). Let u(r) be the third derivative of 1/300*r**5 + 0 + 1/40*r**4 + 0*r + h*r**3 - r**2. Find z, given that u(z) = 0.
-2, -1
Let w(q) be the third derivative of -q**5/60 - q**4/4 + 3*q**3/2 + q**2. Let z be w(-7). Factor 3*y**z + 0*y**2 + 42*y**3 - 4*y - y**2.
2*y*(3*y + 1)*(7*y - 2)
Solve -8/17*g**3 - 14/17*g**2 + 2/17 - 4/17*g = 0 for g.
-1, 1/4
Let o be 86/(-90) - 0 - (1 + -2). Let i(u) be the third derivative of -4/315*u**7 + 0*u**3 - 1/18*u**5 - o*u**6 + 0 - 1/36*u**4 + u**2 + 0*u. Factor i(y).
-2*y*(y + 1)*(2*y + 1)**2/3
Let i(r) be the second derivative of 3*r**5/20 + r**4/4 - r**3 + 5*r. Let i(a) = 0. What is a?
-2, 0, 1
Let c be ((-1)/(-219))/((-6)/(-12)). Let w = 448/1095 - c. Factor 4/5*t - 4/5*t**3 - w*t**4 + 0*t**2 + 2/5.
-2*(t - 1)*(t + 1)**3/5
Let w be (-6 - 117/(-18))*3. Factor 3/4*p**3 + 0 - w*p**2 + 3/4*p.
3*p*(p - 1)**2/4
Suppose -2*q + 0*f - 5 = f, 5*q + 10 = -2*f. Let t(j) be the first derivative of q*j - 1/3*j**3 - 1 + 0*j**2 + 1/4*j**4. Factor t(c).
c**2*(c - 1)
Suppose -3*f - 1 = -2*f. Let w be (0 + f)*(5 + -5). Determine c, given that w*c + 0 + 1/3*c**2 = 0.
0
Let g = -457 + 461. Factor 3/4*r - 3/4*r**g + 0 - 9/4*r**2 + 9/4*r**3.
-3*r*(r - 1)**3/4
Let o(s) = s**2 + s + 6. Let f be o(0). Let c = 17 - f. Solve -d**2 + c - 11 - d = 0 for d.
-1, 0
Let w(s) be the first derivative of 5*s**3/3 + 5*s**2 + 9. Determine z, given that w(z) = 0.
-2, 0
Factor 6*h**5 + 3*h**2 - 9*h**4 + 12*h**2 + 3*h + 27*h**3 + 30*h**4.
3*h*(h + 1)**3*(2*h + 1)
Let d(o) be the third derivative of 0*o + 5*o**2 + 0 - 3/8*o**4 + 1/20*o**5 + 0*o**3. Factor d(q).
3*q*(q - 3)
Let n(x) = x + 6. Let l be n(-8). Let p be -3 + 3*(l - -3). Solve -4/3*i**3 - 2/3*i**2 + p - 2/3*i**4 + 0*i = 0.
-1, 0
Let b(a) be the first derivative of 13 + 8*a + a**4 + 3 - 6*a**2 - 24. Factor b(j).
4*(j - 1)**2*(j + 2)
Let q(c) = 20*c**2 + 72*c. Let f(n) = 7*n**2 + 24*n. Let s(p) = 8*f(p) - 3*q(p). Factor s(h).
-4*h*(h + 6)
Factor -1/4*g - 3/4*g**4 + 5/4*g**3 + 0 - 1/4*g**2.
-g*(g - 1)**2*(3*g + 1)/4
Let d(u) be the first derivative of u**6/45 + 2*u**5/25 + u**4/10 + 2*u**3/45 - 9. Factor d(k).
2*k**2*(k + 1)**3/15
What is s in 0 - 3*s**3 + 0*s**2 + 3/2*s**5 + 3/2*s + 0*s**4 = 0?
-1, 0, 1
Let k(r) = -2*r**3 + 11*r**2 - 8*r - 1. Let o(w) = -45*w**2 + 92*w + 3 + 59*w - 118*w + 9*w**3. Let z = 33 - 12. Let u(y) = z*k(y) + 5*o(y). Factor u(g).
3*(g - 1)*(g + 1)*(g + 2)
Let g(x) be the third derivative of -x**7/4410 + 2*x**6/315 - 8*x**5/105 - 5*x**4/24 - 2*x**2. Let o(b) be the second derivative of g(b). Factor o(i).
-4*(i - 4)**2/7
Let u(v) = -3*v**2 - 64*v - 128. Let b(g) = -20*g**2 - 416*g - 832. Let t(o) = 5*b(o) - 32*u(o). Suppose t(p) = 0. What is p?
-4
Let y = -71 + 48. Let p be (-10)/35 + y/(-7). Let p*x**3 + x + 4*x**2 + 2*x**3 + x**3 - 3*x**3 = 0. What is x?
-1, -1/3, 0
Let u(n) = -2*n**4 + 2*n + 2. Let c(m) = m**3 - m - 1. Let w(l) = -4*c(l) - 2*u(l). Factor w(y).
4*y**3*(y - 1)
Let a be (-3)/4 + 32 + -31. Find u, given that -a*u**2 - 1/4*u + 0 = 0.
-1, 0
Let u be (-3)/8 + 30/80. Determine m so that -4/9*m**2 - 2/9*m**5 + u*m**3 + 4/9*m**4 + 2/9*m + 0 = 0.
-1, 0, 1
Suppose -14*h**2 - 18/7 - 12*h = 0. What is h?
-3/7
Let b(q) be the third derivative of q**8/168 - 2*q**7/35 + 7*q**6/30 - 8*q**5/15 + 3*q**4/4 - 2*q**3/3 - 14*q**2. Factor b(p).
2*(p - 2)*(p - 1)**4
Let f(a) = -7*a**2 - a - 1. Let s be f(-3). Let l = 185/3 + s. Let 2*c - 4/3 - l*c**2 = 0. Calculate c.
1, 2
Let u(a) = a**2 + 1. Let s(r) = -8*r**2 - 7. Let x(y) = 4*s(y) + 28*u(y). Suppose x(q) = 0. What is q?
0
Let n(v) be the third derivative of 0*v + 1/30*v**5 + 0 + 4/3*v**3 - 2*v**2 + 1/3*v**4. Find k, given that n(k) = 0.
-2
Let o(y) be the first derivative of 1/9*y**4 + 6 + 0*y - 2/27*y**6 + 2/27*y**3 + 0*y**2 - 2/45*y**5. Find h such that o(h) = 0.
-1, -1/2, 0, 1
Let v(h) be the second derivative of -h**7/1680 - h**6/360 - h**5/240 + 5*h**3/6 - 6*h. Let c(f) be the second derivative of v(f). Factor c(o).
-o*(o + 1)**2/2
Let w(m) be the second derivative of -1/4*m**4 + 0 + 0*m**2 + 0*m**3 + 27/20*m**5 - 27/10*m**6 + 7*m + 27/14*m**7. Suppose w(k) = 0. Calculate k.
0, 1/3
Let k(r) be the first derivative of 0*r**2 - 1 + 0*r - 1/8*r**4 + 1/6*r**3. Solve k(j) = 0 for j.
0, 1
Let i be (-6)/(-5 + -1) + 1 + 2. Factor 0*k - 1/3*k**3 - 1/3*k**i + 0*k**2 + 0.
-k**3*(k + 1)/3
Let f(l) = -l**3 + l**2 + 1. Let g(u) = -16*u + 25*u**3 + 5*u**3 - 2 + 0 + 46*u**2. Let m(v) = -2*f(v) - g(v). Suppose m(d) = 0. Calculate d.
-2, 0, 2/7
Let g be (-9)/(-2) + (0 - 4). Suppose 0*p + 10 = 5*p. Solve 1/4*r + g*r**p + 1/4*r**3 + 0 = 0.
-1, 0
Let w(l) = -9*l + 156. Let x be w(17). Solve -2/3*i - i**2 - 1/3*i**x + 0 = 0.
-2, -1, 0
Suppose -5*g - 21 = -36. Let w(y) be the second derivative of 3*y**3 + 2*y**4 + 0 + g*y + 1/2*y**5 + 2*y**2. Suppose w(b) = 0. What is b?
-1, -2/5
Let r(a) be the third derivative of -a**6/60 + a**5/10 + a**4/12 - a**3 - 2*a**2 - 34. Factor r(u).
-2*(u - 3)*(u - 1)*(u + 1)
Let k(p) be the first derivative of 1 + 1/60*p**5 - 1/6*p**2 + 1/36*p**4 - 1/18*p**3 - 3*p. Let d(i) be the first derivative of k(i). Find j such that d(j) = 0.
-1, 1
Factor 3/7*o**2 + 3/7*o**4 - 6/7*o**3 + 0*o + 0.
3*o**2*(o - 1)**2/7
What is a in 14/5*a**3 - 4/5*a**2 - 2/5*a - 8/5*a**4 + 0 = 0?
-1/4, 0, 1
Let i(x) = 4*x**5 + 4*x**4 - 8*x**3 - 2*x**2 + 10*x - 14. Let y(w) = w**5 - w**4 + w**3 - w - 1. Let q(d) = -i(d) + 6*y(d). Suppose q(n) = 0. What is n?
-1, 1, 2
Let x(r) be the third derivative of r**6/900 - r**5/150 + r**4/60 - r**3/3 + 2*r**2. Let c(n) be the first derivative of x(n). Factor c(y).
2*(y - 1)**2/5
Let d = 5 - 2. Suppose 3*a + b = 9, -3*a + 5*b + d = -2*a. Suppose 4*m - a*m + m**3 + m + 3*m**2 = 0. What is m?
-2, -1, 0
Let x(f) = -2*f**2 - 11*f + 6. Let u be x(-6). Suppose -4*t + 23 - 3 = u. Factor 2/11*d**t + 0*d**4 + 2/11*d - 4/11*d**3 + 0*d**2 + 0.
2*d*(d - 1)**2*(d + 1)**2/11
Let y(l) be the second derivative of l**5/140 + l**4/28 - 2*l**2/7 - 13*l. Factor y(r).
(r - 1)*(r + 2)**2/7
Let t(f) be the third derivative of f**5/240 + f**4/96 + 7*f**2. Factor t(x).
x*(x + 1)/4
Let z(j) be the third derivative of 1/72*j**4 + 1/180*j**5 + 0*j**3 + 3*j**2 + 0 + 0*j. Factor z(h).
h*(h + 1)/3
Factor 42*r + 63*r**2 + 38*r**3 + 15*r**4 + 6 + 13*r**3 - 9*r.
3*(r + 1)**3*(5*r + 2)
Let t(d) = d**3 + 6*d + 7. Let a(u) = u**3 + 1. Let b(z) = 3*a(z) - t(z). Solve b(n) = 0.
-1, 2
Let z be 3/(-2)*(-8)/4. Let j(c) be the first derivative of 0*c + 2/5*c**5 + 2/3*c**z - c**4 + 0*c**2 + 2. Find u such that j(u) = 0.
0, 1
Let f = 6 + -2. Let y(l) be the third derivative of 0*l - l**2 + 0 + 1/6*l**f - 1/15*l**5 - 1/6*l**3. Factor y(i).
-(2*i - 1)**2
Let n be (-4 - -1 - 0) + 6. What is p in -3*p - n*p**2 + p + p = 0?
-1/3, 0
Determine g, given that -4*g - 2*g + g**2 + g**2 = 0.
0, 3
Suppose -4*b = -3*o + 8, -2*o + 18 - 14 = -2*b. Factor 1/4*t**2 + o - 1/2*t.
t*(t - 2)/4
Let -38/5*d**2 - 2/5 - 21/5*d**3 - 19/5*d = 0. Calculate d.
-1, -2/3, -1/7
Let l(p) = p**2 - 9*p + 4. Let q be l(9). Factor -23 - 8*r**3 - 4*r**2 + 23 - q*r**4.
-4*r**2*(r + 1)**2
Let p(i) be the second derivative of i**4/36 - i**3/6 + i**2/3 + 5*i. Let p(k) = 0. Calculate k.
1, 2
Factor 366 + 387*y**2 + 17*y**4 - 115*y**3 - 3*y**5 + y**5 - 648*y + y**5 + 66.
-(y - 4)**2*(y - 3)**3
Let j be (-28 + 1)/(-2 + 3). Let b = 82/3 + j. Determine m so that -b*m**3 + m**2 + 0*m - 4/3 = 0.
-1, 2
Factor -3/11*i**2 + 1/11*i**4 + 0 + 0*i**3 + 2/11*i.
i*(i - 1)**2*(i + 2)/11
Suppose -s + 3*s - 72 = 0. Let j be 21/s - 2/6. Solve 1/4*h**3 + 0 + 1/2*h**2 + j*h = 0.
-1, 0
Let s(d) = -d**2. Let u(x) = -x - 1. Let c(m) = s(m) + 4*u(m). Factor c(n).
-(n + 2)**2
Let p(m) be the first derivative of -m**6/80 - m**5/40 + 3*m**2 - 4. Let r(a) be the second derivative of p(a). Factor r(g).
-3*g**2*(g + 1)/2
Let z = 3622/3 - 1207. Factor -k**2 + 4/3*k + 4/3 + z*k**4 - 2/3*k**3.
(k - 2)**2*(k + 1)**2/3
Let j(k) = -k**3 - 5*k**2 - k +