+ 2)/4
Let v(x) be the second derivative of x**5/60 + x**4/12 + x**3/9 - 20*x. Determine n, given that v(n) = 0.
-2, -1, 0
Factor -2/15*r**2 + 0 + 4/5*r.
-2*r*(r - 6)/15
Let y = 0 + -1. Let v = -1 - y. Factor -2*l + v - 4*l**2 - 4 + 2*l**2 + 8*l.
-2*(l - 2)*(l - 1)
Let t = 10 + -2. Let n = t - 6. Factor -1 + 2*a**n - a**3 - 5*a**2 + 0*a**2 - 3*a.
-(a + 1)**3
Let q(r) be the first derivative of r**5/4 + 5*r**4/4 + 5*r**3/6 - 5*r**2/2 - 15*r/4 - 14. Suppose q(o) = 0. What is o?
-3, -1, 1
Let g(u) be the first derivative of -8/3*u - 470/9*u**3 + 4 + 1936/15*u**5 + 11/12*u**4 + 58/3*u**2 + 1331/18*u**6. Factor g(r).
(r + 1)**2*(11*r - 2)**3/3
Let u(q) = -4*q**5 + 12*q**4 - 14*q**3 + 10*q**2 + 24*q - 10. Let z(j) = -j**5 + j**4 + j**3 + j**2 + j. Let g(n) = u(n) - 6*z(n). Factor g(o).
2*(o - 1)**3*(o + 1)*(o + 5)
Let x(o) be the third derivative of -o**8/1008 + o**7/630 + o**6/180 - o**5/90 - o**4/72 + o**3/18 - 2*o**2. Factor x(j).
-(j - 1)**3*(j + 1)**2/3
Suppose -2*l = l + 3. Let k be (l/(-6))/((-3)/(-12)). Solve k*q + 0 + 2/3*q**2 = 0 for q.
-1, 0
Suppose -3*j**4 - 3*j**5 - 2*j**5 + 3*j**2 - 2*j + 0*j**5 + 7*j**3 = 0. What is j?
-1, 0, 2/5, 1
Let l(y) = -y**2 + 6*y + 4. Let g be l(5). Let v be (12/g)/(28/6). Solve -2/7*i**4 + 2/7*i**2 - 2/7*i + 0 + v*i**3 = 0.
-1, 0, 1
Let r be 14/14*1/2. Let m(b) be the second derivative of -b + 1/3*b**4 - r*b**5 + 0 + 5/3*b**3 - 2*b**2. Factor m(h).
-2*(h - 1)*(h + 1)*(5*h - 2)
Let y = 1/265 - -1049/2915. Let d = -74 + 77. Let 14/11*p**4 + 4/11*p**d - 16/11*p**2 + y*p - 8/11*p**5 + 2/11 = 0. Calculate p.
-1, -1/4, 1
Let x(i) be the first derivative of 5 + 1/12*i**3 + i + 5/8*i**2. Let x(w) = 0. What is w?
-4, -1
Let v(f) = 21*f**3 - 42*f**2 + 27*f - 12. Let i(y) = 21*y**3 - 43*y**2 + 28*y - 11. Let b(r) = 6*i(r) - 5*v(r). Factor b(l).
3*(l - 1)**2*(7*l - 2)
Let b be (-58)/14 + (-4)/(-28). Let f be 15/(-50)*b/3. Factor -2/5*o + 0 + 2/5*o**2 + f*o**3 - 2/5*o**4.
-2*o*(o - 1)**2*(o + 1)/5
Let r(u) be the second derivative of -u**6/45 + u**5/10 - u**4/6 + u**3/9 - 5*u. Factor r(k).
-2*k*(k - 1)**3/3
Let x be 1127/5 + (-22)/55. Let u be 30/x*(2 + 1). Suppose u*o**4 + 2/5*o**3 - 6/5*o**2 - 2/5*o + 4/5 = 0. Calculate o.
-2, -1, 1
Suppose 0 = -9*c + 13*c. Let z(l) be the second derivative of 0*l**5 + c - 1/120*l**6 + 1/48*l**4 + 0*l**3 + 0*l**2 - l. Solve z(f) = 0 for f.
-1, 0, 1
Suppose 5*d - 31 = -1. Let o = d - 4. Find w, given that -2 - 4*w**2 + 3*w**o + w + 3*w - w**2 = 0.
1
Let l = -13/16 - -113/80. Factor 0 + 3/5*s**2 - 3/5*s**4 + 3/5*s**3 - l*s.
-3*s*(s - 1)**2*(s + 1)/5
Let x be 4 + -2 - (1 + -1). Suppose -x*v + 0*v = 4, -5*o = -2*v - 24. Let 6*g + 2 + 1/2*g**o + 3*g**3 + 13/2*g**2 = 0. What is g?
-2, -1
Factor 14/9*z - 8/9*z**2 + 4/9.
-2*(z - 2)*(4*z + 1)/9
Suppose 0 = 3*y - 2 - 4. Let s(c) = -4*c**3 - 17*c**2 - 9*c - 9. Let q(x) = -x**3 - 4*x**2 - 2*x - 2. Let o(t) = y*s(t) - 9*q(t). Factor o(b).
b**2*(b + 2)
Let k be (-24)/18 + 4 + 0. Factor k*m**2 + 2/3 + 10/3*m.
2*(m + 1)*(4*m + 1)/3
Let o(g) = 2*g - 13. Let b be o(9). Let x(m) be the third derivative of -1/12*m**4 + 0 + 0*m - 3*m**2 - 1/30*m**b + 0*m**3. Factor x(k).
-2*k*(k + 1)
Let o(y) be the second derivative of 7*y**5/20 + y**3 + 4*y. Let d(s) = s**3 + s. Let r(h) = 6*d(h) - o(h). Determine z so that r(z) = 0.
0
Let t(l) = 3*l**4 + 2*l**3 + 3*l**2 + 4. Let u(m) = m**4 + m**3 + m**2 + 1. Let j(r) = 5*t(r) - 20*u(r). Solve j(y) = 0.
-1, 0
Factor 25 + 7*k + 13*k - 4*k**3 + 0*k**3 + 4*k**2 - 13.
-4*(k - 3)*(k + 1)**2
Suppose -f + 21 = 2*f + 5*y, 4*f = -4*y + 20. Suppose 0 = 6*h - 3*h. Find i such that h*i + 0 + 1/4*i**f = 0.
0
Let q(j) be the first derivative of -3 - 2/45*j**5 + 0*j**2 - 1/27*j**6 + 2/27*j**3 + 1/18*j**4 + 0*j. Factor q(z).
-2*z**2*(z - 1)*(z + 1)**2/9
Let h(z) = 2*z**2 + 2*z. Let r = -9 - -7. Let j be h(r). Factor 52/9*d**3 - 28/9*d**j + 2/3*d**5 - 4/9 - 16/3*d**2 + 22/9*d.
2*(d - 1)**4*(3*d - 2)/9
Let u(q) be the third derivative of -1/1008*q**8 + 1/180*q**5 - q**2 + 0*q**4 + 1/210*q**7 + 0*q + 0*q**3 - 1/120*q**6 + 0. Let u(k) = 0. What is k?
0, 1
Let h(d) be the first derivative of 0*d - 1/15*d**3 - 1/25*d**5 + 1/10*d**4 + 0*d**2 - 3. Suppose h(q) = 0. Calculate q.
0, 1
Let v(o) = o**3 + o**2 - o. Let y(i) = -2*i**3 - 3*i**2 - 2. Let a = -2 + 4. Let n be -4*3/(-24)*a. Let f(w) = n*y(w) + 3*v(w). What is x in f(x) = 0?
-1, 2
Let w(k) be the second derivative of -k**4/114 + 5*k**3/57 - 4*k**2/19 + 2*k. Solve w(r) = 0 for r.
1, 4
Let z(f) be the first derivative of -3*f**5/25 - 3*f**4/20 + 1. What is m in z(m) = 0?
-1, 0
Determine r, given that 54*r**4 - 35*r - 65*r - 90*r**2 + 66*r - 54*r**3 - 7 + 3 = 0.
-1/3, 2
Suppose -4*h = u + 3 + 2, 5*h - 4*u + 1 = 0. Let z(p) = p**3 - p**2 - p - 1. Let l(d) = -d**3 - 5*d**2 + 13*d + 1. Let n(r) = h*l(r) - 4*z(r). Factor n(g).
-3*(g - 1)**3
Let x = 1024 + -7166/7. Factor 6/7*p**3 + 4/7*p**2 - x*p + 0.
2*p*(p + 1)*(3*p - 1)/7
Let l(c) be the first derivative of c**6/9 - 14*c**5/15 + 3*c**4 - 44*c**3/9 + 13*c**2/3 - 2*c - 19. Factor l(v).
2*(v - 3)*(v - 1)**4/3
Let z(g) be the third derivative of 0*g**4 - 4*g**2 + 0 + 1/315*g**7 + 0*g - 1/180*g**6 + 0*g**3 - 1/90*g**5 + 1/504*g**8. Solve z(h) = 0 for h.
-1, 0, 1
Let i(r) be the third derivative of -r**6/210 - r**5/35 - r**4/14 - 2*r**3/21 + 15*r**2. Find f, given that i(f) = 0.
-1
What is z in -3*z**3 + 8*z**3 - 5*z**3 + 4*z**3 + 8*z**2 = 0?
-2, 0
Let c(b) be the third derivative of 0*b**7 + 1/75*b**5 + 0*b - 3*b**2 + 1/840*b**8 + 0 + 1/20*b**4 - 1/75*b**6 - 2/15*b**3. Let c(i) = 0. Calculate i.
-2, -1, 1
Let o(m) = -m**3 + 4*m**2 + 2. Let x be o(4). Solve -9*k + 3*k + 6*k - k**x + 2*k**3 = 0 for k.
0, 1/2
Let d(r) = -7*r**3 - 22*r**2 - 22*r - 2. Let w(l) = -8*l**3 - 23*l**2 - 23*l - 3. Let z(t) = -3*d(t) + 2*w(t). Factor z(g).
5*g*(g + 2)**2
Factor 0*x**2 + 2*x**2 - 3 + 37 + 16*x - 2.
2*(x + 4)**2
Let j(d) = d + 4. Let q be j(5). Suppose -22 = -s - 6. Determine f so that -2*f**3 - q*f**5 + 10*f - 2*f + 18*f**4 - s*f**2 - 2 + 3*f = 0.
-1, 1/3, 2/3, 1
Let m = -1/536 - -539/1608. Find x such that 0 + x**3 - 1/3*x**5 + 1/3*x**4 - 2/3*x - m*x**2 = 0.
-1, 0, 1, 2
Let n(o) = -o**2 - 11*o - 8. Let k be n(-10). What is m in -m - m**2 + 0*m + k + m**3 - 2 + m**4 = 0?
-1, 0, 1
Let z = -1 + -3. Let n be (-2 - 1)/30*z. Let 0*p + 0 + n*p**4 - 2/5*p**5 + 2/5*p**3 - 2/5*p**2 = 0. Calculate p.
-1, 0, 1
Let o(x) be the third derivative of x**8/168 - x**7/105 - x**6/15 + 2*x**5/15 + 11*x**2. Factor o(k).
2*k**2*(k - 2)*(k - 1)*(k + 2)
Factor 60 + 132*h**2 + 28*h**3 + 72*h + 24 - 116.
4*(h + 1)*(h + 4)*(7*h - 2)
Suppose 2*s**4 + 13/2*s**2 + 9/2 - 10*s**3 + 15*s = 0. Calculate s.
-1/2, 3
Suppose 3*s - 5*r = 22, 5*r + 12 = 5*s - 18. Suppose s = 4*n - 8. Suppose -6*z**3 + 4*z**n - 4*z + 2*z**2 - 2 + 6*z = 0. What is z?
-1, 1
Let a be 0/((-3 - 0)/1). Suppose 3*g - 19 + a = -2*h, 0 = -g + 5. Factor 3*b**h - 2*b + 6*b**3 - 2*b**3 - 2*b**3 - 2*b**4 - b**2.
-2*b*(b - 1)**2*(b + 1)
Factor 1/2*a**4 - 5/2*a**2 + 2 + 3/2*a - 3/2*a**3.
(a - 4)*(a - 1)*(a + 1)**2/2
Let g(y) be the third derivative of y**8/1512 - y**7/189 + y**6/54 - y**5/27 + 5*y**4/108 - y**3/27 - 2*y**2. Solve g(z) = 0.
1
Let a(q) = 2*q**2 - 2. Suppose 1 = -4*f - 7. Let y(w) = -w**2 + 1. Let d(s) = f*a(s) - 5*y(s). Suppose d(j) = 0. What is j?
-1, 1
Let p(f) be the first derivative of f**6/60 - f**4/4 - 2*f**3/3 - f**2/2 + 6. Let r(x) be the second derivative of p(x). Factor r(i).
2*(i - 2)*(i + 1)**2
Let r(k) be the second derivative of 0*k**3 - 1/30*k**5 + 0 - 2*k + 1/18*k**4 + 0*k**2. Find c such that r(c) = 0.
0, 1
Suppose -5*x = a + 15, -3*x - 3 = -2*x. Suppose -o + 5*o = a. Factor -s**2 + 2 + 0*s**2 + o - s**2.
-2*(s - 1)*(s + 1)
Let v(m) = -2*m**2 + m + 3. Suppose 0 = 3*t - 28 + 1. Let y(f) = -3*f**2 + 2*f + 0*f**2 + t - 4. Let c(k) = -8*v(k) + 5*y(k). Let c(s) = 0. Calculate s.
-1
Let h = 3 + -6. Let v be h/(12/10)*-2. Suppose 3*s**5 + 3*s**5 - v*s**5 + s**4 = 0. Calculate s.
-1, 0
Factor 3*n**4 - 2*n**3 - 4*n**5 - 4*n - 7*n**4 - 4 + 5*n**3 + 5*n**3 + 8*n**2.
-4*(n - 1)**2*(n + 1)**3
Let n(u) = 7*u**2 + 2*u - 9. Let c(o) = 3*o**2 + o - 4. Let t(y) = -5*c(y) + 2*n(y). Factor t(k).
-(k - 1)*(k + 2)
Factor -4*r**4 - 3*r**2 + 0*r**3 - 6*r**3 + r**4.
-3*r**2*(r + 1)**2
Let o(g) be the first derivative 