 given that g(n) = 0.
0, 1/3
Let o(k) be the third derivative of k**8/20160 + k**7/1260 + k**6/240 + k**5/20 + 2*k**2. Let v(j) be the third derivative of o(j). Factor v(a).
(a + 1)*(a + 3)
Let h(q) = q. Let b be h(0). Let o(z) be the third derivative of b + 0*z + 3*z**2 - 1/90*z**5 - 1/9*z**3 + 1/18*z**4. Find s, given that o(s) = 0.
1
Suppose -3 + 12 = -3*k, 5*k = 3*v - 21. Suppose v*w - 2 = -0. Solve 1/4*o**2 + w - o = 0 for o.
2
Let m = 151 - 149. What is n in 1/4*n**m + 3/4*n + 1/2 = 0?
-2, -1
Let a = 24 + -22. Let d = a + -2. Suppose 0*r - 1/3*r**4 + d + 2/3*r**3 - 1/3*r**2 = 0. Calculate r.
0, 1
Let f = -2979/5 - -596. Factor 1/5*y**2 + f*y - 2/5.
(y - 1)*(y + 2)/5
Let d(i) = -i**2 + 5. Suppose 12*p + 10 = 7*p. Let f(a) = 6*a**2 - 36. Let b(k) = p*f(k) - 15*d(k). Find o, given that b(o) = 0.
-1, 1
Suppose 2*l + 16 = 5*o - 6, 0 = -o - 2*l + 2. Let x(y) be the second derivative of 0 - 1/36*y**o - 1/9*y**3 - 1/6*y**2 + 2*y. Find p such that x(p) = 0.
-1
Suppose 0 = -3*v + 3*b - 5*b - 4, -3*b = v + 6. Solve 3/5*a**2 + 6/5*a + v = 0.
-2, 0
Let k be -8 + 5 - 144/(-40). Find o, given that -1/5*o**3 - 3/5*o + 1/5 + k*o**2 = 0.
1
Let f(i) be the second derivative of -i**7/21 - i**6/5 - i**5/5 + i**4/3 + i**3 + i**2 + 32*i. Factor f(p).
-2*(p - 1)*(p + 1)**4
Suppose -4*f + 17 = 3*q - 0*f, -4*q - f = -14. Factor 0*t**2 - q*t**4 - 3*t**2 + 5*t**4 + t**2.
2*t**2*(t - 1)*(t + 1)
Let y be 3/4 - 6/8. Suppose -2*a = 2*l, y = l + 4*l + a - 4. Factor -l + t**2 + 0*t**2 + 0*t + 0*t.
(t - 1)*(t + 1)
Let j(d) be the first derivative of 6 - 1/8*d**4 + 0*d + 1/3*d**3 - 1/4*d**2. Factor j(k).
-k*(k - 1)**2/2
Find u such that -2/7*u**2 + 0*u + 0 - 2/7*u**3 = 0.
-1, 0
Suppose -3*n + 4 = -2*n. Factor 0*l**2 + 0*l**4 - 2*l**3 + 0*l**2 + 2*l**n.
2*l**3*(l - 1)
Let m be (8 - 136/20)*5/2. Let l(z) be the second derivative of 0 + 0*z**2 + 0*z**m - 2/3*z**4 - 25/21*z**7 + 4*z + 8/5*z**5 - 1/3*z**6. Factor l(w).
-2*w**2*(w + 1)*(5*w - 2)**2
Let t(v) be the third derivative of v**5/30 + v**4/4 + 2*v**3/3 - 40*v**2. Let t(y) = 0. What is y?
-2, -1
Let y = -18 + 20. Factor -b**2 + 5*b**2 - 3*b**2 - 4 + 3*b**y.
4*(b - 1)*(b + 1)
Let t(s) be the second derivative of s**5/10 - s**4 + 4*s**3 - 8*s**2 + 7*s. Suppose t(a) = 0. Calculate a.
2
Let r(o) = -o**2 - 6*o + 2. Let n be r(-6). Factor -4/5*t - 2/5*t**n - 2/5.
-2*(t + 1)**2/5
Let w = 0 + -4. Let o(n) = -n**2 - 5*n - 4. Let q be o(w). Factor 2/7*m**2 - 6/7*m**3 + q*m + 0.
-2*m**2*(3*m - 1)/7
Let h(a) be the third derivative of -a**8/84 + 4*a**7/105 + a**6/15 - 4*a**5/15 - a**4/6 + 4*a**3/3 - 11*a**2. Suppose h(t) = 0. What is t?
-1, 1, 2
Let o be 2/(-3) - 34/(-6). Suppose 5*c - 7*k - 15 = -3*k, k = 4*c - 12. Factor 0*f + 0 + 0*f**c + 0*f**2 - 2*f**o + 1/2*f**4.
-f**4*(4*f - 1)/2
Let k(s) be the second derivative of -5*s**6/6 + 19*s**5/4 - 55*s**4/12 - 5*s**3/2 + 7*s + 4. Determine y so that k(y) = 0.
-1/5, 0, 1, 3
Let a be ((-4)/6*3)/(-1). Factor 4*j + 2*j**3 + 2*j - j**3 + a*j**2 - 5*j.
j*(j + 1)**2
Factor 72*r - 8*r**3 + 0*r**2 - 4/3*r**4 + 108.
-4*(r - 3)*(r + 3)**3/3
Suppose -4*w = w - 10. Let n(h) = -h**2 + 4*h - 1. Let x be n(w). Factor -6*b**2 + 4*b**2 + b**x + b**3.
2*b**2*(b - 1)
Factor -5/3*a**3 + 5/3*a**2 + 0 + 0*a.
-5*a**2*(a - 1)/3
Let c be (-3)/((-12)/4) - -3. Let t(m) be the first derivative of 1 + c*m - 3*m**4 + m**2 - 14/3*m**3. Find j such that t(j) = 0.
-1, -2/3, 1/2
Suppose 2*t - 7 = -3. Factor j**t - 2 + 4*j - 4*j**2 + 3*j**2 - 2*j**2.
-2*(j - 1)**2
Suppose 5*i - 34 = 6. Let j be (4/(-50))/(i/(-40)). Find t, given that 0*t**4 - 2/5*t + 0*t**2 + 0 - j*t**5 + 4/5*t**3 = 0.
-1, 0, 1
Let x be 5/(-3) + 2 - 0. Solve -2/3*d**2 + 2/3*d**4 + 0*d**3 + 0 + x*d - 1/3*d**5 = 0 for d.
-1, 0, 1
Let k(c) be the third derivative of -c**8/84 + c**6/30 + 5*c**2. Determine t, given that k(t) = 0.
-1, 0, 1
Let m = 48 + -46. Let -4*l - 2/3*l**m - 6 = 0. What is l?
-3
Suppose -2*p = 3*p - 20. Let q = -4 + p. Let -4/7*u**2 + 0*u + q - 12/7*u**4 + 2*u**3 = 0. Calculate u.
0, 1/2, 2/3
Determine v, given that 0*v**2 - 3*v**4 - 2*v + v**2 + 126*v**3 - 122*v**3 = 0.
-2/3, 0, 1
Let c be (-4)/(-4)*-10 - 3. Let d(v) = 3*v**2 + 12*v + 9. Let r(l) = 6*l**2 + 25*l + 19. Let f(w) = c*d(w) + 6*r(w). Factor f(g).
-3*(g + 1)**2
Let m be 19/120 + 2/(-16). Let g(f) be the third derivative of -2*f**2 + 0*f**3 + 0 + 0*f - m*f**5 - 1/12*f**4. Factor g(l).
-2*l*(l + 1)
What is g in 0*g**2 + 2*g - 8*g - 2*g**2 = 0?
-3, 0
Let g(d) be the second derivative of d**4/24 - 13*d**3/12 - 7*d**2/2 - 56*d. Factor g(f).
(f - 14)*(f + 1)/2
Solve -1 + 4*j**4 + 1 + 0 = 0.
0
Factor 24/5*o**2 + 0 - 16/5*o - 9/5*o**3 + 1/5*o**4.
o*(o - 4)**2*(o - 1)/5
Let n(h) be the second derivative of -5*h - 1/10*h**5 + 1/6*h**4 + 0 - h**2 + 1/3*h**3. Factor n(t).
-2*(t - 1)**2*(t + 1)
Let b = -231 + 233. What is l in 0*l - 8/3 + 2/3*l**b = 0?
-2, 2
Let r be 1 + -1 + 0 + 4. Factor -2*v**4 + 0*v**4 - 2*v**5 - v**r + v**4.
-2*v**4*(v + 1)
Factor 4*l**2 + 45 - 8*l - 45.
4*l*(l - 2)
Let s(p) be the third derivative of -12*p**5/5 + 2*p**4 - 2*p**3/3 + 8*p**2. Solve s(c) = 0.
1/6
Let r(x) be the second derivative of -x**5/4 - 5*x**4/12 - 5*x. Factor r(k).
-5*k**2*(k + 1)
Let l(h) = 4*h**3 + 2*h**2 - 16*h - 2. Let b(p) = p**3 - p**2 - p - 1. Let a(y) = -6*b(y) + l(y). Factor a(m).
-2*(m - 2)*(m - 1)**2
Solve -5*m**3 + 62*m**2 - 60*m**2 + m**5 - 2*m**5 + 4*m**4 = 0 for m.
0, 1, 2
Let a(x) be the second derivative of x**6/60 - 3*x**5/20 + x**4/2 - 2*x**3/3 - 20*x. Factor a(l).
l*(l - 2)**3/2
Let s(w) be the first derivative of -2 - 1/30*w**5 + 0*w**3 + 1/2*w**2 + 0*w - 1/12*w**4. Let l(i) be the second derivative of s(i). Factor l(k).
-2*k*(k + 1)
Let t(h) be the first derivative of -3*h**5/10 + 3*h**4/2 - h**3 - 3*h**2 + 9*h/2 - 50. Let t(r) = 0. Calculate r.
-1, 1, 3
Let g = 22 + -20. Suppose 6 - 8*d**2 + 9*d**g - 3 + 0*d - 4*d = 0. What is d?
1, 3
Solve -4/7*j**3 + 0*j**2 + 4/7*j + 0 = 0 for j.
-1, 0, 1
Let l(g) be the third derivative of g**6/90 - g**4/18 + 44*g**2. Solve l(s) = 0 for s.
-1, 0, 1
Let t(x) be the second derivative of x**6/10 + x**3/3 - x**2/2 - 3*x. Let o(w) = -13*w**4 - w**2 - 9*w + 5. Let k(y) = 2*o(y) + 9*t(y). Solve k(u) = 0 for u.
-1, 1
Determine d so that -d + 5*d**3 - 4*d**3 - 1 + 242*d**2 - 241*d**2 = 0.
-1, 1
Let j(q) be the second derivative of 0 - 1/40*q**5 + 1/12*q**3 - 2*q - 1/4*q**2 + 1/24*q**4. Factor j(z).
-(z - 1)**2*(z + 1)/2
Let y be (11 - 14) + 2/(-2). Let p = -4 - y. Suppose 0*u - 5/4*u**4 + 1/2*u**5 + p + 1/4*u**3 + 1/2*u**2 = 0. What is u?
-1/2, 0, 1, 2
Factor 4/3*u**2 - 2/3*u**5 + 8/3*u**4 - 10/3*u**3 + 0 + 0*u.
-2*u**2*(u - 2)*(u - 1)**2/3
Let t be 4/7 + 18/(-7) + 4. Determine i, given that 2/3 - 8/3*i**t + i**3 + i = 0.
-1/3, 1, 2
Let k(b) be the third derivative of 2*b**7/15 - 8*b**6/15 + 11*b**5/15 - b**4/3 - 13*b**2. Factor k(w).
4*w*(w - 1)**2*(7*w - 2)
Factor 0*x**4 + 5*x**4 + 367*x**2 - 342*x**2 + 20*x**3 + 10*x.
5*x*(x + 1)**2*(x + 2)
Let i(h) be the second derivative of -2/5*h**2 + 7*h + 1/50*h**5 + 0*h**4 - 1/5*h**3 + 0. Solve i(m) = 0 for m.
-1, 2
Determine j, given that -4*j**3 - 8*j**2 + 0*j**2 - 3*j + 0*j**2 + 15*j = 0.
-3, 0, 1
Factor 4*r**4 + 1 - 2*r**3 + 8*r**2 + r**5 - 5*r**5 - 12*r**4 - r**4 + 6*r.
-(r - 1)*(r + 1)**3*(4*r + 1)
Let w(m) = -m**3 + 8*m**2 - 7*m + 6. Let q(t) = -t**3 + 9*t**2 - 8*t + 7. Let f(a) = 6*q(a) - 7*w(a). Determine h, given that f(h) = 0.
0, 1
Let x(r) be the second derivative of -r**5/70 + 5*r**4/21 - 17*r**3/21 + 8*r**2/7 + 28*r. Factor x(n).
-2*(n - 8)*(n - 1)**2/7
Let h = -528/5 + 106. Let a = 1/28 - -51/140. Let -h*b**5 + 0 + 8/5*b**4 + 8/5*b**2 - 12/5*b**3 - a*b = 0. What is b?
0, 1
Let p = 35 + -97/3. Factor -p*f**2 - 8/3*f**3 + 4/3*f**5 + 4/3 + 4/3*f**4 + 4/3*f.
4*(f - 1)**2*(f + 1)**3/3
Factor 39/2*i - 6 + 21/4*i**2.
3*(i + 4)*(7*i - 2)/4
Factor -1/2*f**4 + 32 - 8*f - 63/2*f**2 + 8*f**3.
-(f - 8)**2*(f - 1)*(f + 1)/2
Let q(v) be the third derivative of 5*v**8/336 + v**7/42 - v**6/8 - 5*v**5/12 - 5*v**4/12 + 5*v**2. Factor q(j).
5*j*(j - 2)*(j + 1)**3
Let v(a) be the first derivative of 0*a**2 + 1/8*a**4 - 1/2*a**3 + 2*a - 2. Suppose v(m) = 0. What is m?
-1, 2
Let j be ((-32)/42)/((-132)/154). Let o(g) be the first derivative of -5/3*g**2 - 1 + j*g**3 + 4/3*g - 1/6*g**4. Let o(f) = 0. Calcu