et k(i) be the second derivative of -1/6*i**4 - 8*i + 0 - 3*i**2 + 4/3*i**3. Determine n so that k(n) = 0.
1, 3
Let d(p) be the first derivative of p**3 - 15*p**2/2 + 12*p - 7. Factor d(u).
3*(u - 4)*(u - 1)
Suppose 1 - 5 = -2*p. Find v such that 48 + 15*v - 144*v**p + 142*v - 420*v**3 + 225*v**4 - 13*v = 0.
-2/5, 2/3, 2
Let o(u) be the first derivative of -3*u**5/5 + 9*u**4/4 - 6*u**2 - 8. Factor o(q).
-3*q*(q - 2)**2*(q + 1)
Let 4*q + 1/2*q**2 + 8 = 0. What is q?
-4
Let j(x) = 5*x**4 - 15*x**3 - 15*x**2 + 28*x - 12. Let z(a) = -14*a**4 + 46*a**3 + 46*a**2 - 84*a + 36. Let y(g) = 10*j(g) + 3*z(g). Factor y(p).
4*(p - 1)**3*(2*p + 3)
Solve 0 + 4/5*i**3 - 4/5*i**2 - 8/5*i = 0.
-1, 0, 2
Let s be ((-8)/12)/(80/(-738)). Let f = s + -23/4. Factor -2/5*x**3 + 2/5*x**2 + f*x - 2/5*x**4 + 0.
-2*x*(x - 1)*(x + 1)**2/5
Let c(h) = h - 3. Let g(s) = s**3 + s**2 - s + 3. Let j be g(0). Let p be c(j). Factor 2/7*y**3 + 0*y + p + 4/7*y**2.
2*y**2*(y + 2)/7
Let g(t) = 2*t - 6. Let y = -12 + 18. Let v be g(y). What is j in -3 - v*j + 2*j**2 + 7 + 0 = 0?
1, 2
Factor r + r**2 + r**5 - r**4 + r - 8*r**3 + 5*r**3.
r*(r - 2)*(r - 1)*(r + 1)**2
Let m(i) be the third derivative of 0*i - i**2 - 1/240*i**6 + 0*i**5 + 1/48*i**4 + 0 + 0*i**3. Let m(s) = 0. What is s?
-1, 0, 1
Suppose 2*l + 4 = -0*l. Let y(w) = 4*w**4 + 9*w**3 + 4*w**2 - w + 2. Let h(g) = 16*g**4 + 37*g**3 + 17*g**2 - 4*g + 9. Let z(i) = l*h(i) + 9*y(i). Factor z(d).
d*(d + 1)**2*(4*d - 1)
Let k(g) be the third derivative of -g**5/90 + g**4/3 - 4*g**3 - 14*g**2. Factor k(n).
-2*(n - 6)**2/3
Determine f, given that -35/2*f**2 + 15/2 - 10*f = 0.
-1, 3/7
Let f(t) be the first derivative of 1/3*t**2 + 0*t + 3 - 2/9*t**3. Factor f(h).
-2*h*(h - 1)/3
Let o(r) be the second derivative of r**5/20 + 5*r**4/12 + 7*r**3/6 + 3*r**2/2 + 6*r. Factor o(g).
(g + 1)**2*(g + 3)
Let k(a) = -a**4 + 7*a**3 - 5*a**2 - 1. Let g(z) = -z**4 + 6*z**3 - 4*z**2 - 1. Let x(p) = 7*g(p) - 6*k(p). Factor x(j).
-(j - 1)**2*(j + 1)**2
Let a be -2 - (-6 - (-80)/24). Solve -20/3*v**2 - 10/3*v**4 + 20/3*v**3 - a + 10/3*v + 2/3*v**5 = 0 for v.
1
Let r(d) be the third derivative of -d**5/12 + 5*d**4/3 - 35*d**3/6 + 19*d**2. Determine i, given that r(i) = 0.
1, 7
Let x(m) be the second derivative of m**4/15 - m**3/15 - m**2/5 + 12*m. Factor x(q).
2*(q - 1)*(2*q + 1)/5
Let y = 7 - 5. Factor 3*b**2 + 0*b**y + 4 + 12*b + 8.
3*(b + 2)**2
Suppose -3 = -3*v + 3. Determine f, given that 2*f - f**2 + 3*f**2 - 3*f - 5*f**v = 0.
-1/3, 0
Let p(o) be the third derivative of o**7/42 + o**6/24 - o**5/12 - 5*o**4/24 + 12*o**2. Factor p(i).
5*i*(i - 1)*(i + 1)**2
Let q(c) = c**3 - 6*c**2 + 5*c + 2. Let x be q(5). Suppose -w + w**3 + w**x + 1 + 1 - 3*w**2 = 0. What is w?
-1, 1, 2
Let r = -2 + 1. Let t(f) = -f. Let p(j) = 3*j**3 - 7*j. Let d(v) = -v**3 - v**2 + v. Let c(z) = -2*d(z) - p(z). Let q(o) = r*c(o) - 5*t(o). Solve q(x) = 0.
0, 2
Let a(o) be the first derivative of -o**3 - 7 + 1/3*o**2 + 0*o + 7/12*o**4. Factor a(p).
p*(p - 1)*(7*p - 2)/3
Suppose -8 = 2*d - 6*d. Factor -2*o**2 + 0*o**d - 2*o**3 - 2*o**2 - 2*o.
-2*o*(o + 1)**2
Let p = -8655 - -207755/24. Let l(r) be the second derivative of p*r**4 + 5/16*r**5 + 11/6*r**3 + r**2 - 3*r + 0. Find j, given that l(j) = 0.
-2, -2/5
Let j be 7/((-84)/(-30)) - 2/(-4). Let l(h) be the second derivative of 1/36*h**4 + 1/9*h**3 + 0 + j*h - 1/60*h**5 + 0*h**2. Suppose l(c) = 0. What is c?
-1, 0, 2
Let d(n) = -n**2 + 5*n + 6. Let q be d(6). Let x(i) be the third derivative of q + 2*i**2 + 2/9*i**3 + 1/18*i**4 + 1/180*i**5 + 0*i. Find c such that x(c) = 0.
-2
Let b(l) = -l**2 + 3*l + 3. Suppose 0 = -5*o + 15. Let p be b(o). Factor -2/7*q**2 + 0 + 4/7*q - 2/7*q**p.
-2*q*(q - 1)*(q + 2)/7
Let o(p) = -2*p**2 + 12*p. Let i(x) = x. Let y(g) = 12*i(g) - o(g). Factor y(b).
2*b**2
Let x(t) be the first derivative of 2*t**3/27 - 2*t**2/3 + 2*t - 1. Factor x(m).
2*(m - 3)**2/9
Suppose -4*r + h + 2*h = -9, -4*r + 5*h = -7. Let b(t) = 2*t**2 + 7*t + 6. Let p be b(-4). Find u, given that -4 - 4*u**2 + 4 - p*u**r = 0.
-2/5, 0
Let o(k) = -k**3 + k. Let d(x) be the first derivative of 3*x**5/5 - x**4 - 2*x**3 + 2*x**2 + 3*x - 3. Let a(n) = -d(n) + 4*o(n). Factor a(j).
-3*(j - 1)**2*(j + 1)**2
Let u(w) = 2*w - 2. Let a(v) = -v + 1. Let y(s) = -5*a(s) - 3*u(s). Let g be y(-1). Find r, given that -g*r**3 + 0*r**2 - 2*r**2 + 5*r - 5*r = 0.
-1, 0
Let n(a) be the first derivative of -2*a**5/55 - 3*a**4/22 - 2*a**3/11 - a**2/11 + 29. Factor n(m).
-2*m*(m + 1)**3/11
Let s(z) be the first derivative of -z**6/9 + 2*z**5/5 - z**4/3 - 4*z**3/9 + z**2 - 2*z/3 - 1. Factor s(t).
-2*(t - 1)**4*(t + 1)/3
Let j(q) be the third derivative of 0*q + 1/30*q**5 + 1/35*q**7 + 0*q**3 + 0*q**4 - 1/20*q**6 - 1/168*q**8 + 0 + 2*q**2. Suppose j(r) = 0. What is r?
0, 1
Let k be ((-16)/6)/((-14)/3). Find n such that 2/7*n + 2/7*n**3 + k*n**2 + 0 = 0.
-1, 0
Let q = 30 - -87. Let g be 1 - 0 - 63/q. Factor g*i + 2/13 - 8/13*i**2.
-2*(i - 1)*(4*i + 1)/13
Factor -2/9*k**2 + 0 - 2/9*k**3 + 0*k.
-2*k**2*(k + 1)/9
Suppose 11 = 2*g - 2*y + 3, -2*y = 8. Suppose -u + 3*u - 10 = g. Factor -w**5 - u*w**3 + 3*w**3 - w**4 + 2*w**3.
-w**4*(w + 1)
Let h(v) be the first derivative of -4*v**7/105 + v**6/75 + 2*v**5/25 - v**4/30 + 3*v - 5. Let f(l) be the first derivative of h(l). Let f(r) = 0. What is r?
-1, 0, 1/4, 1
Let b(q) = q**2 + q + 5. Let i be b(0). Factor 4*k**3 + 4*k**4 - k**3 - k**3 - 2*k**5 + 4*k**i.
2*k**3*(k + 1)**2
What is s in -6*s - 3*s**2 - 29 + 12 + 14 = 0?
-1
Factor -56 - 9*s**2 + 11*s**2 - 17*s**2 - 204*s - 13*s**2.
-4*(s + 7)*(7*s + 2)
Let d = -28 - 14. Let z be (-9)/d*(-12)/(-9). Factor -4/7*l**2 - 2/7*l - 2/7*l**5 + 2/7*l**4 + z + 4/7*l**3.
-2*(l - 1)**3*(l + 1)**2/7
What is d in -4*d + 3090 - 3084 + 13*d - 3*d**3 = 0?
-1, 2
Factor 0 + 0*g + 2/11*g**3 + 0*g**2 + 2/11*g**5 + 4/11*g**4.
2*g**3*(g + 1)**2/11
Let y(a) = -14*a**4 + 15*a**3 - 7*a**2 - 3*a - 3. Let k(v) = v**5 + v**4 - v**3 + v**2 + v + 1. Let z(o) = -3*k(o) - y(o). Let z(h) = 0. Calculate h.
0, 2/3, 1, 2
Suppose -2*f - 150 = 3*f. Let l be ((-4)/10)/(18/f). Determine v, given that 8/3*v**2 - l - 5/3*v - 2*v**4 - 3*v**5 + 14/3*v**3 = 0.
-1, -1/3, 2/3, 1
Suppose -4*i + 3 = 23, -4*l = 5*i + 17. Factor -v + 3*v - 2 + l - 2*v**2.
-2*v*(v - 1)
Let b be (65/40 + -2)/((-1)/2). Let v be (-3*2/8)/(-3). Factor 0 - v*o**3 - 1/2*o - b*o**2.
-o*(o + 1)*(o + 2)/4
Let v be -3 + -3 + 2 - (1 - 5). Solve v - 1/4*j**2 - 1/2*j = 0.
-2, 0
Let i(q) = q**4. Let t(w) = w**4 + 3*w**2 - 2*w. Let j(s) = -2*i(s) + t(s). Factor j(h).
-h*(h - 1)**2*(h + 2)
Let v(w) be the second derivative of -1/20*w**5 + 3*w + 1/6*w**3 + 0 + 1/2*w**2 - 1/12*w**4. Factor v(h).
-(h - 1)*(h + 1)**2
Let i = 4065 - 7693/2. Let l = i + -214. Factor -l - 1/2*v**2 + 3*v.
-(v - 3)**2/2
Let d(c) be the second derivative of -4*c + 0 - 2/5*c**4 - 7/10*c**3 - 3/10*c**2 + 12/25*c**5. Find a, given that d(a) = 0.
-1/4, 1
Let v(k) = -6*k + 1. Let g be v(-4). Suppose -8*l + g = -3*l. Factor 0 - 1/4*d**2 + 1/4*d**l - 1/4*d**3 + 0*d + 1/4*d**4.
d**2*(d - 1)*(d + 1)**2/4
Let t(u) be the third derivative of u**6/40 - u**5/20 - u**4/4 - 27*u**2. Factor t(v).
3*v*(v - 2)*(v + 1)
Suppose 0 = -3*m + 2*m - 8. Let z(q) = -q**3 - 8*q**2 - 2*q. Let s be z(m). Factor -8*v**2 - s*v**4 + 56*v**3 + 8*v**4 - 90*v**4.
-2*v**2*(7*v - 2)**2
Suppose 2 = 2*h - 2. Suppose -2 = h*o - 10. Let -4*w**5 + 2*w**4 - w**o + 2*w**4 + 5*w**3 - 3*w**2 - w = 0. What is w?
-1, -1/4, 0, 1
Let f(b) be the second derivative of -b**6/15 - 2*b**5/5 + b**4/6 + 4*b**3/3 + 4*b + 2. Determine g so that f(g) = 0.
-4, -1, 0, 1
Let c(h) = -h**3 + h. Let i(j) = 10*j**3 - j**2 - 4*j. Let w(f) = 4*c(f) + i(f). Let q(v) = 7*v**3 - v**2. Let u(b) = -5*q(b) + 6*w(b). Factor u(k).
k**2*(k - 1)
Suppose -8 = 2*g - 4*d, -4*g + g - d + 9 = 0. Factor 2/3*y**g + 6 - 4*y.
2*(y - 3)**2/3
Let s be (-128)/28*(-2)/1. Factor -s*x**4 - 8/7*x**2 + 0*x + 44/7*x**3 + 0 + 4*x**5.
4*x**2*(x - 1)**2*(7*x - 2)/7
Let z(s) be the first derivative of 4*s**5/5 - 3*s**4 + 4*s**3 - 2*s**2 + 2. Factor z(l).
4*l*(l - 1)**3
Find k, given that 0 + 14/5*k**5 - 8/5*k**2 + 8*k**3 - 46/5*k**4 + 0*k = 0.
0, 2/7, 1, 2
Let k be 4/(-16) + (-9)/(-12). Factor 1/4*o**2 + 1/4*o - k.
(o - 1)*(o + 2)/4
Let z(y) be the second derivative of 1/5*y**5 - 4*y 