*2 + 5. Let n(v) = -2*m(v) + x(v). Determine k, given that n(k) = 0.
-1, 1
Let r(o) be the first derivative of 0*o - 1/3*o**3 - 5/8*o**4 - 3 + 0*o**2. What is x in r(x) = 0?
-2/5, 0
Let p(y) be the second derivative of y**6/30 - y**4/6 + y**2/2 + 2*y. Find f, given that p(f) = 0.
-1, 1
Determine a so that -706 - 907*a - 5*a**3 + 10*a**2 - 68*a - 419 + 135*a**2 = 0.
-1, 15
Let a(u) be the second derivative of -289*u**7/14 - 323*u**6/5 - 1287*u**5/20 - 19*u**4 - 2*u**3 + 35*u. Factor a(i).
-3*i*(i + 1)**2*(17*i + 2)**2
Suppose -2*j + 28 = z + 3*j, j - 12 = -z. Let l be z/(-5)*(-1)/4. Suppose 0 - l*d**4 - 6/5*d**3 - 6/5*d**2 - 2/5*d = 0. Calculate d.
-1, 0
Let i = 56 + -166/3. Let r be (-2)/(-10) + 70/25. Find t, given that -2/3*t**r + 2/3*t - 2/3*t**2 + i*t**4 + 0 = 0.
-1, 0, 1
Let d(h) be the first derivative of -h**3/3 + h**2 - h - 2. What is x in d(x) = 0?
1
Let u be 135/(-63)*1578/10. Let k = u + 339. Solve 0 - 6/7*m**2 - 2/7*m**4 - 2/7*m - k*m**3 = 0 for m.
-1, 0
Let n(u) be the second derivative of -4*u**4/3 + 14*u**3/3 + 4*u**2 - 5*u. Factor n(v).
-4*(v - 2)*(4*v + 1)
Let b(x) = x**4 - x**3 + x**2 + x + 1. Let v(g) = -g**4 + 6*g**3 - 3*g**2 - 4*g - 3. Let h = -17 - -11. Let f(u) = h*b(u) - 2*v(u). Factor f(o).
-2*o*(o + 1)**2*(2*o - 1)
Factor -t**2 - t**2 + 3*t - 5*t + 4*t.
-2*t*(t - 1)
Let h be 4 + 12/54 + -4. Factor 2/3*m**3 - h*m - 8/9*m**2 + 4/9.
2*(m - 1)**2*(3*m + 2)/9
Let v(k) be the third derivative of -k**8/1848 - k**7/231 - 2*k**6/165 - 2*k**5/165 + 22*k**2. Suppose v(t) = 0. What is t?
-2, -1, 0
Let s(r) be the second derivative of -r**7/28 + 3*r**6/20 - 9*r**5/40 + r**4/8 + 4*r. Factor s(b).
-3*b**2*(b - 1)**3/2
Suppose -80/7*s**2 - 120/7*s**5 - 274/7*s**3 + 0 - 8/7*s - 358/7*s**4 = 0. Calculate s.
-2, -2/5, -1/3, -1/4, 0
Let g(u) be the second derivative of 5*u**4/12 + 10*u**3/3 + 10*u**2 - 7*u. Factor g(c).
5*(c + 2)**2
Let s(j) be the third derivative of -j**6/720 + j**5/180 + j**4/48 - 22*j**2. Solve s(f) = 0.
-1, 0, 3
Suppose 1 = 8*j + 1. Determine u so that 0*u**2 + 1/4*u**4 - 1/4*u**3 + 0 + j*u = 0.
0, 1
Let w(v) be the third derivative of v**8/2352 - v**7/490 + v**6/280 - v**5/420 + 5*v**2. Factor w(a).
a**2*(a - 1)**3/7
Let f = -2 + 2. Let c = f + 0. Factor 0*d**2 + 0*d + 1/3*d**4 + c*d**3 - 1/3*d**5 + 0.
-d**4*(d - 1)/3
Let r be ((-6)/8)/((-3)/12). Factor -4*w**4 + 3*w**2 - 3*w**r + w**2 - 3*w**2.
-w**2*(w + 1)*(4*w - 1)
Factor -8/7*a + 16/7 - 4/7*a**2 + 2/7*a**3.
2*(a - 2)**2*(a + 2)/7
Let h(g) be the first derivative of -g**6/18 + 4*g**5/15 - 5*g**4/12 + 2*g**3/9 + 7. Determine b, given that h(b) = 0.
0, 1, 2
Let c(t) = -t**4 + 20*t**3 - 15*t**2 - 4. Let y(a) = -2*a**4 + 20*a**3 - 15*a**2 - 3. Let k(o) = -3*c(o) + 4*y(o). Factor k(z).
-5*z**2*(z - 3)*(z - 1)
Let c(q) be the third derivative of -q**5/150 + 4*q**3/15 - 6*q**2. Factor c(s).
-2*(s - 2)*(s + 2)/5
Suppose 11*b - 28 - 16 = 0. Let l(d) be the first derivative of -1/5*d**5 - 1/4*d**b + 1/2*d**2 + 1/3*d**3 + 3 + 0*d. Factor l(g).
-g*(g - 1)*(g + 1)**2
Let l(s) be the second derivative of -s**5/15 - s**4/9 + 4*s**3/9 + 10*s. Suppose l(y) = 0. What is y?
-2, 0, 1
Let w(t) be the first derivative of t**6/150 - 2*t**5/75 - t**4/10 - 3*t**2/2 + 5. Let n(k) be the second derivative of w(k). Factor n(r).
4*r*(r - 3)*(r + 1)/5
Let n = 3390/11 - 308. Find h such that -2/11*h**4 - 2/11*h**3 + 0 + n*h**2 + 2/11*h = 0.
-1, 0, 1
Let r = 7/6 + 1/6. What is t in 2/3*t**4 + 0 + 0*t - r*t**2 - 2/3*t**3 = 0?
-1, 0, 2
Let w = 0 - -2. Factor -w*s**3 - 4*s + 3*s - 2*s**3 - 3*s**2 + 2*s.
-s*(s + 1)*(4*s - 1)
Factor 0 + 0*o + 2/9*o**3 - 4/9*o**2.
2*o**2*(o - 2)/9
Let a(r) be the first derivative of r**3/15 + 2*r**2/5 + 3*r/5 - 16. Determine q so that a(q) = 0.
-3, -1
Let k(s) = s**3 - 13*s**2 + 11*s + 14. Let f = -11 + 23. Let l be k(f). Factor -1/3*u - 1/3*u**l + 0.
-u*(u + 1)/3
Let t be 2/((32/3)/8) + 1. Find s, given that 0 + t*s**2 + 3/2*s**3 + 1/2*s - 9/2*s**4 = 0.
-1/3, 0, 1
Find c, given that -1/2*c**3 - 3/2*c + 1/2 + 3/2*c**2 = 0.
1
Suppose -2*d = -7 - 1. Let w(s) = s**2 + 6*s - 3. Let t(o) = 2*o**2 + 6*o - 3. Let z(g) = d*t(g) - 5*w(g). Factor z(r).
3*(r - 1)**2
Let i(k) be the first derivative of -1/2*k**2 - 2/5*k**5 - 4 - 1/2*k + 1/2*k**3 + 1/2*k**4. Factor i(l).
-(l - 1)**2*(2*l + 1)**2/2
Let m(z) be the second derivative of z**5/18 - 4*z**4/27 - 19*z**3/27 - 2*z**2/3 + 53*z. Factor m(t).
2*(t - 3)*(t + 1)*(5*t + 2)/9
Let h(k) be the second derivative of -k**4/78 - 4*k**3/13 - 36*k**2/13 + k. Solve h(y) = 0.
-6
Let n = -10 + 10. Let -k**4 + 3 + 5 - 4*k**2 - 5*k**3 + n*k**4 + 4*k - 2*k**2 = 0. What is k?
-2, 1
Factor -4/3*f**2 - 8/3*f - 4/3.
-4*(f + 1)**2/3
Let x(w) be the second derivative of -w**5/60 + w**4/36 + w**3/9 - 8*w. Solve x(k) = 0 for k.
-1, 0, 2
Factor -i + 1/3*i**2 + 2/3.
(i - 2)*(i - 1)/3
Let b(f) be the third derivative of f**5/30 - f**4/60 - 4*f**3/15 - 14*f**2. Let b(r) = 0. What is r?
-4/5, 1
Let n = 8 + -6. Factor 6*h**2 + 4 + 6*h - n + 0*h**2 + 2*h**3.
2*(h + 1)**3
Let 3*a**2 + 5*a**2 + 2 + a**2 + 9*a = 0. Calculate a.
-2/3, -1/3
Factor -4191*f + f**4 - 2*f**4 + 4192*f - f**3 + f**2.
-f*(f - 1)*(f + 1)**2
Let u(h) = -h**2. Let v(a) = -5*a**3 + 40*a**2 - 25*a + 10. Let k(q) = 20*u(q) + v(q). Determine w, given that k(w) = 0.
1, 2
Let b(m) be the first derivative of 1/9*m**3 + 0*m + 1/6*m**4 + 1/15*m**5 + 0*m**2 - 4. Factor b(q).
q**2*(q + 1)**2/3
Let p = -25 + 27. Factor 4/5*f + 0 + 2*f**p.
2*f*(5*f + 2)/5
Let b(h) be the second derivative of -5*h**7/42 + h**6/6 + 3*h**5/4 - 5*h**4/12 - 5*h**3/3 + 15*h. Determine a, given that b(a) = 0.
-1, 0, 1, 2
Let c(t) be the first derivative of 27*t**5/5 + 9*t**4/4 - 23*t**3 + 39*t**2/2 - 6*t + 2. Factor c(b).
3*(b - 1)*(b + 2)*(3*b - 1)**2
Let v be 1/(-14) + 11/22. Let l(a) be the first derivative of 1/21*a**6 + v*a**4 + 0*a - 4 + 8/35*a**5 + 1/7*a**2 + 8/21*a**3. Suppose l(s) = 0. What is s?
-1, 0
Let w(p) be the third derivative of -p**8/9240 + p**6/495 + 7*p**3/6 + 4*p**2. Let t(o) be the first derivative of w(o). Find j such that t(j) = 0.
-2, 0, 2
Let d(j) = -j**3 - 8*j**2 - j - 4. Let b be d(-8). Let l(r) be the first derivative of -1/4*r**b - 1/5*r**5 + 0*r**3 + 0*r + 1 + 0*r**2. Factor l(g).
-g**3*(g + 1)
Let m be (-1 + 1)/((-45)/15). Factor m*q + 2/5*q**2 - 2/5*q**4 + 0 + 0*q**3.
-2*q**2*(q - 1)*(q + 1)/5
Let q(s) be the second derivative of 0*s**2 + 0 + 1/35*s**6 + 0*s**3 - 1/35*s**5 + 0*s**4 - 2*s. Solve q(c) = 0 for c.
0, 2/3
Suppose 4*d - 33 = 5*q, -2*q = d - 6*q - 22. Let p(v) = -2*v - 7. Let k be p(-5). Factor -2*z**2 + 2*z**5 - d + k*z + 1 - 2*z**3 + 3*z**4 - 3*z**5.
-(z - 1)**4*(z + 1)
Suppose -33 = 3*t - 39. Determine d so that -t*d**2 - 2/3*d + 0 - 2*d**3 - 2/3*d**4 = 0.
-1, 0
Let r = 15 - 6. Suppose 3*i - r = -0. Let t(f) = f**4 + f**2 + 1. Let y(c) = -5*c**4 + c**2 - 5. Let s(j) = i*t(j) + y(j). Factor s(z).
-2*(z - 1)**2*(z + 1)**2
Let g(s) be the second derivative of -s**4/32 + s**3/6 - s**2/4 - 4*s. Factor g(f).
-(f - 2)*(3*f - 2)/8
Let -q - 2*q**2 - q**4 - 20*q**5 + 1 + 2*q**4 + 19*q**5 + 2*q**3 = 0. Calculate q.
-1, 1
Let o be 3*(-5)/(-3) - 28/6. Factor 0*c + 2/3*c**3 + 0*c**2 + 0 + o*c**4.
c**3*(c + 2)/3
Let p(n) be the second derivative of 0*n**6 + 0*n**4 + 1/15*n**3 - 3*n - 1/25*n**5 + 0*n**2 + 0 + 1/105*n**7. Factor p(k).
2*k*(k - 1)**2*(k + 1)**2/5
Let y = 21854 + -852256/39. Let x = y - 8/13. Factor -4/3 + 2*n - x*n**2.
-2*(n - 2)*(n - 1)/3
Let r = -35 - -39. Solve -2/9*k**3 + 2/9*k + 0 - 2/9*k**r + 2/9*k**2 = 0 for k.
-1, 0, 1
Let p(o) be the first derivative of o**3/3 - o**2 + o - 6. Factor p(h).
(h - 1)**2
Let j be 18/(-12) + 14/4. Factor 2*u**j - u**3 + 1 + 2*u**3 - u - 3*u**2.
(u - 1)**2*(u + 1)
Factor 1/4*s - 10*s**4 + 0 - 5/2*s**2 + 4*s**5 + 33/4*s**3.
s*(s - 1)**2*(4*s - 1)**2/4
Let l = 66 + -64. Let q(p) be the third derivative of 1/24*p**4 + 0*p - 1/70*p**7 + 2*p**l + 0 - 1/120*p**6 + 1/20*p**5 + 0*p**3. Factor q(a).
-a*(a - 1)*(a + 1)*(3*a + 1)
Factor 46*m - 2*m**2 + 2*m**3 - 48*m - 2*m**2 + 4.
2*(m - 2)*(m - 1)*(m + 1)
Let p(z) = -73*z**3 + 92*z**2 + 106*z + 22. Let i(n) = -72*n**3 + 93*n**2 + 105*n + 21. Let s(t) = 2*i(t) - 3*p(t). Factor s(k).
3*(k - 2)*(5*k + 2)**2
Let h be (1*1/7)/((-9)/(-18)). Factor h*r**2 - 2/7*r - 4/7.
2*(r - 2)*(r + 1)/7
Let m(o) be the