+ -1). Factor 0*o**s + 1/2*o**5 - o**4 + 0 + o**2 - 1/2*o.
o*(o - 1)**3*(o + 1)/2
Let p(q) be the first derivative of 2*q**6/27 - 2*q**5/15 - q**4/18 + 2*q**3/9 - q**2/9 + 3. What is k in p(k) = 0?
-1, 0, 1/2, 1
Suppose 11*q**3 - 14*q**3 + 6*q + 4*q**2 - 3*q**5 - 9*q**4 + 5*q**2 = 0. What is q?
-2, -1, 0, 1
Suppose -36 + 2*p**2 + 36 - 2*p + 0*p**2 = 0. Calculate p.
0, 1
Let u(a) be the first derivative of -a**4/6 - 8*a**3/9 - 5*a**2/3 - 4*a/3 - 5. Factor u(w).
-2*(w + 1)**2*(w + 2)/3
Factor 5*o**2 + 0*o**2 - 6130*o + 6165*o.
5*o*(o + 7)
Let u(x) = x**4 - 4*x**3 - 2*x**2 + 18*x - 18. Let p(i) = -5*i**4 + 20*i**3 + 11*i**2 - 91*i + 91. Let r(j) = -2*p(j) - 11*u(j). Solve r(n) = 0.
-2, 2
Let g(l) be the third derivative of l**2 + 1/3*l**3 + 4/15*l**5 + 0 + 7/120*l**6 + 0*l + 11/24*l**4. Let g(b) = 0. What is b?
-1, -2/7
Let x(m) be the third derivative of -m**7/525 + m**5/150 + 10*m**2. Find n such that x(n) = 0.
-1, 0, 1
Let v(t) = -t**3 - 3*t**2 + t + 2. Let m(u) = -u**3 - 2*u**2 + u + 2. Let a(j) = 3*m(j) - 4*v(j). Let h be a(-6). Factor 2/5*y**h + 0*y**3 + 0*y + 0 - 2/5*y**2.
2*y**2*(y - 1)*(y + 1)/5
Suppose 4*q - q = -3. Let p be (-2*(3 + -2))/q. Factor -p*m**5 + 2*m**5 - 2*m**5 + 2*m**4.
-2*m**4*(m - 1)
Let v(f) = 8*f**2 - 11*f + 8. Let y(s) = -33*s**2 + 45*s - 33. Suppose 17 - 59 = -2*p. Let a(j) = p*v(j) + 5*y(j). Determine i so that a(i) = 0.
1
Let l(w) be the second derivative of -w**7/5460 + w**6/468 - 7*w**5/780 + w**4/52 - 7*w**3/6 + 3*w. Let r(c) be the second derivative of l(c). Factor r(h).
-2*(h - 3)*(h - 1)**2/13
Suppose 0*d - 5 = u - 3*d, 2*u = 3*d - 4. Suppose -4 = -p - u. Determine y so that 3*y**2 - 5*y**3 + 4*y**p - 5*y**2 = 0.
-2, 0
Let c(r) be the third derivative of -r**7/1260 - r**6/240 + r**5/360 + r**4/48 + 20*r**2. Factor c(n).
-n*(n - 1)*(n + 1)*(n + 3)/6
Let f(s) = -2*s**2 + 4*s - 4. Let w(u) = -u + 1. Let p(v) = f(v) + 4*w(v). Let p(d) = 0. What is d?
0
Let r(h) = -5*h**3 + h**2 - 2*h - 6. Let v = 7 - 4. Let y(t) = t**3 + 3 - 2*t**v - 4. Let b(q) = r(q) - 6*y(q). Find p such that b(p) = 0.
-2, 0, 1
Let d = -817/3 - -276. Let r = 25/6 - d. Find t such that r*t**3 + 0*t**2 - 1/2*t - 1/4 + 1/4*t**4 = 0.
-1, 1
Let r(w) = -7*w**2 + 9*w + 6. Let q(h) = 10*h**2 - 13*h - 9. Let i(k) = -5*q(k) - 7*r(k). Find b such that i(b) = 0.
-1, 3
Let g = -147 + 151. Factor 1/2*n**5 - 1/4*n**2 + 0*n - 5/4*n**g + 0 + n**3.
n**2*(n - 1)**2*(2*n - 1)/4
Let m(t) be the first derivative of t**6/4 + t**5 + 3*t**4/8 - 2*t**3 - t**2 + 12. Find s, given that m(s) = 0.
-2, -1/3, 0, 1
Suppose -12 = -3*f, -3*k - 5*f + 15 = -14. Let -8/13*n + 6/13*n**k + 0 - 140/13*n**4 + 40/13*n**2 - 98/13*n**5 = 0. Calculate n.
-1, 0, 2/7
Let g(p) = -3*p**3 + 39*p**2 - 146*p + 108. Let u(j) = -6*j**3 + 78*j**2 - 293*j + 216. Let x(s) = -5*g(s) + 2*u(s). Factor x(t).
3*(t - 6)**2*(t - 1)
Let k(s) = -s**3 + 6*s**2 + s - 4. Let l be k(6). Suppose -3*g**l + 6*g**2 + 2*g**2 - 6 - 3*g**2 - 4*g = 0. What is g?
-1, 3
Let s(w) be the first derivative of -w**4/48 + w**3/24 - 2*w - 4. Let n(h) be the first derivative of s(h). Suppose n(t) = 0. Calculate t.
0, 1
Let n(b) be the second derivative of b**4/21 - 2*b**2/7 - 2*b. Factor n(k).
4*(k - 1)*(k + 1)/7
Suppose -3*a - 16 = -37. Let g(l) be the second derivative of -1/84*l**a - 2*l + 0*l**4 + 0 + 0*l**2 - 1/60*l**6 + 0*l**3 + 0*l**5. Solve g(j) = 0 for j.
-1, 0
Factor -64/3 - 4*w**2 + 16*w + 1/3*w**3.
(w - 4)**3/3
Let k(s) = -2*s**2 + 25*s + 16. Let j be k(13). Let r(v) be the first derivative of 1/2*v**j + 3 - 3/16*v**4 - 3/8*v**2 + 0*v. Factor r(i).
-3*i*(i - 1)**2/4
Factor 1/3*k**4 + 1/3*k**3 - 1/3*k**2 - 1/3*k + 0.
k*(k - 1)*(k + 1)**2/3
Let l(z) be the second derivative of -z**7/105 + z**6/20 - z**5/30 - z**4/4 + 2*z**3/3 + 3*z**2 - 5*z. Let h(k) be the first derivative of l(k). Factor h(n).
-2*(n - 2)*(n - 1)**2*(n + 1)
Let g(z) = z**2 - z + 6. Let p(c) = 2*c**2 + 7. Let d(q) = -5*g(q) + 4*p(q). What is u in d(u) = 0?
-2, 1/3
Let x be (-5)/(-15) - (-1)/6. Factor -1/2*a**2 - a - x.
-(a + 1)**2/2
Let m(p) be the second derivative of 1/6*p**4 + 0*p**3 - 7/20*p**5 + 0*p**2 - p + 1/6*p**6 + 0. Solve m(r) = 0 for r.
0, 2/5, 1
Let m(g) be the first derivative of -g**3/3 - 3*g**2/2 - 2*g - 12. Factor m(l).
-(l + 1)*(l + 2)
Let a(h) be the first derivative of -2*h**3/15 - 6. Factor a(b).
-2*b**2/5
Let v(y) be the second derivative of -y**4/28 + 3*y**3/7 - 27*y**2/14 + 3*y. Factor v(m).
-3*(m - 3)**2/7
Suppose 0 = 3*i + 2*k - 6, -4*k = -2*i - 8 - 4. Let n(d) be the second derivative of -3*d + 1/4*d**3 + i - 1/8*d**4 + 0*d**2. Suppose n(j) = 0. What is j?
0, 1
Determine y, given that 3/4*y + 3/2*y**2 + 3/4*y**3 + 0 = 0.
-1, 0
Suppose 0*y + 88*y**4 - 4*y + 16*y**5 + 32*y**2 - 48*y**5 - 84*y**3 = 0. What is y?
0, 1/4, 1/2, 1
Let b = 53/6 + -26/3. Solve 0 + 1/6*h**4 - b*h**3 + 1/6*h - 1/6*h**2 = 0 for h.
-1, 0, 1
Factor 4*v + 0*v**3 - v**3 - 4*v**3 + v**3.
-4*v*(v - 1)*(v + 1)
Let j(d) be the second derivative of d**6/10 + d**5/10 - d**4/4 - d**3/3 + 7*d + 1. Factor j(s).
s*(s - 1)*(s + 1)*(3*s + 2)
Factor -3/2*z**2 + 1/4*z + 3/2 - 1/4*z**3.
-(z - 1)*(z + 1)*(z + 6)/4
Suppose 5*u = 3*j + 15, 2*j + 0*u + 26 = -2*u. Let f be 2/j - (-35)/50. Let -f - 1/2*t**3 + 1/2*t**2 + 1/2*t = 0. Calculate t.
-1, 1
Suppose -3*x + 5*q + 21 = -0*x, 5*x + 5*q + 5 = 0. Suppose 4*l + 12 = -2*y, 0 = 2*y - 2*l - 16 + 4. Solve 6*o**3 + x*o**5 + y*o**2 + 6*o**4 - o + o = 0.
-1, 0
Let w(y) be the third derivative of y**7/1575 - y**6/225 + y**5/90 - y**4/90 - y**2. Factor w(l).
2*l*(l - 2)*(l - 1)**2/15
Let g = -16 - -18. Factor -32/9*j**3 + 16/3*j**g + 0 - 2*j.
-2*j*(4*j - 3)**2/9
Let h = 32 - 32. Factor 2/7*l + h + 0*l**2 - 2/7*l**3.
-2*l*(l - 1)*(l + 1)/7
Let m be 2338/(-780) + 7 + -4. Let c(f) be the third derivative of 0*f**6 + 0 + 1/1365*f**7 + f**2 + 0*f**3 + 0*f + 0*f**4 - m*f**5. Factor c(i).
2*i**2*(i - 1)*(i + 1)/13
Let b(j) be the third derivative of j**7/105 + j**6/60 + 6*j**2. Let b(g) = 0. What is g?
-1, 0
Let w = -263/5 + 53. Solve -w - 32/5*j**2 - 16/5*j = 0.
-1/4
Let k(x) be the third derivative of 2*x**7/105 + x**6/10 + x**5/5 + x**4/6 + 8*x**2. Factor k(m).
4*m*(m + 1)**3
Let -2/5*w**2 + 4/5 - 2/5*w = 0. What is w?
-2, 1
Suppose -8 = p - 0*p - 2*q, 5*p + 5*q - 20 = 0. Factor -2/5*u**5 + p*u**2 - 2/5*u + 0 + 4/5*u**3 + 0*u**4.
-2*u*(u - 1)**2*(u + 1)**2/5
Let y be 157/165 + 3/15. Let j = y + -9/11. Factor 0 - 1/3*d**3 + 0*d + j*d**2.
-d**2*(d - 1)/3
Let g(q) be the first derivative of -q**4/7 + 10*q**3/21 - 4*q**2/7 + 5*q - 3. Let d(b) be the first derivative of g(b). Determine h, given that d(h) = 0.
2/3, 1
Suppose 12*h = 3*h + 54. Let o(k) be the third derivative of 0 + 3*k**2 + 1/50*k**5 + 0*k**3 + 1/100*k**h + 1/525*k**7 + 0*k + 1/60*k**4. Factor o(f).
2*f*(f + 1)**3/5
Suppose -3*j = 3*r - 6, -r + 2*r = 4*j + 2. Determine z, given that z - 3*z**r + z**2 - 6*z + 3*z = 0.
-1, 0
Let o = -4/145 + 451/580. Factor 27/4*m**2 + 3/2 + o*m**4 - 15/4*m**3 - 21/4*m.
3*(m - 2)*(m - 1)**3/4
Let s(w) be the second derivative of 0*w**2 + 0*w**4 + 1/168*w**7 + 0*w**6 - 3*w + 0 - 1/80*w**5 + 0*w**3. Find f such that s(f) = 0.
-1, 0, 1
Let k(w) be the third derivative of 11*w**6/420 + w**5/105 + 14*w**2. Factor k(t).
2*t**2*(11*t + 2)/7
Let y be 6 - -1 - 6/3. Factor -y*w - w**3 + 4*w**2 - 2*w + 2*w**3 + 3*w**3 + 2.
(w + 2)*(2*w - 1)**2
Let w be 1/(-1 - (-12)/10). Let i = -1 + 3. Let o(b) = 13*b**2 + 3*b. Let k(r) = -6*r**2 - r. Let a(x) = i*o(x) + w*k(x). What is u in a(u) = 0?
0, 1/4
Let z(s) be the third derivative of -6*s**2 - 1/15*s**3 + 0 + 1/300*s**6 - 1/60*s**4 + 1/150*s**5 + 0*s. Factor z(u).
2*(u - 1)*(u + 1)**2/5
Let h(g) = 2*g**2 + 3*g. Let u be h(-2). Determine t so that 3*t**2 - 3*t**3 - u + 3 + 3*t + 4*t**3 = 0.
-1
Let w(i) be the second derivative of 3*i**5/20 - i**4/2 - 3*i**3/2 + 20*i. Factor w(h).
3*h*(h - 3)*(h + 1)
Let d(j) be the first derivative of -5*j**3/3 - 30*j**2 - 180*j - 7. Factor d(k).
-5*(k + 6)**2
Suppose -6*j = -s - j + 23, -2*s = 2*j + 2. Let l(r) be the first derivative of 3/10*r**5 + 0*r + 0*r**2 - s + 0*r**4 + 0*r**3. Suppose l(c) = 0. Calculate c.
0
Find t such that -4 + 6*t**2 - 3*t + 1 - 6*t**3 - 8*t**4 + 3*t**5 + 6*t + 5*t**4 = 0.
-1, 1
Factor 0*j - 16/11*j**3 + 0 - 2/11*j**2 - 32/11*j**4.
-2*j**2*(4*j + 1)*