ve of -12*b**3 - 4*b**4 + 0*b**2 + 54*b + 2 - 2/5*b**5. Find d, given that h(d) = 0.
-3, 1
Let f be 10/(-82)*4/(-15). Let j = 176/369 - f. Factor j*v + 2/9*v**2 + 2/9.
2*(v + 1)**2/9
Let y(d) be the third derivative of -d**5/20 - d**4/4 + 3*d**3/2 + 23*d**2. Factor y(p).
-3*(p - 1)*(p + 3)
Let l(p) be the second derivative of -p**6/720 + p**5/240 + 5*p**3/6 - p. Let u(t) be the second derivative of l(t). Determine i, given that u(i) = 0.
0, 1
Let l(v) = -v**4 + v**2 + v + 1. Let j(x) = -6*x**5 - 15*x**4 + 9*x**2 + 6*x + 6. Let a(n) = -j(n) + 6*l(n). Suppose a(r) = 0. Calculate r.
-1, 0, 1/2
Suppose 0 = -5*v + 8 + 2. Let x(a) be the second derivative of -1/48*a**4 + 0*a**2 - 1/24*a**3 + 0 - v*a. Solve x(y) = 0 for y.
-1, 0
Let g(m) be the third derivative of m**7/315 - m**6/180 - m**5/30 + m**4/36 + 2*m**3/9 - 4*m**2. Let g(t) = 0. What is t?
-1, 1, 2
Factor -1/6*u**3 + 1/2*u + 0*u**2 - 1/3.
-(u - 1)**2*(u + 2)/6
Let b(m) be the first derivative of -5/3*m**3 - m + 4*m**2 - 25/2*m**4 + 3. Factor b(r).
-(2*r + 1)*(5*r - 1)**2
Let a(f) be the first derivative of f**4/12 - f**3/3 + 3*f + 1. Let y(w) be the first derivative of a(w). Let y(k) = 0. What is k?
0, 2
Suppose 24*h = 72 - 0. Factor -1/2*c**h + 5/6*c**2 - 1/6*c - 1/6.
-(c - 1)**2*(3*c + 1)/6
Let z(u) = -2*u - 3. Let s be z(-4). Let i(p) be the third derivative of -1/24*p**3 + 0 - 2*p**2 + 0*p**4 + 1/240*p**s + 0*p. Factor i(n).
(n - 1)*(n + 1)/4
Let c(h) be the third derivative of -7*h**5/80 - h**4/32 + 3*h**3/4 - 13*h**2. Factor c(q).
-3*(q + 1)*(7*q - 6)/4
Let -4*h**2 - 6*h**2 - 84*h**3 + 89*h**3 = 0. Calculate h.
0, 2
Let y be (0 + 1)*(1 - -3). What is z in -z**2 + 0*z**4 + 0*z**4 + 0*z**4 + 2*z**3 - z**y = 0?
0, 1
Let q(o) be the first derivative of -1/4*o**4 + 0*o + 1/2*o**6 - o**2 + 2 - o**5 + 5/3*o**3. Determine f so that q(f) = 0.
-1, 0, 2/3, 1
What is r in -3*r**3 - 9*r**2 + 29*r**4 + 6*r - 3*r**5 - 40*r**4 + 20*r**4 = 0?
-1, 0, 1, 2
Solve 0 + 11/9*x**3 + 0*x + 2/9*x**2 + 5/3*x**4 = 0.
-2/5, -1/3, 0
Let y(z) be the first derivative of -3/4*z**2 + 3 + 1/8*z**4 - z + 0*z**3. Factor y(l).
(l - 2)*(l + 1)**2/2
Let y(c) = -c**3 + 6*c**2 - c + 4. Let a(u) = u**2 + 1. Let r(f) = 12*a(f) - 3*y(f). Suppose r(d) = 0. Calculate d.
0, 1
Let m(b) be the first derivative of -1/6*b**4 + 1/18*b**6 + 0*b + 1/6*b**2 + 0*b**3 - 8 + 0*b**5. Factor m(n).
n*(n - 1)**2*(n + 1)**2/3
Let p(l) be the second derivative of -l**8/3840 - l**7/5040 - l**4/6 - 2*l. Let x(r) be the third derivative of p(r). Factor x(d).
-d**2*(7*d + 2)/4
Factor 144/7 + 25/7*i**2 - 24*i - 1/7*i**3.
-(i - 12)**2*(i - 1)/7
Suppose 4*q + 13 = -z - 0*q, 0 = -5*z + 4*q + 31. Let -4*f**2 - 2*f + 0*f**2 - 2*f**4 - f**2 - 6*f**z - f**2 = 0. What is f?
-1, 0
Let u(l) be the third derivative of l**5/660 - l**4/132 + l**3/66 + 31*l**2. Solve u(p) = 0.
1
Let u = -1/207 - -70/207. Factor u*d**2 + 2/3*d + 1/3.
(d + 1)**2/3
Suppose 3*t - 10 - 8 = 0. Let m(w) = -w**2 + 3*w + 2. Let x be m(3). Factor -6*d**x - 3 + 1 + 5*d**3 + d**3 - 4*d**3 + t*d.
2*(d - 1)**3
Solve 4/5*v**3 + 0 - 2/5*v**4 + 0*v + 0*v**2 = 0 for v.
0, 2
Factor 6/5*o + 9/5 - 3/5*o**2.
-3*(o - 3)*(o + 1)/5
Let d = 224 - 222. Factor 0 - 1/4*c**d + 1/4*c.
-c*(c - 1)/4
Let s(d) be the first derivative of -d**5/5 + 2*d**3/3 - d - 7. Factor s(i).
-(i - 1)**2*(i + 1)**2
Let h(i) be the third derivative of 0 - 2*i**3 - 1/2*i**4 - 4*i**2 - 1/20*i**5 + 0*i. Find l such that h(l) = 0.
-2
Let k = 836/537 - 2/1611. Let g = -47/36 + k. Factor 0*v + 1/4*v**2 - g.
(v - 1)*(v + 1)/4
Let p(k) be the second derivative of -k**6/40 + k**5/10 - k**4/8 - k**2 - 5*k. Let t(o) be the first derivative of p(o). Find v, given that t(v) = 0.
0, 1
Factor 0*h + 0*h**3 + 0 + 1/3*h**2 - 2/3*h**5 - h**4.
-h**2*(h + 1)**2*(2*h - 1)/3
Let f(b) be the first derivative of -b**6/240 + b**5/120 - 3*b**2/2 - 2. Let z(j) be the second derivative of f(j). Factor z(r).
-r**2*(r - 1)/2
Let d = 11 + -16. Let m = -3 - d. Factor -4*z - m*z**3 + 6*z**2 - 22 + 22.
-2*z*(z - 2)*(z - 1)
Let n(i) = -i**2 + 7*i - 1. Let f(o) = -o. Let k(j) = -15*f(j) - 3*n(j). Factor k(v).
3*(v - 1)**2
Let v = 2 - -3. Let h(p) = 3*p**2 + p - 4. Let n(m) = -5*m**2 - m + 6. Let u(c) = v*n(c) + 8*h(c). Find g, given that u(g) = 0.
1, 2
Let s(o) be the first derivative of o**4/20 - 2*o**3/15 - 3. Factor s(z).
z**2*(z - 2)/5
Let x(y) be the second derivative of -3*y**5/40 + 7*y**4/8 - 7*y**3/2 + 6*y**2 + 52*y. Let x(n) = 0. What is n?
1, 2, 4
Let v(y) = 10*y**5 - 2*y**4 + 2*y**3 - 10*y**2 + 6. Let c(o) = -9*o**5 + o**4 - o**3 + 9*o**2 - 5. Let g(x) = 6*c(x) + 5*v(x). Factor g(a).
-4*a**2*(a - 1)*(a + 1)**2
Let y(c) be the third derivative of c**6/10 + 2*c**5/15 - 7*c**4/6 + 4*c**3/3 + c**2. Determine p so that y(p) = 0.
-2, 1/3, 1
Find c, given that 3*c**3 - 7*c - 6 - 6*c + 10*c + 6*c**2 + 0 = 0.
-2, -1, 1
Let u(o) = o**3 + 2*o**2 - 3*o - 1. Let r be u(-2). Let c = r + -3. Suppose 8 - 3 - 8*s + 3 + c*s**2 = 0. What is s?
2
Let c = 8 - -3. Let v = -8 + c. Suppose -4 - 2*q**v + 3*q**2 + q**3 + 0*q**2 = 0. What is q?
-1, 2
Let r = 1099/9 + -122. Let o(u) be the first derivative of 0*u + 2 + r*u**3 - 1/6*u**2. Determine g, given that o(g) = 0.
0, 1
Let r(c) = 12*c**2 - 4*c - 5. Suppose 0 = 6*a - a - 20. Let p(m) = -13*m**2 + 3*m + 6. Let x(y) = a*r(y) + 3*p(y). Factor x(n).
(n - 1)*(9*n + 2)
Let d(h) be the first derivative of -h**7/105 + 4*h**6/75 - h**5/10 + h**4/15 - h - 2. Let p(k) be the first derivative of d(k). Suppose p(b) = 0. What is b?
0, 1, 2
Let u(q) = -q**3 - 8*q**2 - 17*q - 14. Let l(k) = k**3 + 8*k**2 + 17*k + 16. Let a(m) = 2*l(m) + 3*u(m). Suppose a(o) = 0. Calculate o.
-5, -2, -1
Let a(r) be the first derivative of 2 - 1/4*r**2 - 1/8*r**4 + 1/3*r**3 + 0*r. Solve a(w) = 0 for w.
0, 1
Let k(s) = -7*s**4 + 20*s**3 - 3*s**2 - 5. Suppose -1 = 2*p + 9. Let w(r) = 3*r**4 - 10*r**3 + r**2 + 3. Let h(n) = p*w(n) - 3*k(n). Factor h(i).
2*i**2*(i - 1)*(3*i - 2)
Let b(m) be the first derivative of m**7/630 + m**6/240 - m**4/144 + 3*m**2 + 2. Let r(s) be the second derivative of b(s). Factor r(x).
x*(x + 1)**2*(2*x - 1)/6
Let p = -2339/2 - -1202. Let y = 37 - p. Factor 2*n**3 + y*n**2 + 1/2 + 3*n.
(n + 1)**2*(4*n + 1)/2
Let w = 247/3 + -79. Suppose -4*i - 2 = 3*z, -z + 2*i + 10 = -2*i. Find k such that 4/3 - 2*k - w*k**z = 0.
-1, 2/5
Let c(q) be the third derivative of 9*q**8/56 + 13*q**7/35 + 2*q**6/9 + 2*q**5/45 - 20*q**2. Suppose c(k) = 0. What is k?
-1, -2/9, 0
Let k(m) = -13*m**5 - 37*m**4 - 17*m**3 + 31*m**2 + 30*m + 9. Let r(x) = -x**5 - x**4 + x. Let i(h) = 2*k(h) + 6*r(h). Solve i(y) = 0.
-1, -3/4, 1
Let f(x) = 5*x**2 + 3*x - 6. Let t(a) = 21*a**2 + 12*a - 24. Let y be 2/3 - 16/(-12). Let o(n) = y*t(n) - 9*f(n). Factor o(c).
-3*(c - 1)*(c + 2)
Determine s so that 2*s**2 - 3*s**2 + 0*s**2 = 0.
0
Let s = 524 + -2618/5. Factor 1/5*a - 3/5*a**3 + s - 4/5*a**2.
-(a + 1)**2*(3*a - 2)/5
Let l be (-16)/(-3)*(4 - 1). Factor 11*i**2 + i**2 - 22*i - 2*i - 2*i**3 + l.
-2*(i - 2)**3
Let o be (-2)/(-4)*(-16)/(-6). Let n(t) be the second derivative of 0 + t - 4/3*t**4 + o*t**3 - 1/2*t**2. Factor n(i).
-(4*i - 1)**2
Let f be (1 + 7/(-9))/(25/225). Let u(j) be the first derivative of -1/4*j**3 + 2 + 0*j + 0*j**f. Factor u(t).
-3*t**2/4
Suppose -b = 2*b - 6. Factor h**b + h + 2*h + 2 + 0.
(h + 1)*(h + 2)
Let a(b) = b**3 - 7*b**2 + 2*b - 2. Let l(x) = -x**3 + 8*x**2 - x + 3. Let p(r) = -3*a(r) - 2*l(r). Factor p(k).
-k*(k - 4)*(k - 1)
Let b(h) = h**2 - 17*h + 52. Let a be b(13). Factor 4/7*t**2 + 0 - 4/7*t**4 + 4/7*t**5 - 4/7*t**3 + a*t.
4*t**2*(t - 1)**2*(t + 1)/7
Let i(v) be the second derivative of -3*v + 1/5*v**5 - 2/15*v**6 - 2/3*v**3 + 0 + 1/3*v**4 + 0*v**2. Find w, given that i(w) = 0.
-1, 0, 1
Let g(z) be the second derivative of 0 - 2*z + 0*z**3 + 1/36*z**4 + 0*z**2. Factor g(b).
b**2/3
Let v = 5/4 + -1. Suppose 1/2*q**2 + 0 - 1/4*q**3 - v*q = 0. What is q?
0, 1
Determine n, given that -1/4*n**2 - 1/4 + 1/2*n = 0.
1
Let t(c) be the first derivative of -1 + 4/3*c**3 - 8*c**2 - 4*c + 4*c**4. Find p such that t(p) = 0.
-1, -1/4, 1
Let g be 24/(-72)*(1/4 - 1). Find r, given that 1/2*r**2 + g*r + 0 + 1/4*r**3 = 0.
-1, 0
Let y(w) be the third derivative of -w**5/60 - 13*w**4/12 - 169*w**3/6 - 18*w**2. Factor y(u).
-(u + 13)**2
Let a(s) = s + 7. Let d be a(-