0 + b**5/60 - b**4/12 + 2*b**2. Let a(u) be the second derivative of i(u). Determine y so that a(y) = 0.
-1, 1
Let j = -21 + 30. Let w(s) = -s**2 + 4*s + 2. Let d be w(4). Suppose -2 - 2*y + 0*y**2 - 6*y**d + j*y = 0. What is y?
1/2, 2/3
Let k = -13 + 18. Factor 3*j + 4*j**5 - 2*j**3 - j - 2*j**k - 2*j**3.
2*j*(j - 1)**2*(j + 1)**2
Let d(u) be the second derivative of -8*u + 2/21*u**7 - 1/5*u**5 + 0*u**2 + 0*u**3 + 0 - 1/3*u**4 + 2/15*u**6. Solve d(a) = 0 for a.
-1, 0, 1
Factor p - 4*p**3 - 5*p**4 - 47*p**2 + 3*p**4 + 49*p**2 + 3*p.
-2*p*(p - 1)*(p + 1)*(p + 2)
Let l(f) be the third derivative of -f**8/112 - f**7/70 + 3*f**2. Factor l(o).
-3*o**4*(o + 1)
Let r(c) be the second derivative of 1/10*c**5 - 1/12*c**4 + 0*c**2 + 0*c**3 - 1/30*c**6 + 0 + 3*c. Factor r(u).
-u**2*(u - 1)**2
Let g(c) be the third derivative of 7*c**6/120 - c**5/75 - c**4/30 + 5*c**2. Suppose g(l) = 0. What is l?
-2/7, 0, 2/5
Let b be 4/6 - (-4)/12. Suppose 10 = 5*u, 9 = t + 4*u - b. Let -t*o**3 + 4*o**2 + o + 2*o - 5*o = 0. What is o?
0, 1
Let y(n) be the second derivative of -n**7/168 - n**6/2 - 18*n**5 - 360*n**4 - 4320*n**3 - 31104*n**2 + 9*n + 1. Suppose y(q) = 0. Calculate q.
-12
Let o(s) be the first derivative of 3*s**4/26 - 2*s**3/39 - 2*s**2/13 - 5. Determine h so that o(h) = 0.
-2/3, 0, 1
Let u(t) = -6*t**2 + 2*t. Let g(s) = s + 1. Let l be g(-6). Let n(c) = -7*c**2 + 3*c. Let j(y) = l*u(y) + 4*n(y). Factor j(x).
2*x*(x + 1)
Let i(f) be the second derivative of f**7/70 - f**6/120 - f**2 + 2*f. Let u(b) be the first derivative of i(b). Factor u(o).
o**3*(3*o - 1)
Let u(r) be the second derivative of r**5/30 - 5*r**4/18 + 7*r**3/9 - r**2 - 31*r. Factor u(x).
2*(x - 3)*(x - 1)**2/3
Let n(y) be the third derivative of 1/420*y**7 - 1/60*y**5 + 0*y**4 - 1/240*y**6 - 5*y**2 + 0*y**3 + 0 + 0*y. Factor n(b).
b**2*(b - 2)*(b + 1)/2
Let r(y) = -y**3 + 4*y**2 + 18*y + 23. Let v be r(7). Suppose 2/5*i**4 + 4/5*i - 2/5 - 4/5*i**3 + 0*i**v = 0. Calculate i.
-1, 1
Factor 0*t**2 + 9/4*t**4 + 0 + 3/2*t**5 + 3/4*t**3 + 0*t.
3*t**3*(t + 1)*(2*t + 1)/4
Suppose n + 4 - 6 = 0. Suppose 0*f - 2*f = -4, 2*f = 3*m - 2. Let 0*q**n - m*q**3 - q**2 + 3*q**3 = 0. Calculate q.
0, 1
Let s(k) be the first derivative of -k**8/2520 + k**7/1260 - k**3 - 3. Let n(o) be the third derivative of s(o). Determine g so that n(g) = 0.
0, 1
Let h(d) = -d**2. Suppose -3*y = 4*p + 19, 2*p - 2*y + 4*y = -10. Let o(s) = 6*s**2 + 4*s. Let x(u) = p*h(u) + o(u). Suppose x(j) = 0. Calculate j.
-2/5, 0
Let m = 4/15 + -688/15. Let x = m + 46. Determine l so that x*l - 2/5*l**3 + 0*l**2 + 0 = 0.
-1, 0, 1
Let b(p) be the third derivative of -1/120*p**6 + 0 + 0*p**3 - 1/420*p**7 + p**2 - 1/120*p**5 + 0*p + 0*p**4. Determine i, given that b(i) = 0.
-1, 0
Let u(z) be the third derivative of -z**8/90720 + z**7/22680 - z**5/60 - 3*z**2. Let v(x) be the third derivative of u(x). Factor v(a).
-2*a*(a - 1)/9
Let g(n) be the second derivative of 4*n**2 + 2*n + 0 + 1/5*n**6 - 4/5*n**5 - 1/2*n**4 + 4*n**3. Factor g(p).
2*(p - 2)**2*(p + 1)*(3*p + 1)
Let o(v) = 8*v**5 + 6*v**4 - v**3 + v**2 + 7*v - 7. Let g(j) = -j - 2*j**5 + 2 - 4 + 3 + j**5 - j**4. Let i(c) = -14*g(c) - 2*o(c). Factor i(u).
-2*u**2*(u - 1)**2*(u + 1)
Let y be 0*(-1 + 0) + 56/252. Factor y + 8/9*d**3 + 2/9*d**4 + 4/3*d**2 + 8/9*d.
2*(d + 1)**4/9
Let l(v) be the second derivative of -1/20*v**6 - 6*v + 0*v**5 + 0*v**2 + 0*v**3 + 0 + 0*v**4. Factor l(i).
-3*i**4/2
Let y = -4 + 6. Let k(z) = -z**5 + 6*z**4 - 4*z**3 + 2*z**2 - z - 2. Let h(a) = -a**4 - a**3 + a**2 + 1. Let r(g) = y*h(g) + k(g). Factor r(s).
-s*(s - 1)**4
Let r(s) be the third derivative of s**2 + 1/210*s**7 + 0 + 0*s + 1/40*s**6 + 0*s**3 + 1/30*s**5 + 0*s**4. Factor r(f).
f**2*(f + 1)*(f + 2)
Factor 36 - 36 + 4*o**2.
4*o**2
Let b(h) be the first derivative of 3*h**5/5 - 3*h**4/4 - 3*h**3 + 15*h**2/2 - 6*h - 3. Determine i so that b(i) = 0.
-2, 1
Let k(h) = -2*h**2 - 4*h + 3. Let f(s) = 3*s - 10 - 14 + s**2 + 22. Let z(l) = -6*f(l) - 4*k(l). Factor z(b).
2*b*(b - 1)
Let m(v) be the first derivative of 8*v**5/5 - 7*v**4 + 8*v**3 + 2*v**2 - 8*v + 1. Determine l so that m(l) = 0.
-1/2, 1, 2
Let z(r) be the first derivative of r**4/7 + 8*r**3/3 + 3. Determine u so that z(u) = 0.
-14, 0
Let f(n) be the second derivative of -1/3*n**2 + 1/3*n**3 + 0 + 1/30*n**5 - 1/6*n**4 - 2*n. Find r, given that f(r) = 0.
1
Let o = -5413/15 + 361. Let m(y) be the first derivative of 0*y**2 + 2 + o*y**3 - 1/10*y**4 + 0*y. Factor m(g).
-2*g**2*(g - 1)/5
Let c(j) = 6*j**2 - 8*j - 6. Let p(d) = -5*d**2 + 7*d + 5. Let s(q) = -6*c(q) - 7*p(q). Let x(y) = 7*y**2 + 6*y - 6. Let r(h) = -5*s(h) - x(h). Factor r(l).
-(l + 1)*(2*l - 1)
Let x be 3/(-1)*1/(-9). Let j be 4/(-10) - 11/(-15). Determine b so that x*b**2 - 2/3*b + j = 0.
1
Solve -70 - 36*v**4 + 18*v**2 + 21*v**5 + 47 - 96*v**3 + 75*v + 41 = 0.
-1, -2/7, 1, 3
Suppose 3*k = w + 2*k - 6, 9 = -w - 4*k. Suppose -4*x**2 - 4*x**w - 2 + x + 5*x**3 + 4*x = 0. Calculate x.
1, 2
Suppose 4 = -0*m + m. Suppose -3 + 43 = 4*n + m*v, 4*v = -n + 25. Let -2*b**n + b**4 - 5*b**3 - b**2 + 3*b**5 + 4*b**3 = 0. Calculate b.
-1, 0, 1
Let b(i) be the second derivative of i**4/42 - i**3/7 - 10*i**2/7 - i - 2. Factor b(a).
2*(a - 5)*(a + 2)/7
Let t(n) be the third derivative of n**8/672 + n**7/105 + n**6/240 - n**5/12 - n**4/12 + 2*n**3/3 - 23*n**2 - 2*n. Factor t(q).
(q - 1)**2*(q + 2)**3/2
Let d(z) be the second derivative of 0 + 4/15*z**3 - z + 3/5*z**2 + 1/30*z**4. Factor d(u).
2*(u + 1)*(u + 3)/5
Suppose v = 4*q + 13, -3*q + v + 4*v = 31. Let r be q/(-15) + (-6)/(-9). Solve 0 + 0*c**2 - r*c**4 + 2/5*c**3 + 0*c + 2/5*c**5 = 0 for c.
0, 1
Let q(r) = 5*r**5 + 2*r**4 - 5*r**3 - 2*r**2 + 4. Let x(w) = -4*w**5 - w**4 + 4*w**3 + w**2 - 3. Let n(s) = -3*q(s) - 4*x(s). Factor n(a).
a**2*(a - 2)*(a - 1)*(a + 1)
Let m(f) = f**2 - 9*f + 2. Let n(p) = p**2 - 8*p + 1. Let s(d) = -4*m(d) + 5*n(d). Let g be s(5). Factor -4*o - 5*o**2 - o**3 - o**3 - o**g.
-2*o*(o + 1)*(o + 2)
Suppose 4*p = w + 2*w + 49, 0 = 2*w + 2*p + 28. Let t be (-4)/6 + (-20)/w. Find q, given that 2*q**3 + 0 + 2/3*q**4 - 2/3*q**5 - 4/3*q - t*q**2 = 0.
-1, 0, 1, 2
Let c(v) be the second derivative of 0 - 2*v - 1/2*v**3 - 1/12*v**4 - v**2. Factor c(u).
-(u + 1)*(u + 2)
Solve 0 + 5/3*h**3 + 5/3*h - 10/3*h**2 = 0 for h.
0, 1
Let n(a) = a**3 - 1. Let z(p) = 16*p**5 + 24*p**4 - 9*p**3 - 23*p**2 - 9*p + 1. Let v(h) = -2*n(h) - z(h). Find s such that v(s) = 0.
-1, -1/4, 1
Suppose 3 + 5 = 2*l. Let m(y) be the first derivative of -2 - 2/27*y**3 + 1/6*y**l - 1/3*y**2 + 2/9*y. What is a in m(a) = 0?
-1, 1/3, 1
Let j(l) be the third derivative of l**5/80 - l**3/8 - 6*l**2. Factor j(y).
3*(y - 1)*(y + 1)/4
Let d(o) = -o**3 + 16*o**2 + 17*o + 5. Let t be d(17). Let 12*n**3 - 4*n**5 + 4*n**5 + 8*n**2 - 4*n**t + 0*n**5 = 0. What is n?
-1, 0, 2
Let p(r) be the third derivative of -1/120*r**5 + 1/420*r**7 + 1/1344*r**8 + 0*r + 0*r**6 - 1/96*r**4 + 0 + 0*r**3 - 3*r**2. Suppose p(s) = 0. Calculate s.
-1, 0, 1
Suppose 4*l = -18 + 46. Let v be (-240)/(-56) + (-2)/l. Factor 1 + n**2 - 3*n**2 - 1 + 2*n**v.
2*n**2*(n - 1)*(n + 1)
Let y(x) be the first derivative of -1/12*x**4 + 1/20*x**5 + 0*x**3 - 1 + 0*x**2 - 2*x. Let u(l) be the first derivative of y(l). Suppose u(t) = 0. Calculate t.
0, 1
Let g = -45 + 45. Let r(o) be the second derivative of 0 + 1/40*o**5 + 1/48*o**4 + 0*o**3 + o + 1/120*o**6 + g*o**2. Factor r(p).
p**2*(p + 1)**2/4
Let f(x) = 9*x**2 + 5*x - 4. Let w(g) = -10*g**2 - 5*g + 5. Let m(a) = 5*f(a) + 4*w(a). Find s, given that m(s) = 0.
-1, 0
Let b(m) be the third derivative of -m**5/60 - m**4/8 - 3*m**2. Factor b(v).
-v*(v + 3)
Let 2/5*l**3 - 2/5*l + 0 + 0*l**2 = 0. Calculate l.
-1, 0, 1
Let r(d) = d + 2 - 5 + 2 - d**2. Let v(g) = g**4 + g**3 - 2*g**2 - 1. Suppose 0 = -5*u - 10 - 0. Let o(n) = u*r(n) + 2*v(n). Factor o(t).
2*t*(t - 1)*(t + 1)**2
Let n(s) be the third derivative of -5*s**2 + 1/100*s**5 - 1/40*s**4 + 1/30*s**3 + 0 - 1/600*s**6 + 0*s. Factor n(k).
-(k - 1)**3/5
Let j = -31 - -34. Let v = 6 + -1. What is d in -3 + 4*d + v*d**2 + 5 - j*d**2 = 0?
-1
What is p in 20*p**3 - 62*p**4 + 33*p**4 + 49*p**4 + 5*p**5 = 0?
-2, 0
Let r(a) be the second derivative of a**7/210 + a**6/120 - a**5/30 + 5*a**2/2 - 6*a. Let o(n) be the first derivati