*r - 2/9 = 0?
-1, 1
Let x(h) be the third derivative of -h**7/630 + h**6/120 - h**5/60 + h**4/72 - 5*h**2. Determine l so that x(l) = 0.
0, 1
Let q(c) = c + 8. Let l be q(-6). Solve -4*v - l*v**2 - 2 - 12 - 2*v + 10 = 0.
-2, -1
Let g(j) be the first derivative of -1/480*j**6 + 0*j + 1/120*j**5 - 1/96*j**4 + 0*j**3 + j**2 + 1. Let t(w) be the second derivative of g(w). Factor t(i).
-i*(i - 1)**2/4
Let y = -54/7 - -8. Factor -4/7*i**3 + y*i**4 + 0*i + 0 + 2/7*i**2.
2*i**2*(i - 1)**2/7
Let h be 2 - (-13 - (0 + -3)). Let g be h/7 - 6/(-21). Determine t so that -2/3*t**g + 2/3*t + 0 = 0.
0, 1
Let a(i) be the first derivative of -i**7/70 + i**6/20 - i**4/4 + i**3/2 + i**2 - 5. Let m(v) be the second derivative of a(v). Suppose m(p) = 0. Calculate p.
-1, 1
Let b(r) = -r**3 + r**2 - r. Let v(d) = 16*d**3 - 26*d**2 - 6*d. Let m(h) = -4*b(h) - 2*v(h). Determine a so that m(a) = 0.
-2/7, 0, 2
Let y(t) = -11*t**3 + 60*t**2 - 186*t - 6. Let g(k) = -23*k**3 + 120*k**2 - 373*k - 13. Let u(o) = 6*g(o) - 13*y(o). Factor u(r).
5*r*(r - 6)**2
Let r = 257/2 + -128. Solve 1/2*f**3 - f**4 + 0*f + 0 + 0*f**2 + r*f**5 = 0 for f.
0, 1
Let o(x) be the second derivative of -x**8/1344 - x**7/840 + x**6/160 + x**5/48 + x**4/48 - 3*x**2/2 + x. Let p(m) be the first derivative of o(m). Factor p(k).
-k*(k - 2)*(k + 1)**3/4
Let v(z) be the first derivative of -7*z**6/12 - z**5/5 + 7*z**4/8 + z**3/3 + 1. Solve v(t) = 0.
-1, -2/7, 0, 1
Let 3 + 4/3*i**2 - 4*i = 0. What is i?
3/2
Let o(y) = y**4 + y**3 + y**2 + y. Let r(b) = -b**4 + 2*b**3 + 3*b**2. Let n(z) = 4*o(z) + 2*r(z). Suppose n(k) = 0. What is k?
-2, -1, 0
Let a be ((-3)/(-9))/((-25)/(-30)). Let t = 9/10 - a. Factor 0*j**3 + 1/4 + 1/4*j**4 + 0*j - t*j**2.
(j - 1)**2*(j + 1)**2/4
Find a such that -4/3*a**5 - 28/3*a**2 - 4*a - 6*a**4 - 32/3*a**3 - 2/3 = 0.
-1, -1/2
Let a(f) = -f**2 - 5*f - 4. Let o(k) = k**2 + 3*k + 2. Let i(v) = 6*a(v) + 10*o(v). Let i(d) = 0. What is d?
-1, 1
Let z(n) = 2*n + 17. Let y be z(-7). Factor -2/3*d**y + 4/3*d**2 + 0 + 0*d.
-2*d**2*(d - 2)/3
Factor 3*s**3 + s**4 + s**4 - s**3.
2*s**3*(s + 1)
Let w(h) be the third derivative of h**6/360 - 4*h**2. Find f, given that w(f) = 0.
0
Let a(u) be the second derivative of 0*u**2 + 1/7*u**3 + 7*u + 0 + 1/42*u**4. Find w such that a(w) = 0.
-3, 0
Let x(d) = d**3 + 7*d**2 + 8*d + 15. Let a be x(-6). Let 0 + 1/2*j**a - 1/4*j**2 - 1/2*j + 1/4*j**4 = 0. Calculate j.
-2, -1, 0, 1
Let a = -3/136 - -349/408. Let y(c) be the second derivative of -3*c + 1/2*c**2 + a*c**3 + 0 + 1/2*c**4. Determine g, given that y(g) = 0.
-1/2, -1/3
Let x(b) = b**2 + 2*b - 3. Let v be x(1). Let i(h) be the first derivative of -1/20*h**5 - 3 - 1/16*h**4 + 0*h + 0*h**2 + v*h**3. Factor i(n).
-n**3*(n + 1)/4
Let y(k) = 40*k**2 - 32*k + 4. Let n(h) = 40*h**2 - 31*h + 3. Let g(o) = 2*n(o) - 3*y(o). Factor g(z).
-2*(4*z - 1)*(5*z - 3)
Let o(w) = -w**3 + 4. Let t be o(0). Factor -3*l**4 + 6*l**3 - t*l**3 - 4*l**3.
-l**3*(3*l + 2)
Let s = -28 + 169/6. Let r(l) be the second derivative of 1/15*l**6 + 0*l**2 + 0*l**3 - s*l**4 + 0*l**5 + 0 + 2*l. Determine y so that r(y) = 0.
-1, 0, 1
Let p(u) = 2*u**3 - 3*u**2 - u + 2. Let y be p(2). Find n, given that -4*n**3 - 4*n**2 + 4 + 5*n**3 - y*n + 3*n**3 = 0.
-1, 1
Let s = -2 + 2. Suppose 0*n = -n + 2. Factor k**3 + s*k**n + 0*k**2.
k**3
Let f(w) = 8*w**3 + 19*w**2 - 5*w. Let d(t) = 4*t**3 + 9*t**2 - 3*t. Let j(a) = 5*d(a) - 3*f(a). Factor j(s).
-4*s**2*(s + 3)
Let n = 209/1182 + -2/197. Let m(u) be the third derivative of 1/210*u**7 - 2*u**2 + 1/6*u**4 + 1/30*u**6 + n*u**3 + 1/10*u**5 + 0 + 0*u. Factor m(d).
(d + 1)**4
Suppose 5*c + 9 = 8*c. Let -3*s**c - 4 + 2*s**2 + 4 + s**2 = 0. Calculate s.
0, 1
Let v(g) be the second derivative of -g**4/24 - g**3/12 + 5*g. What is d in v(d) = 0?
-1, 0
Let m(n) be the first derivative of n**4/22 - 8*n**3/33 + 3*n**2/11 + 22. Factor m(c).
2*c*(c - 3)*(c - 1)/11
Let g(x) be the second derivative of 3*x - 25/66*x**4 - 10/33*x**3 - 1/11*x**2 + 0. Factor g(a).
-2*(5*a + 1)**2/11
Let m(t) be the second derivative of -t**6/6 + t**5/2 + 5*t**4/12 - 5*t**3/3 - 29*t. Factor m(w).
-5*w*(w - 2)*(w - 1)*(w + 1)
Suppose 30 + 3*d**2 - 111*d + 179*d - 89*d = 0. What is d?
2, 5
Let i(j) be the third derivative of 0 + 0*j - 1/280*j**7 - 1/1344*j**8 - 1/240*j**5 - 1/160*j**6 + 2*j**2 + 0*j**3 + 0*j**4. Factor i(v).
-v**2*(v + 1)**3/4
Let a be (-2 - 39/(-12)) + -1. Let h = a - -1/4. Solve -h*q**4 + 1/4*q**3 + 1/4*q**5 + 0*q + 0 + 0*q**2 = 0.
0, 1
Let x(p) = 18*p**3 - 43*p**2 + 6*p - 7. Let r(y) = 9*y**3 - 21*y**2 + 3*y - 3. Let b(n) = 13*r(n) - 6*x(n). What is a in b(a) = 0?
-1/3, 1
Let k(i) = i - 1. Suppose 6 = -3*f - 9. Let c(h) = 3*h**3 + 9*h**2 + 14*h - 2. Let g(m) = f*k(m) + c(m). Factor g(t).
3*(t + 1)**3
Suppose 3*f - 9 = 3. Solve -7*a**2 - 2*a**2 + 0*a**4 - 3*a**f - 6*a**2 - 12*a**3 - 6*a = 0.
-2, -1, 0
Let r(j) be the first derivative of 32/5*j + 24/5*j**2 + 1/10*j**4 + 9 + 6/5*j**3. What is i in r(i) = 0?
-4, -1
Let x = -203/3 + 68. Find l such that -x - 1/3*l**3 + 1/3*l + 1/3*l**2 = 0.
-1, 1
Let p(y) be the second derivative of -2/21*y**7 + 6*y + 0*y**2 - 1/3*y**4 + 0 + 1/5*y**5 + 2/15*y**6 + 0*y**3. Solve p(t) = 0 for t.
-1, 0, 1
Let s(h) = -32*h**3 + h**2 - 1. Let i be s(-1). Let k be 1*4 + i/(-8). Let 0*n**2 + 1/3*n**3 + 0 + k*n = 0. What is n?
0
Suppose 0*f = -4*f + 20. Let o be 1/4*(-2 + f). Let -1 + o*j**2 + j + 1/4*j**4 - j**3 = 0. Calculate j.
-1, 1, 2
Let r(u) be the third derivative of 3*u**2 + 1/6*u**3 + 0*u + 1/16*u**4 + 0 + 1/120*u**5. Factor r(d).
(d + 1)*(d + 2)/2
Let d(t) = -t**2 - 20*t - 27. Let a = -13 - -16. Let q(o) = -2 - 5*o - 16*o - 17 - 8. Let y(n) = a*d(n) - 2*q(n). Determine c so that y(c) = 0.
-3
Let s(p) be the second derivative of p**5/5 + 9*p**4 + 130*p**3 + 338*p**2 + 61*p. Factor s(k).
4*(k + 1)*(k + 13)**2
Let b = -3 + 3. Suppose -3*u = -b*u. Factor u + 2/5*l**5 + 2/5*l**2 - 2/5*l**4 - 2/5*l**3 + 0*l.
2*l**2*(l - 1)**2*(l + 1)/5
Suppose -l + 2 = 5*n - 3*n, -3*l + n + 6 = 0. Factor 4*x - 4*x**l - x**5 - 30 - 3*x**3 + 30 + 4*x**4.
-x*(x - 2)**2*(x - 1)*(x + 1)
Let d be -2 + 18 + 0 + -1. Suppose -5*j + 3*b + d = 0, 4 - 24 = j + 4*b. Factor -m**3 + m**4 + j*m**3 + 0 + 0.
m**3*(m - 1)
Let c(k) = -k**2 + 16*k + 4. Let d be c(16). Let z(l) be the second derivative of l + 0 + 0*l**3 - 1/54*l**d + 0*l**2. Determine q, given that z(q) = 0.
0
Let f(j) be the third derivative of -j**5/390 + j**3/39 + j**2. Find h, given that f(h) = 0.
-1, 1
Factor u**3 + 10*u + 0*u**3 + 5 - 8*u**4 + 3*u**4 - 11*u**3.
-5*(u - 1)*(u + 1)**3
Let h(q) be the first derivative of -3*q**4/16 - q**3/3 + 13*q**2/8 - 3*q/2 - 18. Find i such that h(i) = 0.
-3, 2/3, 1
Let a(v) be the second derivative of v**4/24 + v**3/3 + v**2 - 2*v. Factor a(p).
(p + 2)**2/2
Let w(j) be the first derivative of j**4/32 - 3*j**2/16 - 4*j - 1. Let m(b) be the first derivative of w(b). Factor m(q).
3*(q - 1)*(q + 1)/8
Factor 1/3*p**5 - 1/9*p**3 - 4/9*p**4 + 2/9*p**2 + 0*p + 0.
p**2*(p - 1)**2*(3*p + 2)/9
Let p = 3 - 1. Let m = -1 - -3. Factor -2*s**p + s - s**3 - m*s + 0*s.
-s*(s + 1)**2
Let h(t) be the third derivative of t**10/226800 + t**9/45360 - t**7/3780 - t**6/1080 + t**5/20 + 2*t**2. Let a(c) be the third derivative of h(c). Factor a(k).
2*(k - 1)*(k + 1)**3/3
Let y(p) be the second derivative of -p**6/180 - 3*p**5/140 - p**4/42 - p**3/6 - 3*p. Let i(q) be the second derivative of y(q). Factor i(c).
-2*(c + 1)*(7*c + 2)/7
Let d(z) = z**3 - z**2 - 4*z + 4. Let f be d(3). Let b be 1/(f/4 + -2). Factor -y - 2*y**4 + 2*y**b - y**3 + y**5 + y**3.
y*(y - 1)**3*(y + 1)
Let z(a) be the second derivative of -a**7/21 - 4*a**6/15 - a**5/2 - a**4/3 + 19*a. Factor z(j).
-2*j**2*(j + 1)**2*(j + 2)
Suppose -w = -4*t - 11 - 10, 0 = 3*w - t - 19. Let x be (-4)/15*w/(-2). Factor 4/3 + x*d**2 - 2*d.
2*(d - 2)*(d - 1)/3
Let a(j) = j**2 + 2*j - 5. Let o be a(-4). Let -o + 2*c**4 - 9*c**3 + 3*c**4 + c**4 + 9*c - 3*c**2 = 0. What is c?
-1, 1/2, 1
Let v(n) be the first derivative of n**4/42 + 4*n**3/63 + n**2/21 - 9. Factor v(c).
2*c*(c + 1)**2/21
Let b(h) be the second derivative of 6*h**7/7 - 17*h**6/10 - 47*h**5/20 + 2*h**4/3 + 2*h**3/3 - 3*h. Let b(g) = 0. What is g?
-2/3, -1/4, 0, 1/3, 2
Determine k, given that 5/3*k**5 - 5/3*k**2 + 5/3*k**4 - 5/3*k**3 +