2 + s**2 = 0.
0
Let r(p) = -20*p**2 + 42*p + 28. Let a(n) = -7*n**2 + 14*n + 10. Let q(i) = -14*a(i) + 5*r(i). Determine k, given that q(k) = 0.
0, 7
Factor -2/9*n + 0*n**3 + 1/3*n**2 - 1/9*n**4 + 0.
-n*(n - 1)**2*(n + 2)/9
Let w(f) be the second derivative of -f**7/12600 - f**6/1800 - f**5/600 - f**4/12 + f. Let p(o) be the third derivative of w(o). Factor p(x).
-(x + 1)**2/5
Let u(b) be the third derivative of -5*b**8/336 + b**7/42 + b**6/12 - b**5/6 - 5*b**4/24 + 5*b**3/6 - 12*b**2. Determine l so that u(l) = 0.
-1, 1
Suppose 8 = 2*j - 2*p, -3*j - 4 = 2*p + 4. Let w = 117/5 - 23. Suppose w*f + j - 4/5*f**2 + 2/5*f**3 = 0. Calculate f.
0, 1
Let s(b) be the first derivative of b**3/18 - b**2/6 + 2. Factor s(p).
p*(p - 2)/6
Let b(g) be the second derivative of 16*g**6/105 + 4*g**5/7 + 17*g**4/42 + 2*g**3/21 - 4*g. Factor b(j).
2*j*(j + 2)*(4*j + 1)**2/7
Let k = 33891/7 - 4829. Let 16/7 + k*f + 64/7*f**4 + 22*f**3 + 172/7*f**2 + 10/7*f**5 = 0. Calculate f.
-2, -1, -2/5
Let w(u) be the third derivative of u**8/840 - u**6/180 + u**3/6 - 3*u**2. Let s(v) be the first derivative of w(v). Factor s(d).
2*d**2*(d - 1)*(d + 1)
Determine n so that 39*n - n**2 - 4 - 5 - 18*n - 27*n = 0.
-3
Let a(o) = 3*o**4 - 9*o**3 + 6*o**2 + 9*o. Suppose 4*v + 26 = 2*s, -6*s + 35 = -s + 5*v. Let w(y) = y. Let x(u) = s*w(u) - a(u). Factor x(k).
-3*k**2*(k - 2)*(k - 1)
Let x(w) be the first derivative of -2 + w**3 - 2*w**2 + 5*w**2 - 2*w**2 + w**3. Suppose x(u) = 0. Calculate u.
-1/3, 0
Let g = 18 + -17. Suppose 4*y = 3*m + 6, 13 = 4*y + m - g. Suppose -1/5*p - 2/5*p**4 + 0 + 3/5*p**y + 0*p**2 = 0. What is p?
-1/2, 0, 1
Let d(a) = -a**4 - a**3 + a**2 - 1. Let q(g) = 28*g**4 + 38*g**3 - 43*g**2 - 20*g + 3. Let p(f) = 3*d(f) + q(f). Factor p(i).
5*i*(i - 1)*(i + 2)*(5*i + 2)
Let l(x) = -2*x**2. Let n be l(0). Suppose n = -0*s + 3*s. Let -2/3*d**4 + s*d**3 + 0 - 1/3*d + 2/3*d**2 + 1/3*d**5 = 0. What is d?
-1, 0, 1
Let y(w) = 15*w**3 + 204*w**2 - 80*w + 4. Let h(q) = 30*q**3 + 408*q**2 - 159*q + 9. Let a(p) = 4*h(p) - 9*y(p). Determine g so that a(g) = 0.
-14, 0, 2/5
Let q = 40 - 118/3. Solve q*x**3 - 2*x + 0*x**2 + 4/3 = 0 for x.
-2, 1
Let q(r) be the third derivative of -r**2 + 0*r**3 + 0*r**5 - 1/540*r**6 + 0*r + 0 + 0*r**4. Solve q(t) = 0 for t.
0
Suppose -15 + 7 = d. Let a be d/(-3) - 6/9. Factor 0*l - 2/3*l**a + 2/3.
-2*(l - 1)*(l + 1)/3
Let p(w) = w**3 + 6*w**2 + 8*w + 5. Let v be p(-5). Let m be 10/3*(-12)/v. Factor -m*y - 4 + 4*y - y**3 + 3*y**2.
-(y - 2)**2*(y + 1)
Let t = 207 - 207. Determine i so that 0 + t*i - 1/5*i**4 + 0*i**2 + 0*i**3 = 0.
0
Determine g so that -g + 1/4*g**2 + 1 = 0.
2
Let i = 43883651/230 - 190798. Let c = i + 2/115. Factor 3/4*x**3 - c - 3/4*x + 1/2*x**2.
(x - 1)*(x + 1)*(3*x + 2)/4
Let r(u) = -u + 4. Let t be r(-8). Suppose 2*n + t = 6*n. Factor -1/2*c**n + 0*c**2 - 1 + 3/2*c.
-(c - 1)**2*(c + 2)/2
Factor 6*a**5 + 7*a**4 - 3*a**4 + 23*a**4 + 15*a**2 - 9*a - 6 + 39*a**3.
3*(a + 1)**3*(a + 2)*(2*a - 1)
Let q be -3 - (-342)/12*16/150. Let u(s) be the second derivative of 0*s**3 - 1/75*s**6 + 0 - q*s**5 + 0*s**2 - 4*s - 1/30*s**4. Let u(i) = 0. What is i?
-1, 0
Suppose 0 = -4*p + 8 + 4. Solve 0 + 0*k - 2/7*k**2 - 2/7*k**p = 0 for k.
-1, 0
Determine o, given that -16/9 - 2/9*o**4 + 8/9*o - 2/9*o**3 + 4/3*o**2 = 0.
-2, 1, 2
Factor 14*h + 4 - 8 + 4*h**2 + 5*h**3 - 8*h - 13*h**3 + 2*h**5.
2*(h - 1)**3*(h + 1)*(h + 2)
Let v(k) be the second derivative of k**5/20 + 7*k**4/12 - k**3/6 - 7*k**2/2 + 10*k - 1. Let v(f) = 0. Calculate f.
-7, -1, 1
Solve -2/5 + 2/5*n**3 - 6/5*n**2 + 6/5*n = 0.
1
Let a(u) = -u**2. Let g(m) be the second derivative of 1/6*m**3 + 0 + 3*m + 0*m**2 - 1/12*m**4. Let w(k) = -2*a(k) + g(k). Factor w(q).
q*(q + 1)
Let f = -21 - -25. Let b(l) be the third derivative of 0 + 0*l + 1/180*l**5 + 1/24*l**f + l**2 + 1/9*l**3. What is s in b(s) = 0?
-2, -1
Let r(w) be the second derivative of w**7/56 + 3*w**6/40 + 3*w**5/80 - 3*w**4/16 - w**3/4 - 22*w. Let r(h) = 0. Calculate h.
-2, -1, 0, 1
Let k(g) be the third derivative of g**8/280 + 4*g**7/105 + 17*g**6/100 + 31*g**5/75 + 3*g**4/5 + 8*g**3/15 + 5*g**2. Suppose k(i) = 0. What is i?
-2, -1, -2/3
Let u(g) be the third derivative of 1/6*g**3 + 1/60*g**5 + 0*g - g**2 + 0 + 1/18*g**4 + 1/540*g**6. Let z(d) be the first derivative of u(d). Factor z(j).
2*(j + 1)*(j + 2)/3
Solve 6*c**2 - 2*c**2 - 16*c + 4 + 17*c + 7*c = 0 for c.
-1
Factor 6/19*r + 8/19*r**2 - 36/19 - 2/19*r**3.
-2*(r - 3)**2*(r + 2)/19
Factor 20*j**4 + 28*j**2 - 25 + 25 + 4*j**5 + 35*j - 27*j + 36*j**3.
4*j*(j + 1)**3*(j + 2)
Factor 6*v**2 + 11*v**4 + 8*v**4 - 6*v**3 - 17*v**4 - 2*v.
2*v*(v - 1)**3
Let d(n) be the second derivative of -n**5/50 + n**4/10 - n**3/5 + n**2/5 - 4*n. Solve d(f) = 0.
1
Let j(i) be the second derivative of i**4/4 - i**3/2 + 10*i. Solve j(o) = 0 for o.
0, 1
Suppose 4*q - 10 = b, -2*b - 20 = -0*b + 5*q. Let k be 8/(-7) - b/5. Factor 4/7 + k*y + 2/7*y**2.
2*(y + 1)*(y + 2)/7
Let z(f) = -2*f**2 + 2*f - 1. Let g(r) be the second derivative of -r**4/12 + r**3/6 - r**2/2 + r. Let u(y) = -g(y) + z(y). Determine m, given that u(m) = 0.
0, 1
Find u such that -5/4 + 5/4*u**4 + 5/2*u + 0*u**2 - 5/2*u**3 = 0.
-1, 1
Let s be (-6)/2 - (-2 + -3). Let r(o) be the second derivative of -1/30*o**4 + 0 - 2/15*o**3 + o - 1/5*o**s. Factor r(m).
-2*(m + 1)**2/5
Let u(z) = z**5 + z**4 + z**3 + z**2 - z + 1. Let v(w) = -9*w**5 - 6*w**4 - 12*w**3 - 18*w**2 + 9*w - 12. Let h(x) = -12*u(x) - v(x). Factor h(o).
-3*o*(o - 1)*(o + 1)**3
Let o(z) be the first derivative of -2/33*z**3 + 0*z + 1/11*z**2 + 2. Factor o(a).
-2*a*(a - 1)/11
Let g(r) be the third derivative of r**7/10080 - r**6/2880 - r**5/240 - r**4/8 + r**2. Let o(h) be the second derivative of g(h). Suppose o(k) = 0. Calculate k.
-1, 2
Let v(s) be the second derivative of s**6/45 + s**5/15 + s**4/18 + 3*s. Factor v(d).
2*d**2*(d + 1)**2/3
Suppose 5*y - 27 = -4*y. Let l(s) be the third derivative of -1/60*s**6 + 1/3*s**y + 0*s - 1/4*s**4 + 3*s**2 + 1/10*s**5 + 0. Solve l(f) = 0 for f.
1
Let z(b) be the third derivative of b**8/1008 + b**7/315 - b**6/180 - b**5/45 + b**4/72 + b**3/9 + 58*b**2. Determine y, given that z(y) = 0.
-2, -1, 1
Suppose -4*z + 21 - 9 = 0. Factor -o - 4*o + z*o + o**2 + 1.
(o - 1)**2
Let f(w) = -39*w**4 - 67*w**3 - 37*w**2 - 19*w + 11. Let j(r) = 20*r**4 + 33*r**3 + 18*r**2 + 10*r - 6. Let u(n) = 6*f(n) + 11*j(n). Factor u(d).
-d*(d + 2)*(2*d + 1)*(7*d + 2)
Suppose 0 = -5*v + 54 + 16. Let d = 14 - v. Factor d - 2/3*m + 0*m**2 + 2/3*m**3.
2*m*(m - 1)*(m + 1)/3
Let m be (4/6)/(3/18). Suppose m*j - 2*j = 0. Factor 2/9*o**5 + 0*o**3 + j + 0*o**2 + 0*o + 0*o**4.
2*o**5/9
Let g(f) be the third derivative of -5*f**8/1008 - f**7/35 + f**6/45 + 20*f**2. Factor g(b).
-b**3*(b + 4)*(5*b - 2)/3
Let i(c) = -10*c**3 - 16*c**2 - c - 3. Let q = 6 + -5. Let o(b) = -3*b + 0*b + 2*b + q + b**3. Let g(s) = -2*i(s) - 6*o(s). Determine k, given that g(k) = 0.
-2, -2/7, 0
Factor 16*a**2 - 7*a**2 - 3*a**3 + 4 - 9*a - 1.
-3*(a - 1)**3
Suppose -5*b + 22 = -3*s, -5*b - s + 2 + 4 = 0. Solve 2/11*j**b + 0*j - 2/11 = 0.
-1, 1
Let i be (18/15)/((-6)/(-20)*3). Suppose i*q**3 + 0*q**2 - 4/3*q + 0 = 0. Calculate q.
-1, 0, 1
Let g(d) = -6*d**2 + 2*d + 2. Let y(n) = n**2 + n. Let k(q) = -4*g(q) - 12*y(q). Factor k(z).
4*(z - 2)*(3*z + 1)
Let j(q) be the first derivative of q**9/3024 - q**8/840 + q**6/180 - q**5/120 - 4*q**3/3 + 4. Let v(l) be the third derivative of j(l). Solve v(y) = 0.
-1, 0, 1
Let o(d) be the first derivative of -d**6/18 - d**5/15 + d**4/4 + 5*d**3/9 + d**2/3 + 2. Factor o(b).
-b*(b - 2)*(b + 1)**3/3
What is u in 9*u**3 - 7*u - 3*u**5 + 3*u**2 + 10*u - 9*u - 3*u**4 = 0?
-2, -1, 0, 1
Let c be 19/(-12) + 4/6. Let q = -1/4 - c. Suppose 0 + 0*y + 2*y**4 + q*y**2 + 8/3*y**3 = 0. What is y?
-1, -1/3, 0
Let o(c) be the first derivative of c**3/4 - 3*c/4 + 12. Factor o(m).
3*(m - 1)*(m + 1)/4
Let m(k) be the first derivative of -4*k**4/19 - 44*k**3/57 - 17*k**2/19 - 6*k/19 + 32. Let m(a) = 0. What is a?
-3/2, -1, -1/4
Factor 9*k**5 + k**2 - 3*k**2 - 7*k**5 - 2*k**3 + 4*k**2 - 2*k**4.
2*k**2*(k - 1)**2*(k + 1)
Let k be (-112)/(-16) + 1 + -6. Find c such that 0 + 1/3*c + 1/3*c**3 + 2/3*c**k = 0.
-1, 0
Let d(p) be the second derivative of 3*p**5/20 - p**4/14 + 10*p. Det