et k(p) be the second derivative of 0 + 1/8*p**4 + 7/12*p**3 - 2*p - 3/2*p**2. Let k(v) = 0. What is v?
-3, 2/3
Suppose 13 = 4*p + 5*o, o = -3*o - 12. Let t(j) = 2*j**2 - 3*j + 3. Let f(q) = -3*q**2 + 5*q - 5. Let d(k) = p*t(k) + 5*f(k). Let d(w) = 0. What is w?
2
Factor 0 + 0*t - 1/3*t**4 + t**3 - 2/3*t**2.
-t**2*(t - 2)*(t - 1)/3
Let x(h) = -2*h**3 - 12*h**2 - 4*h. Let n(l) = 2*l**3 + 11*l**2 + 4*l. Let r(k) = -2*k**2 - 4*k. Let i be r(-3). Let c(z) = i*n(z) - 5*x(z). Factor c(f).
-2*f*(f + 1)*(f + 2)
Let h be 1/(-5) - (-98)/180*2. Let -h - 2/3*v**2 + 32/9*v + 14/9*v**4 - 32/9*v**3 = 0. Calculate v.
-1, 2/7, 1, 2
Let t(m) be the second derivative of -m**5/140 - m**4/4 - 20*m**3/7 - 50*m**2/7 - 43*m. Find z such that t(z) = 0.
-10, -1
Suppose 0 = -u - 5*z + 6*z + 6, -5*u - 4*z + 21 = 0. Factor 6/5*w**u + 0 + 0*w**2 - 2/5*w**3 + 0*w + 4/5*w**4.
2*w**3*(w + 1)*(3*w - 1)/5
Let s(b) = 15*b - 42. Let l be s(3). Find h, given that 0 - 1/2*h**l - 2*h**2 - 2*h = 0.
-2, 0
Let s be (-9)/(-3) - (6 + -3). Factor -4 + 2*n**2 - 3*n + s - 2*n + 3*n.
2*(n - 2)*(n + 1)
Let o(r) be the first derivative of 1/6*r**2 + 0*r**3 + 0*r - 1/12*r**4 + 8. Find z, given that o(z) = 0.
-1, 0, 1
Let n = -12 - -16. Factor -p**n + 3*p**4 + 2*p - 4*p**4 + 6*p**2 - 2*p**3 - 4.
-2*(p - 1)**2*(p + 1)*(p + 2)
Let r = 17 - 7. Suppose 8*p = 3*p + r. Factor -6*o - 2 + 7/2*o**p.
(o - 2)*(7*o + 2)/2
Factor 2/19*k**3 + 6/19*k**2 + 0 + 4/19*k.
2*k*(k + 1)*(k + 2)/19
Let p(g) = -g**3 - 7*g**2 + 2*g - 4. Let n be p(-7). Let d be 4/12 + (-38)/n. Factor 32/9*f**4 + 0 + 14/9*f**5 + 4/9*f**2 + d*f**3 + 0*f.
2*f**2*(f + 1)**2*(7*f + 2)/9
Let h = 1012 + -1012. What is t in 3/2*t**2 + 1/2*t**3 + h*t + 0 = 0?
-3, 0
Let p(a) be the first derivative of 5*a**6/6 + 5*a**5 + 15*a**4/2 - 10*a**3/3 - 35*a**2/2 - 15*a - 39. Factor p(q).
5*(q - 1)*(q + 1)**3*(q + 3)
Let i(p) = -20*p**2 - 85*p - 35. Let w(u) = -3*u**2 - 12*u - 5. Let y(o) = -2*i(o) + 15*w(o). Factor y(z).
-5*(z + 1)**2
Let w(y) = -y**5 - y**4 - y. Let i(s) = 2*s**5 - s**4 - 6*s**3 - 4*s**2 + 2*s. Let g(c) = -i(c) - 3*w(c). Factor g(v).
v*(v + 1)**4
Let g(o) be the second derivative of -o**7/15120 - o**6/1080 - o**5/180 - o**4/3 + 6*o. Let y(f) be the third derivative of g(f). Factor y(c).
-(c + 2)**2/6
Let q(d) = -d**3 - 3*d**2 - 2*d - 3. Let t be q(-3). Suppose -t*i + 2*p = -8, 4*i + 4*p - 6*p = 10. Factor 14/9*h**3 + 22/9*h + 32/9*h**i + 4/9.
2*(h + 1)**2*(7*h + 2)/9
Let n(g) = g + 3. Let q be n(0). Suppose -q*i + 4*f + 11 = 0, -2*f - 33 = -5*i + f. Factor -9 + 21*z**2 - i - 6*z + 18.
3*z*(7*z - 2)
Suppose -3*t = 3*t. Let p(h) be the third derivative of 0*h + 1/18*h**4 - 1/9*h**3 - 1/90*h**5 + h**2 + t. Determine c, given that p(c) = 0.
1
Suppose -3*o - 2*j + 7 = 0, -2 - 18 = 5*j. Let t(g) be the first derivative of 2 + 0*g**2 + 0*g**3 + 2/5*g**o + 0*g**4 + 1/3*g**6 + 0*g. Factor t(c).
2*c**4*(c + 1)
Let y(p) be the second derivative of p**8/6720 - p**6/720 + p**4/96 + 2*p**3/3 + p. Let g(k) be the second derivative of y(k). Factor g(l).
(l - 1)**2*(l + 1)**2/4
Let f be -2 + (5 - (-2 + 2)). Suppose 2*c**4 - 11*c**3 + 12*c**2 - 3*c**f + 2*c**3 + 2*c**4 - 4*c = 0. What is c?
0, 1
Let d(j) = -j**2 - 2*j + 15. Let t be d(3). Factor 1/2*n**4 + 0 + 0*n**3 - 1/2*n**2 + t*n.
n**2*(n - 1)*(n + 1)/2
Determine o, given that -6/5*o + 2/5*o**3 + 0 - 4/5*o**2 = 0.
-1, 0, 3
Suppose -4*d + s + 10 = -2*d, -4*d + 4 = 2*s. Factor d*l - 5 + l**2 + 5 - l.
l*(l + 2)
Solve -4*i**2 - 7*i**3 + 7*i**3 + 4*i**3 = 0.
0, 1
Suppose 4*j - 6 = 3*j. Let z = 9 - j. Solve 3*u - 3*u**z + 3 - 7*u + 11*u**2 - 2*u**2 - 5*u = 0.
1
Let k = 124 - 120. Solve -2/5*t**k + 2/5*t + 6/5*t**3 - 6/5*t**2 + 0 = 0.
0, 1
Let r(a) be the third derivative of a**7/252 - 2*a**6/135 - a**5/45 - a**3/6 + a**2. Let t(w) be the first derivative of r(w). Factor t(u).
2*u*(u - 2)*(5*u + 2)/3
Let v(i) = i**3 - 7*i**2 + 6*i + 2. Let j be v(6). Solve 2/3 + r + 1/3*r**j = 0.
-2, -1
Let f = -1 + -2. Let r be 2*f*(-4)/6. Determine m so that -7 + 2*m**2 - r*m + 7 = 0.
0, 2
Let x(v) = 5*v**2 - 3*v + 9 - 2*v**2 - 12*v. Let g(o) = -o - 1. Let p(t) = 3*g(t) - x(t). Factor p(s).
-3*(s - 2)**2
Let c(u) be the second derivative of u**5/80 - u**4/48 - u**3/24 + u**2/8 + 20*u. Let c(g) = 0. Calculate g.
-1, 1
Let a(b) be the third derivative of -1/36*b**4 + 1/18*b**3 + 0 + 0*b**5 + 1/180*b**6 + 2*b**2 - 1/630*b**7 + 0*b. Solve a(f) = 0.
-1, 1
Let c be 96/9*3/2. Let j be -2 - (-3)/(18/c). Determine p, given that j + 4*p**2 + 2/3*p**4 - 8/3*p - 8/3*p**3 = 0.
1
Let w(p) be the first derivative of -p**6/45 + 2*p**5/75 + p**4/30 - 2*p**3/45 - 2. Factor w(z).
-2*z**2*(z - 1)**2*(z + 1)/15
Let d be (1 - (-2 + 3))/(-6 + 4). Factor 14/3*j**2 - 10/3*j**3 + d - 4/3*j.
-2*j*(j - 1)*(5*j - 2)/3
Let q(w) be the second derivative of -1/40*w**5 + 0 - w + w**2 - 2/3*w**3 + 5/24*w**4. Factor q(h).
-(h - 2)**2*(h - 1)/2
Let a(i) = -1010*i**2 + 3*i + 2. Let z be a(-1). Let s = 2103/2 + z. Let -2 - 18*w - s*w**2 = 0. What is w?
-2/9
Let b(l) = 23*l**2 - 87*l - 48. Let j(x) = 3*x**2 - 11*x - 6. Let r(h) = -6*b(h) + 51*j(h). Determine f so that r(f) = 0.
-2/5, 3
Let u be 3*(0 + 2) + -3. Let c(x) be the first derivative of 2 - 3/4*x**2 + 1/6*x**6 + 2/3*x**u + 1/8*x**4 + 1/4*x - 9/20*x**5. Factor c(g).
(g - 1)**3*(g + 1)*(4*g - 1)/4
Let c(v) = 2*v - 3. Let x be c(3). Suppose -3*y + 13 = 4*j, 3*j + 2*y - x = 7. What is a in -2*a**j - 4*a**3 + 4*a**3 = 0?
0
Let g be 4/11*1 - 0. Let n = 2378/11 - 216. Factor -n - 6/11*c + 4/11*c**3 + 6/11*c**4 - g*c**2 + 2/11*c**5.
2*(c - 1)*(c + 1)**4/11
Let q be (-1 - 183/(-187))*74. Let w = q + 30/17. Solve w*n + 0 - 4/11*n**2 + 0*n**3 + 4/11*n**4 - 2/11*n**5 = 0.
-1, 0, 1
Let n(h) be the second derivative of -h**4/8 - 3*h**3/4 - 3*h**2/2 + 21*h. Find g, given that n(g) = 0.
-2, -1
Solve -2/7*k**2 + 2/7*k**3 - 2/7*k + 0 + 2/7*k**4 = 0.
-1, 0, 1
Let s(y) be the third derivative of -y**6/1260 - y**5/126 - 2*y**4/63 - 4*y**3/63 + 16*y**2. Factor s(z).
-2*(z + 1)*(z + 2)**2/21
Factor -3*j**3 + 51*j**3 + 33*j + 102*j**2 + 24*j**3 + 3.
3*(j + 1)*(4*j + 1)*(6*j + 1)
Suppose -2*q = -3*b + 4 + 6, 4*q = -b - 6. Factor -3/5 + 1/5*u**b - 2/5*u.
(u - 3)*(u + 1)/5
Let k(a) = 2*a - 12. Let o be k(7). Let m(y) be the first derivative of 0*y + 10/3*y**3 + y**4 + 2 + o*y**2. Suppose m(l) = 0. What is l?
-2, -1/2, 0
Suppose 2*t = 0, -5*t + 350 + 55 = 3*s. Let h be 120/s - (-2)/(-3). Factor h*m**2 - 2/9*m**4 + 2/9*m - 2/9*m**3 + 0.
-2*m*(m - 1)*(m + 1)**2/9
Let x(v) be the third derivative of -v**9/60480 + v**8/26880 - v**4/8 - v**2. Let s(a) be the second derivative of x(a). Factor s(h).
-h**3*(h - 1)/4
Suppose 2*h - 3*w - 1 = -0, 0 = -3*h + 3*w + 3. Let v = -8 - -11. Solve -h*m**3 - v*m**3 + 3*m**3 = 0 for m.
0
Let b(t) = t**3 - 11*t**2 + 30*t + 9. Let u(i) = 2*i**2 - 6*i - 2. Let h(p) = -2*b(p) - 11*u(p). Determine w so that h(w) = 0.
-1, 2
Let s(c) be the second derivative of c**4/6 - c**3 + 2*c**2 - 8*c. Determine a so that s(a) = 0.
1, 2
Let z be 5/15*(1 - 1). Factor 2/9*u**2 - 2/9*u**3 + 0 + z*u.
-2*u**2*(u - 1)/9
Let z = 17 - 13. Determine b so that b**3 - 2*b + 1 - z*b + 3 + b**3 = 0.
-2, 1
Let j(q) be the first derivative of -7/3*q**6 + 13/2*q**4 + 2/5*q**5 - 2*q - 2 - 4*q**2 - 4/3*q**3. Let t(b) be the first derivative of j(b). Solve t(d) = 0.
-1, -2/7, 2/5, 1
Let t(c) be the first derivative of -c**4/36 - c**3/9 - 3*c + 3. Let y(b) be the first derivative of t(b). Solve y(u) = 0 for u.
-2, 0
Let j(h) be the second derivative of 1/48*h**4 + 1/8*h**3 + 0 - 3*h + 1/4*h**2. Solve j(k) = 0.
-2, -1
Let t = -29 + 117/4. Factor 0 - t*q**2 + 1/4*q.
-q*(q - 1)/4
Let w(o) be the first derivative of 52*o**3/3 + 22*o**2 - 8*o - 4. Factor w(m).
4*(m + 1)*(13*m - 2)
Determine w, given that 4*w**4 - 2*w**3 - 2*w**3 + 4*w**2 - 4*w**3 = 0.
0, 1
Let c(m) = 5*m**5 - 26*m**4 + 6*m**3 + 15*m**2 - 11*m + 11. Let u(x) = x**5 - 5*x**4 + x**3 + 3*x**2 - 2*x + 2. Let p(i) = -6*c(i) + 33*u(i). Factor p(n).
3*n**2*(n - 3)*(n - 1)*(n + 1)
Suppose 0 = 5*u + 10 - 55. Suppose -2*q = -d + 3 + u, 5*d - 27 = -q. Factor -7*g + 4*g**2 + 2 - 2*g**2 - 3*g**3 + d*g**2.
-(g - 1)**2*(3*g - 2)
Let c(y) be the first derivative of -2*y**5/15 - y**4 - 26*y**3/9 - 4*y**2 - 8*y/3 - 3. Factor c(l).
-2*(l + 1)**2*(l + 2)**2/3
Let p = -37439/90 + 416. Let d(z)