 o(f) be the second derivative of -1/8*f**2 - 1/80*f**p + 1/24*f**3 + 3*f + 1/48*f**4 + 0. Factor o(s).
-(s - 1)**2*(s + 1)/4
Let h(n) be the first derivative of -2*n**5/35 + 5*n**4/7 + 24*n**3/7 + 38*n**2/7 + 26*n/7 - 174. Determine i, given that h(i) = 0.
-1, 13
Suppose 5*w + 2*n = 12, -2*w + 20*n = 16*n. Suppose 2*o + 0*a - 5*a + 5 = 0, 4*o - w*a = -2. Solve -1/6*t**2 - 1/2*t + o = 0 for t.
-3, 0
Let v(l) be the second derivative of -l**7/840 + 17*l**6/360 - 31*l**5/120 + 5*l**4/8 + l**3/6 + l + 7. Let n(r) be the second derivative of v(r). Factor n(t).
-(t - 15)*(t - 1)**2
Let k(m) = 8*m**4 - 32*m**3 + 86*m**2 - 98*m + 34. Let v(s) = 2*s**4 - s**2 - s - 1. Let d(w) = -k(w) + 2*v(w). Factor d(c).
-4*(c - 3)**2*(c - 1)**2
Let b(j) be the first derivative of 14 - 2/33*j**3 + 0*j - 1/11*j**2. Factor b(d).
-2*d*(d + 1)/11
Let a(z) be the first derivative of -z**5/12 + 10*z**4/3 - 160*z**3/3 + 15*z**2/2 + 33. Let d(g) be the second derivative of a(g). Factor d(s).
-5*(s - 8)**2
Let w = 15 - 11. Suppose 0*a = -5*a, u - 2 = -a. Solve 2*o**2 + 3*o**2 - u*o**2 - 3*o**3 + 0*o**4 - o + o**w = 0.
0, 1
Factor 23/3*m**2 + 7*m - 2/3.
(m + 1)*(23*m - 2)/3
Let h(f) be the first derivative of -6 + 2/35*f**5 - 6/7*f**2 + 3/7*f**4 - 18/7*f + 16/21*f**3. Factor h(p).
2*(p - 1)*(p + 1)*(p + 3)**2/7
Let t(l) be the first derivative of l**6/180 - l**5/60 + 4*l**3/3 - 1. Let r(h) be the third derivative of t(h). Solve r(x) = 0 for x.
0, 1
Let p(y) = -3*y**4 - 32*y**3 + 282*y**2 + 688*y + 361. Let u(f) = f**4 - f**3 + f**2 - f. Let v(o) = -5*p(o) - 20*u(o). Find d such that v(d) = 0.
-1, 19
Let q(w) be the third derivative of -w**7/840 - 7*w**6/360 - 2*w**5/15 - w**4/2 + 7*w**3/6 - 21*w**2. Let u(f) be the first derivative of q(f). Factor u(t).
-(t + 2)**2*(t + 3)
Let k(r) = r + 12. Let w be k(-10). Factor -40*i**4 + 1 + 4*i**2 + 2*i + 2*i + 41*i**4 + 2*i**w + 4*i**3.
(i + 1)**4
Let x(c) be the first derivative of 2 + 0*c + 9/35*c**5 - 1/14*c**6 - 4/7*c**3 + 0*c**2 + 0*c**4. Determine q so that x(q) = 0.
-1, 0, 2
Suppose 0 = f - 3*o + 8, 0*o + o = 4. Factor f*z**2 - 3 - 2*z**3 + 4*z**3 + 28*z - 30*z - z**4.
-(z - 3)*(z - 1)*(z + 1)**2
Let i(n) = 2*n - 9. Let u be -1 - (-10 + (5 - 2)). Let y be i(u). Suppose 2*t**3 - 2*t**3 + 27*t**4 - 18*t**3 + 6*t + 0*t**y - 15*t**2 = 0. Calculate t.
-2/3, 0, 1/3, 1
Let c be 0/(5*22/55). Let z(x) be the first derivative of -3/28*x**4 + 0*x + c*x**2 + 1/7*x**3 + 5. Factor z(o).
-3*o**2*(o - 1)/7
Let h(c) = 6*c**2 - 6*c - 4. Let k be h(6). Suppose 3*i + 4 = 3*j - 11, -12 = 4*i. Determine u, given that 4*u**j - 2*u**2 - 2*u - 180 + k = 0.
-1, 2
Let x(z) be the third derivative of 3/7*z**3 - 5/56*z**4 - 1/70*z**5 + 0 + 13*z**2 + 1/280*z**6 + 0*z. Factor x(c).
3*(c - 3)*(c - 1)*(c + 2)/7
Suppose 0 = 14*v - 7*v. Let s(h) be the third derivative of h**2 + 0*h**3 + 0*h + 1/6*h**4 + 0 + 1/210*h**7 + v*h**5 - 1/40*h**6. Let s(d) = 0. Calculate d.
-1, 0, 2
Let q(k) = 3*k**4 + 24*k**3 + 26*k**2 - 5*k. Let r(z) = 3*z**4 + 24*z**3 + 25*z**2 - 4*z. Let u(s) = -4*q(s) + 5*r(s). Suppose u(l) = 0. Calculate l.
-7, -1, 0
Let j(v) = -9*v**3 - 25*v**2 + 87*v - 43. Let s(w) = -14*w**3 - 36*w**2 + 130*w - 64. Let y(h) = -8*j(h) + 5*s(h). Factor y(o).
2*(o - 1)**2*(o + 12)
Suppose 55 = 4*q - 33. Factor -27*r**2 + q*r**5 + 6*r - 11*r**5 - 33*r**4 + 45*r**3 - 2*r**5.
3*r*(r - 1)**3*(3*r - 2)
What is i in 782/3*i**2 - 56/3 - 56/3*i**3 + 32/3*i = 0?
-2/7, 1/4, 14
Find v such that -2/9*v - 4/3 + 10/9*v**2 = 0.
-1, 6/5
Let c be 14/30 - 1*(-20)/(-150). Let t(a) be the second derivative of a**3 - 6*a + 0 + 0*a**2 - 1/10*a**5 - c*a**4. Factor t(r).
-2*r*(r - 1)*(r + 3)
Let y(v) be the first derivative of v**6/9 - 14*v**5/15 - v**4/6 + 14*v**3/9 - 137. Determine t so that y(t) = 0.
-1, 0, 1, 7
Factor 0*d**3 + 0*d**3 - d**4 + 14*d**2 + d**2 + 10*d**3 - 31*d**2.
-d**2*(d - 8)*(d - 2)
Let x(o) be the first derivative of -1/240*o**6 + 0*o**2 + 0*o + 0*o**4 - 2 - 1/40*o**5 + 8/3*o**3. Let l(w) be the third derivative of x(w). Factor l(t).
-3*t*(t + 2)/2
Suppose 1/2*a**2 + 2*a + 2 = 0. Calculate a.
-2
Suppose 4*o = 2*p + 326, -5*o + 351 = 5*p + 1196. Let c = -2167/13 - p. Find w such that -2/13*w**3 - 4/13*w**2 + 2/13*w + c = 0.
-2, -1, 1
Solve -178*b**2 - 175*b**2 + b**3 + 4*b**3 + 338*b**2 = 0 for b.
0, 3
Let z be (12970/30 + 2)*(-3)/(-5). Let g = 264 - z. Factor 14/5*h - h**3 + g*h**2 - 8/5.
-(h - 4)*(h + 1)*(5*h - 2)/5
Let w(o) = -o**4 - 5*o**3 - 4*o**2 - 6*o. Let p(n) = -n**4 - 4*n**3 - 3*n**2 - 7*n. Let x(i) = 6*p(i) - 7*w(i). Factor x(l).
l**2*(l + 1)*(l + 10)
Let k = 1 - -2. Suppose k*u + 0*u = 6. What is h in 2 - 2 - h**3 + h + h**u + h = 0?
-1, 0, 2
Suppose 4*a = -57 + 21. Let n(i) = -15*i**3 + 9. Let z(p) = -7*p**3 + 8 - 3 - p**3. Let r(g) = a*z(g) + 5*n(g). Factor r(j).
-3*j**3
Let h(f) be the third derivative of -1/90*f**5 + 0*f**4 - 7*f**2 + 0 + 0*f**3 + 0*f + 1/360*f**6. Factor h(q).
q**2*(q - 2)/3
Let b = -44 + 48. Suppose 0 = -z - l + b, -z - 2*l = -11 + 3. Factor 4/5*p**2 + z + 6/5*p**3 - 2*p**4 + 0*p.
-2*p**2*(p - 1)*(5*p + 2)/5
Suppose -89*c = -64*c - 75. Let s(w) = -4*w**2 + 10 - 34*w - w**2 + 3*w**2. Let l(o) = o**2 + 11*o - 3. Let f(q) = c*s(q) + 10*l(q). Factor f(j).
4*j*(j + 2)
Let k(u) be the second derivative of -u**4/66 - 2*u**3/33 + 3*u**2/11 + 327*u. Find a such that k(a) = 0.
-3, 1
Let l(c) be the first derivative of c**9/756 - c**7/70 + c**6/45 - 13*c**3/3 + 11. Let f(y) be the third derivative of l(y). Factor f(k).
4*k**2*(k - 1)**2*(k + 2)
Factor 16/11 + 2/11*a**2 + 18/11*a.
2*(a + 1)*(a + 8)/11
Let z(u) be the second derivative of -u**4/4 - 5*u**3/2 + 37*u + 3. Factor z(g).
-3*g*(g + 5)
Factor -54*b + 37*b + 25*b - b**2 + 2 - 9.
-(b - 7)*(b - 1)
Let b be 18/(-42)*-5 + ((-32)/4)/4. Factor 4/7*v**2 - 3/7*v**3 + 0 + 0*v - b*v**4.
-v**2*(v - 1)*(v + 4)/7
Let n(k) be the second derivative of 36*k - 2*k**2 - 2/3*k**3 + 0 + 1/4*k**4 + 1/5*k**5 + 1/30*k**6. Factor n(r).
(r - 1)*(r + 1)*(r + 2)**2
Let o(c) be the third derivative of c**7/280 - c**6/480 - c**5/120 - 68*c**2. Find p, given that o(p) = 0.
-2/3, 0, 1
Suppose -4*z + 8 = 4*d, 2*z = -3*z + 3*d + 10. Suppose -12 = 4*p, -4*p - 12 = 4*o - z*o. Factor o - 1/6*h**5 - h**3 - 1/6*h - 2/3*h**2 - 2/3*h**4.
-h*(h + 1)**4/6
Let d be (-11 - 3660/(-336))/((-6)/32). Solve -16/7*v**2 + 0 + v**3 + d*v = 0 for v.
0, 2/7, 2
Let n = 55 - 53. Factor -17*v + 31*v + n*v**2 - v**3 - 15*v.
-v*(v - 1)**2
Suppose -g + 8 = -5*o - 0, 2*g + 2 = o. Let p be -8*o/4 - (3 - 1). Suppose 1/2*d - 1/4*d**p - 1/2*d**3 + 0 + 1/4*d**4 = 0. What is d?
-1, 0, 1, 2
Let h be 4 + (5 - 9 - -3). Let d be 0*h*(-5)/(-15). Find m, given that d + 1/2*m**2 - m + 1/2*m**3 = 0.
-2, 0, 1
Suppose 29*u = 19*u + 30. Suppose u*k = -4*q + 11, q - 4 = -0*k - 2*k. Factor 1/4*n**q + 1/4*n - 1/2.
(n - 1)*(n + 2)/4
Suppose -7 + 3 = -2*a. Factor -7*w**a + 3*w + 0*w + 3 - 3.
-w*(7*w - 3)
Let a(s) be the second derivative of -1/4*s**5 - 25/6*s**3 - 5/3*s**4 - 5*s**2 + 0 + 15*s. Factor a(w).
-5*(w + 1)**2*(w + 2)
Determine q so that -18605/3 - 5/3*q**2 - 610/3*q = 0.
-61
Suppose -s = -2*l - 2 + 5, -4*l + 12 = 0. Let v be ((-3)/s)/((-2)/10). Factor d**5 - 4*d**4 + 6*d**4 + 0*d**v.
d**4*(d + 2)
Let m(p) = 9*p**3 - 18*p**2 - 200*p + 512. Let z(n) = 6*n**3 - 12*n**2 - 133*n + 340. Let k(j) = -5*m(j) + 7*z(j). Factor k(x).
-3*(x - 4)*(x - 3)*(x + 5)
Let f = 47 + -20. Let p(r) = -r**3 - 2*r**2 + 9*r - 6. Let g(j) = 12*j**3 + 27*j**2 - 117*j + 78. Let n(y) = f*p(y) + 2*g(y). Factor n(o).
-3*(o - 1)**2*(o + 2)
Let m(l) = -l**3 - l**2 - 3*l - 27. Let q be m(-3). Let x(d) be the first derivative of 1 - 1/5*d**2 + 0*d + q*d**3 + 1/10*d**4. Factor x(b).
2*b*(b - 1)*(b + 1)/5
Let k(q) be the first derivative of -3*q**2 - 3/5*q**5 + q**3 + 0*q + 3/2*q**4 + 33. Find r such that k(r) = 0.
-1, 0, 1, 2
Determine y, given that 308/3*y**2 + 4/3*y**4 - 64/3*y**3 - 392/3*y + 0 = 0.
0, 2, 7
Let x be -13 - -1 - (-7448)/399. Determine r so that -8/3 - x*r - 4*r**2 = 0.
-1, -2/3
Let q(t) = 2*t**2 - 12*t + 14. Let n = 85 - 90. Let x(f) = 3*f**2 - 22*f + 29. Let j(u) = n*q(u) + 2*x(u). Factor j(p).
-4*(p - 3)*(p - 1)
What is l in 1/2*l**2 + 4*l + 15/2 = 0?
-5, -3
Let r be (-1)/3*-1*(-27)/(-63). Let w(m) be the second derivative of 7*m + 1/7*m**3 - 1/14*m**2 - 1/70*m**6 + 1/14