16/54. Factor h*g**2 - 16/9 + 4/3*g.
4*(g - 1)*(g + 4)/9
Let u = 33 - 21. Suppose -3*o = -5*c - 20, 4*o - u = 2*c + c. Find i such that 2/9*i**4 + 0*i + o + 4/9*i**2 - 2/3*i**3 = 0.
0, 1, 2
Let r(q) be the first derivative of -15 + 0*q - 2/75*q**5 + 4/45*q**3 + 0*q**2 + 1/30*q**4. Factor r(v).
-2*v**2*(v - 2)*(v + 1)/15
Factor -1024/3 + 4/3*a**3 - 80/3*a**2 + 512/3*a.
4*(a - 8)**2*(a - 4)/3
Determine q so that 0 + 22/3*q**3 + 0*q - 4*q**2 = 0.
0, 6/11
Let y be (0 - (-2)/(-4))*(-63 + 65). Let s be (y - -3)*6/(-18)*-3. Factor 3/4*g**s + 1/2*g**3 - g - 1 - 1/4*g**4.
-(g - 2)**2*(g + 1)**2/4
Let z(d) = -115 - d**2 + 53 + 61. Let g(a) = 3*a**3 + 22*a**2 - 24*a + 1. Let u(y) = g(y) + z(y). Let u(j) = 0. What is j?
-8, 0, 1
Let o(n) be the first derivative of n**6/24 - n**5/5 + 5*n**4/16 - n**3/6 + 179. Determine k, given that o(k) = 0.
0, 1, 2
Let r(g) = 6*g**5 + 39*g**3 - 77*g**2 + 32*g - 10. Let t(k) = 16*k**5 + 118*k**3 - 230*k**2 + 96*k - 28. Let l(f) = 14*r(f) - 5*t(f). Solve l(b) = 0 for b.
-4, 0, 1, 2
Let j(i) = 37*i + 6. Let n be j(0). Let z(o) be the second derivative of 0 + 0*o**4 + 1/120*o**n + 0*o**3 + 1/40*o**5 + 0*o**2 - o. Factor z(m).
m**3*(m + 2)/4
Let s(a) = 147*a**2 - 11166*a + 657072. Let l(z) = 9*z**2 - 698*z + 41067. Let t(w) = -33*l(w) + 2*s(w). Factor t(k).
-3*(k - 117)**2
Let n(k) be the third derivative of 2/15*k**5 + 0 + 0*k + 0*k**6 - 4/105*k**7 - 1/84*k**8 + 1/6*k**4 + 3*k**2 + 0*k**3. Suppose n(m) = 0. Calculate m.
-1, 0, 1
Let f(t) be the first derivative of t**3/3 - 2*t**2 - 5*t - 64. Factor f(j).
(j - 5)*(j + 1)
Let t be (-8)/((-2)/1)*(-51)/(-68). Factor -16*p**t + 4*p**3 + 4*p**3 + p**2 + 9*p**2 - 2*p**4.
-2*p**2*(p - 1)*(p + 5)
Let o(m) = 65*m**5 + 610*m**4 + 1625*m**3 - 40*m**2 + 40*m. Let p(b) = -5*b**5 - 47*b**4 - 125*b**3 + 3*b**2 - 3*b. Let y(q) = -3*o(q) - 40*p(q). Factor y(t).
5*t**3*(t + 5)**2
Let a = -101 - -103. Factor -98*y**2 + 2 + 93*y**a + 3.
-5*(y - 1)*(y + 1)
Find p, given that -56*p**4 + 23*p - 40*p + 56*p**2 + 4*p**5 + 192*p**3 - 179*p = 0.
-1, 0, 1, 7
Suppose -345*t = -347*t. Factor 0*l + 4/5*l**3 - 4/5*l**2 + t.
4*l**2*(l - 1)/5
Suppose -11*g = 103 + 7. Let i be (-22)/g - ((-42)/(-35))/(-6). Find u, given that -4/5*u**2 - 16/5*u - i = 0.
-3, -1
Factor -13/5*a**5 + 0 - 24/5*a**4 + 0*a - 9/5*a**3 + 2/5*a**2.
-a**2*(a + 1)**2*(13*a - 2)/5
Factor 37629/2*r + 38307/2 - 675/2*r**2 + 3/2*r**3.
3*(r - 113)**2*(r + 1)/2
Let q(l) = -8*l**2 + 70*l - 718. Let f(p) = 11*p**2 - 67*p + 716. Let w(i) = -4*f(i) - 6*q(i). Suppose w(g) = 0. What is g?
19
Let t(f) be the second derivative of -19/60*f**3 - 3/10*f**2 - 23*f - 1/40*f**4 + 0. Let t(c) = 0. What is c?
-6, -1/3
Let t be ((-98)/(-14) - (3 + -5)*-2) + 0. Factor 13/4*a**2 - 3/2*a**t + 1/4 - 2*a.
-(a - 1)**2*(6*a - 1)/4
Let o(k) = -k**2 + 35*k - 34. Let t be o(1). Let s(u) be the second derivative of 5/3*u**3 + 0 + t*u**2 - 10*u + 5/4*u**4 + 1/4*u**5. Factor s(j).
5*j*(j + 1)*(j + 2)
Suppose 4*y = -3*v + 1, -4*y = -5*v - 5*y + 13. Factor v*o**2 + o**3 - 1 + 16*o - 13*o + 2.
(o + 1)**3
Factor 557*p - 3*p**4 - 555*p + 6*p**3 + 6*p**2 + 5*p**4.
2*p*(p + 1)**3
Factor -2*p**5 - 60*p**4 - 6*p + 48*p**4 - 3*p**3 - 20*p**2 + 0*p**5 - 21*p**3.
-2*p*(p + 1)**3*(p + 3)
Let n(x) be the second derivative of 0 + 8*x - 13/20*x**5 + 0*x**2 + 1/5*x**6 - 2/3*x**3 - 1/42*x**7 + x**4. Find f such that n(f) = 0.
0, 1, 2
Let o(n) be the first derivative of -2*n**6/5 + 4*n**5/25 + 3*n**4/5 - 4*n**3/15 + 65. Solve o(q) = 0 for q.
-1, 0, 1/3, 1
Let l(w) be the third derivative of -14*w**2 + 1/68*w**4 - 1/51*w**3 + 0 + 0*w - 1/170*w**5 + 1/1020*w**6. Factor l(g).
2*(g - 1)**3/17
Suppose 3*a + 5*p = 24, a = -3*a - p + 32. Suppose 7*i + 8*i**2 + a*i + 6 + 3*i**3 + 4*i**2 = 0. What is i?
-2, -1
Let h(u) be the first derivative of u**7/280 - 7*u**6/120 + 3*u**5/8 - 9*u**4/8 + 11*u**3/3 - 3. Let l(z) be the third derivative of h(z). Factor l(f).
3*(f - 3)**2*(f - 1)
Let d be (3/10)/(-2*2*29/(-232)). Solve 14/5*o**2 - 9/5 - o**4 - 1/5*o**5 + d*o - 2/5*o**3 = 0 for o.
-3, -1, 1
Let d(a) be the second derivative of a**4/96 - 25*a**3/24 + 625*a**2/16 - 2*a + 38. Suppose d(m) = 0. What is m?
25
Let u(p) be the second derivative of p**7/147 - 2*p**6/35 - 3*p**5/70 + 4*p**4/3 - 4*p**3/7 - 144*p**2/7 + 368*p - 1. Find h such that u(h) = 0.
-2, 3, 4
Let r(f) = -1 - 10*f**2 - f**2 + 3 + 2*f**2 + 8*f + f**3. Let j be r(8). Let -1/2*u**5 - 2*u**2 + 0 - j*u**4 - 1/2*u - 3*u**3 = 0. Calculate u.
-1, 0
Let r = -9 + 11. What is g in 2 - 100*g**r - 2 + 104*g**2 = 0?
0
Factor -3*f**4 - 21*f**2 - 15*f**3 - 24026 - 9*f + 24026.
-3*f*(f + 1)**2*(f + 3)
Let f(t) be the third derivative of -t**8/168 + 11*t**7/210 + 7*t**6/120 - t**5/10 - 243*t**2. Solve f(w) = 0 for w.
-1, 0, 1/2, 6
Let n(r) = -2*r - 57. Let a be n(-12). Let g be a/39 + -2 - (-2 + -1). Factor -4/13*i + 4/13*i**3 + 0*i**2 + g - 2/13*i**4.
-2*(i - 1)**3*(i + 1)/13
Let y = 11372 + -11370. Suppose 2/9*v + 0 + 2/9*v**y = 0. What is v?
-1, 0
Let i(t) be the first derivative of t**4/20 - 4*t**3/15 + 2*t**2/5 + 396. Determine x so that i(x) = 0.
0, 2
Let q(g) be the second derivative of -g**4/120 - g**3/10 - g**2/4 + 261*g. Find z, given that q(z) = 0.
-5, -1
Let c = 317 - 317. Let i(l) be the second derivative of l + c*l**4 + l**2 + 0 - 1/5*l**5 - 1/15*l**6 + 2/3*l**3. Solve i(t) = 0 for t.
-1, 1
Suppose 0*f = 3*f. Suppose 4*u - v - 30 - 4 = f, -u = 4*v. Factor -15*k**2 - 4*k**3 - 36*k - 17*k**2 + u*k**2.
-4*k*(k + 3)**2
Let r(i) be the second derivative of -13/9*i**3 - 1/36*i**4 - 46*i + 0 - 169/6*i**2. What is h in r(h) = 0?
-13
Solve 1120*o**2 + 69*o + 0 + 145*o**3 + 911*o + 0 + 5*o**4 = 0 for o.
-14, -1, 0
Factor 2/9*l**3 + 8/9*l + 0 + 8/9*l**2.
2*l*(l + 2)**2/9
Let m(s) be the third derivative of 0 - 21*s**2 + 0*s + 0*s**3 + 1/360*s**5 + 1/72*s**4. Let m(o) = 0. Calculate o.
-2, 0
Let d(h) be the first derivative of h**5/150 - h**4/45 - 4*h**3/45 + 8*h**2/15 + 4*h - 26. Let p(w) be the first derivative of d(w). Solve p(l) = 0.
-2, 2
Let a(z) be the second derivative of z**7/126 - 7*z**6/90 - 53*z**5/60 + 19*z**4/4 + 72*z**3 + 288*z**2 - z - 1. Solve a(m) = 0.
-3, 8
Let z(g) be the first derivative of 961*g**4/12 + 1798*g**3/9 - 122*g**2/3 + 8*g/3 - 132. Factor z(x).
(x + 2)*(31*x - 2)**2/3
Let j be 29/(-22) + -1 + 3455/1382. Factor 0 + 8/11*m**4 - 10/11*m**3 - j*m**5 + 4/11*m**2 + 0*m.
-2*m**2*(m - 2)*(m - 1)**2/11
Let s(g) be the second derivative of g**4/78 + 28*g**3/39 + 96*g**2/13 + 578*g. Factor s(m).
2*(m + 4)*(m + 24)/13
Let s = -3420 + 3422. Solve 1/8*t**s + 9/2 - 3/2*t = 0 for t.
6
Determine b, given that 14/11 - 26/11*b - 70/11*b**3 - 102/11*b**2 - 8/11*b**4 = 0.
-7, -1, 1/4
Factor -405/4*n**2 + 0 - 3/4*n**4 - 63/4*n**3 - 729/4*n.
-3*n*(n + 3)*(n + 9)**2/4
Suppose 3*p - 5*p + 90 = 0. Suppose 15 - 80*y - 5*y**3 + p - 38*y**2 + 73*y**2 = 0. Calculate y.
2, 3
Let u(f) = -2*f**3 - f**2 + 4*f + 1. Let o be u(-2). Let x = 137 - 137. Factor 6/7*p**4 + x + 0*p + 0*p**2 - 2/7*p**3 + 8/7*p**o.
2*p**3*(p + 1)*(4*p - 1)/7
Let o(c) be the second derivative of 5*c**4/36 + 25*c**3/18 - 5*c**2 + 150*c. Factor o(j).
5*(j - 1)*(j + 6)/3
Let d(c) be the first derivative of -c**7/840 + c**6/180 - c**5/120 + 26*c**3/3 - 21. Let m(v) be the third derivative of d(v). Let m(o) = 0. What is o?
0, 1
Let o(f) = -f**2 + 3*f + 2. Let q be o(3). Factor 0*w**3 + 131*w - 3*w**3 + w**3 + w**q - w**4 - 129*w.
-w*(w - 1)*(w + 1)*(w + 2)
Let h(t) be the third derivative of t**5/60 - 17*t**4/6 + 578*t**3/3 + 11*t**2 + 3. Suppose h(f) = 0. Calculate f.
34
Let f(o) be the third derivative of o**8/13440 - o**7/1680 + o**5/60 + o**4/12 - 7*o**2. Let c(k) be the second derivative of f(k). Factor c(x).
(x - 2)**2*(x + 1)/2
Let r(c) be the third derivative of -c**7/420 + c**6/120 + c**5/10 - c**4/6 - 8*c**3/3 + 2*c**2 + 40. Factor r(y).
-(y - 4)*(y - 2)*(y + 2)**2/2
Factor 8*s**2 - s**4 - 5/2*s**3 + 0 - 9/2*s.
-s*(s - 1)**2*(2*s + 9)/2
Let t(h) be the second derivative of 3/2*h**2 + 1/6*h**4 - 11/12*h**3 + 1/40*h**5 - 27*h + 0. Determine g so that t(g) = 0.
-6, 1
Determine t so that 13/9*t**2 - 5/9*t**4 - 1/3*t**3 - 4/3 - 1/9*t**5 + 8/9*t = 0.
-3, -2, 1
Let y(v) be the third derivative of -v**6/240 - v**5/40 - v**4/16 - 13*v**3/6 - 4*v**2. Let l(o) be the first derivative of