 Let i be 3/9*(3 + z). Let 0 + b**3 + 0*b**2 + i*b - 1/2*b**4 = 0. Calculate b.
0, 2
Let r(h) be the third derivative of h**8/784 - h**7/245 + h**5/70 - h**4/56 + 12*h**2. Let r(y) = 0. What is y?
-1, 0, 1
Let m(q) = 3*q**5 + 9*q**4 - 27*q**3 + 15*q**2 - 12*q. Let h(n) = -2*n**5 - 10*n**4 + 27*n**3 - 16*n**2 + 11*n. Let s(r) = 6*h(r) + 5*m(r). Factor s(w).
3*w*(w - 2)*(w - 1)**3
Let r(i) = 27*i + 138. Let p be r(-5). Solve 2/3*v**2 + 2/3*v - 2/3*v**p - 2/3 = 0.
-1, 1
Let q(t) = -43*t**2 - t. Let b be q(-1). Let j be 2/(-8) + b/(-72). Factor -2/3*d**3 + 1/3*d**4 + j*d**5 + 1/3*d - 2/3*d**2 + 1/3.
(d - 1)**2*(d + 1)**3/3
Let a be -3 - ((-60)/(-2))/(-3). Let y(x) be the first derivative of 1/3*x**6 + 4/5*x**5 - 16/3*x**3 - a*x**2 - x**4 - 3 - 4*x. Determine g so that y(g) = 0.
-1, 2
Let z = -673/7 - -97. Suppose 0 = -5*j - 0*j. Factor -2/7*k**2 + j - 6/7*k**3 - 2/7*k**5 - z*k**4 + 0*k.
-2*k**2*(k + 1)**3/7
Let l(s) be the third derivative of -s**6/120 - s**5/60 + s**4/24 + s**3/6 + 17*s**2. Let l(g) = 0. What is g?
-1, 1
Let d(h) = -h**3 + 13*h**2 + 3*h - 39. Let a be d(13). Solve 2/3*r**2 + 0*r + a - 2/3*r**3 = 0 for r.
0, 1
Let c(a) be the first derivative of 0*a**2 - 7*a**6 + 2 - a**4 + 0*a**3 + 26/5*a**5 + 0*a. Factor c(f).
-2*f**3*(3*f - 1)*(7*f - 2)
Let f(h) be the first derivative of -4/9*h**3 + 5/3*h**4 + 3 + 0*h**2 + 0*h - 5/3*h**5. Factor f(z).
-z**2*(5*z - 2)**2/3
Let d(o) be the second derivative of -o + 1/30*o**3 + 0*o**2 + 0 + 1/60*o**4. Factor d(a).
a*(a + 1)/5
Let q(c) be the second derivative of c**7/6300 + c**4/3 + 6*c. Let d(a) be the third derivative of q(a). Factor d(o).
2*o**2/5
Let y(n) be the first derivative of -3 + 49/16*n**4 + 77/12*n**3 + n + 4*n**2. Factor y(f).
(f + 1)*(7*f + 2)**2/4
Let j(x) be the second derivative of -x**6/150 + x**5/100 + x**4/20 - x**3/30 - x**2/5 + 29*x. Factor j(o).
-(o - 2)*(o - 1)*(o + 1)**2/5
Suppose -4*c - 5*a = 17, 0 = 3*c - 2*a - a - 21. Let z = -119/72 - -15/8. Solve -4/9*t - 2/9 - z*t**c = 0.
-1
Let b(k) be the first derivative of -k**5/30 - k**4/6 - 5*k**3/18 - k**2/6 + 67. What is z in b(z) = 0?
-2, -1, 0
Let a(z) be the third derivative of z**5/30 - z**4/6 + 2*z**2. Factor a(q).
2*q*(q - 2)
Suppose 16 + 5 = 3*w. Let d(z) = -7*z**2 + 2*z - 10. Let h(n) = 8*n**2 - n + 9. Let k(x) = w*d(x) + 6*h(x). Factor k(o).
-(o - 4)**2
Let y = 79/504 + -2/63. Let a(b) be the second derivative of -1/80*b**5 - 1/48*b**4 + y*b**2 + 2*b + 1/24*b**3 + 0. Solve a(k) = 0.
-1, 1
Let y(n) = -n**2 - 2*n + 4. Let f(p) = -2*p**2 - 4*p + 9. Let w(d) = 4*f(d) - 9*y(d). Let w(v) = 0. Calculate v.
-2, 0
Let a(g) = -6*g**4 + 6*g**3 - 6*g**2 + 6*g - 3. Let o(w) = 11*w**4 - 13*w**3 + 13*w**2 - 11*w + 5. Let c(v) = -5*a(v) - 3*o(v). Factor c(u).
-3*u*(u - 1)**3
Let v be (5/15)/(7/24). Factor 0 + v*u**2 + 8/7*u + 2/7*u**3.
2*u*(u + 2)**2/7
Let j(b) = 9*b**4 + 2*b**2 + 3*b - b**4 + 3*b - 5*b**3 + b**3. Let y(m) = 7*m**4 - 3*m**3 + m**2 + 5*m. Let x(c) = -5*j(c) + 6*y(c). What is d in x(d) = 0?
-2, 0, 1
Suppose 0 = -5*q + 3 + 2. Let p(j) = 2*j**2. Let l be p(q). Solve -3*a**l + 4*a - 2*a + 2*a**3 - a**2 = 0 for a.
0, 1
Let z = -52 - -52. Let j(m) be the second derivative of 1/6*m**3 + z*m**2 + 0*m**4 + 1/42*m**7 + 0 - m - 1/10*m**5 + 0*m**6. Find b such that j(b) = 0.
-1, 0, 1
Solve 3/2*w - 1 + 1/2*w**2 + 1/2*w**4 - 3/2*w**3 = 0 for w.
-1, 1, 2
Let p(a) be the second derivative of 0*a**2 - 1/90*a**5 + 1/27*a**3 + 0*a**4 + 5*a + 0. Factor p(l).
-2*l*(l - 1)*(l + 1)/9
Let n(j) be the third derivative of -j**6/40 + j**5/4 - 3*j**4/8 - 9*j**3/2 + 9*j**2. Factor n(l).
-3*(l - 3)**2*(l + 1)
Suppose 3*y + 18 = 5*h, 3*y + 2*h + 3*h = 12. Let r = 4 + y. Solve 2*c**3 + c - r*c + 0*c = 0 for c.
-1, 0, 1
Suppose -y + 24 + 5 = 0. Suppose 0 = 6*b - y + 11. Solve 1/3*k**4 - 1/3*k**2 - 1/3*k**5 + 0 + 0*k + 1/3*k**b = 0 for k.
-1, 0, 1
Let d(a) be the third derivative of -a**6/60 - a**5/30 + a**4/6 - 21*a**2. Suppose d(x) = 0. Calculate x.
-2, 0, 1
Let y(a) be the third derivative of -a**8/84 + a**7/70 + 3*a**6/40 + a**5/30 + 16*a**2. Find l, given that y(l) = 0.
-1, -1/4, 0, 2
Suppose -v - 4*v + 4*w - 75 = 0, -2*w = v + 1. Let f = 15 + v. Factor 0*r**4 - 3*r**4 + 5*r**f + 3*r**3 + r**3.
2*r**3*(r + 2)
Let d be (-4)/(-14) - 4/(-84). Let h = d + 1/6. Determine f, given that 1/2*f - f**2 + 1/2*f**4 + 1/2*f**5 - f**3 + h = 0.
-1, 1
Suppose -2*q = -3*x + 8, -3*q = -3*x - 2*q + 10. Suppose 4*a - 20 = -x. Determine z so that -2*z**2 + a*z**2 + 2*z - z**2 - z = 0.
-1, 0
Let n = 120 + -596/5. Factor -4/5*k**2 + 8/5*k - n.
-4*(k - 1)**2/5
Let m(k) be the first derivative of k**6/10 - 3*k**4/20 + 7. Factor m(y).
3*y**3*(y - 1)*(y + 1)/5
Let j(v) be the second derivative of 0*v**4 - 1/120*v**6 - v**2 - 2*v + 0 - 1/60*v**5 + 0*v**3. Let s(o) be the first derivative of j(o). Factor s(n).
-n**2*(n + 1)
Let c be (-8)/(-6) + 4/(-8). Let o = c + -1/3. Factor -o*i**4 + 0*i + 0 - 1/2*i**2 - i**3.
-i**2*(i + 1)**2/2
Let r(u) be the second derivative of -1/25*u**5 + 0 + 2*u + 1/30*u**4 + 0*u**2 + 0*u**3 + 1/75*u**6. Factor r(m).
2*m**2*(m - 1)**2/5
Let j(l) = 2*l + 15. Let s be j(0). Let m = s - 12. Factor 0*t**4 + 0*t + 0*t**2 + 1/4*t**m + 0 - 1/4*t**5.
-t**3*(t - 1)*(t + 1)/4
Let i = 10 - 4. Let w = i - 4. Let 0*l + l + l**2 - 2*l**w = 0. Calculate l.
0, 1
Let x(p) = -p**4 - 5*p**3 - 2*p**2 - 10*p. Let v(a) = a**4 + 5*a**3 + 3*a**2 + 9*a. Let w(o) = -6*v(o) - 5*x(o). Find m, given that w(m) = 0.
-2, -1, 0
Let i(x) be the first derivative of 15/4*x**4 + 5/2*x**5 + 2*x - 11/6*x**3 - 2 - 3*x**2. Factor i(q).
(q + 1)**2*(5*q - 2)**2/2
Let b = -2701/2 + 1351. Factor 1/4*f**3 + 1 + b*f**2 - 7/4*f.
(f - 1)**2*(f + 4)/4
Let p(w) be the third derivative of 1/10*w**5 + 3/40*w**6 + 0*w + w**2 + 0 + 1/70*w**7 + 0*w**3 + 0*w**4. Factor p(h).
3*h**2*(h + 1)*(h + 2)
Factor -1/4*p**3 - 3/4*p + 3/4*p**2 + 1/4.
-(p - 1)**3/4
Determine r, given that r - 12*r**2 + 7*r - 2*r**4 + 7*r**3 - r**3 + r**4 = 0.
0, 2
Let m(h) be the second derivative of -2*h**6/105 + h**4/7 - 4*h**3/21 + 9*h. Factor m(u).
-4*u*(u - 1)**2*(u + 2)/7
Let d(b) be the third derivative of -b**6/5 - b**5/15 + b**4 + 2*b**3/3 + 28*b**2. Factor d(i).
-4*(i - 1)*(i + 1)*(6*i + 1)
Find s, given that -13*s**2 - 5*s**3 - 26*s**2 - 6*s - 22*s**3 + 6*s**2 = 0.
-1, -2/9, 0
Factor -3*z**3 - 3*z**3 - z**4 + 5*z**3 + 4*z**2 + 2*z**3 - 4*z.
-z*(z - 2)*(z - 1)*(z + 2)
Let f(y) = 7*y**2 - 1. Let s be f(1). What is o in -s*o**2 + o**3 + 6*o**3 - 4*o**3 = 0?
0, 2
Let w(a) be the second derivative of -4/9*a**3 + 0 - 2/15*a**5 + 1/3*a**4 - 3*a + 1/3*a**2 + 1/45*a**6. Suppose w(z) = 0. What is z?
1
Let r(z) be the first derivative of -1/3*z**3 + 0*z - z**2 + 6. Factor r(v).
-v*(v + 2)
Let q(t) be the first derivative of -t**5/15 + 7*t**4/12 - 5*t**3/3 + 13*t**2/6 - 4*t/3 + 21. Factor q(y).
-(y - 4)*(y - 1)**3/3
Let k = -67 - -67. What is s in k + 2*s - 2/3*s**2 = 0?
0, 3
Let m(y) be the second derivative of 0*y**3 + 4*y + 0 + 0*y**4 + 1/15*y**5 + 1/60*y**6 + 3/2*y**2. Let u(f) be the first derivative of m(f). Factor u(n).
2*n**2*(n + 2)
Let r(c) be the third derivative of -c**10/7560 - c**9/1890 - c**8/1680 - c**4/12 - 3*c**2. Let k(t) be the second derivative of r(t). Let k(f) = 0. What is f?
-1, 0
Factor 3/5*q**3 - 9/5*q**2 + 9/5*q - 3/5.
3*(q - 1)**3/5
Let y be (0 + 2 - 0) + 0. Find x such that x + x - 2*x**3 - 2*x - y*x + 5*x**2 = 0.
0, 1/2, 2
Let c(t) = -5*t + 43. Let r be c(8). Let -2/3*i**r + 0 + 0*i - 2/3*i**2 = 0. Calculate i.
-1, 0
Let u(v) be the first derivative of v**6/480 - v**5/80 + v**4/48 - 3*v**2/2 + 2. Let b(p) be the second derivative of u(p). Let b(x) = 0. Calculate x.
0, 1, 2
Let y(k) be the first derivative of -k**7/2940 - k**6/1260 + k**5/420 + k**4/84 - 2*k**3/3 + 4. Let x(b) be the third derivative of y(b). Factor x(m).
-2*(m - 1)*(m + 1)**2/7
Let v = 8 + -8. Suppose -m - 4*m = v. Determine g so that m - 2/5*g**3 - 2/5*g**2 + 2/5*g + 2/5*g**4 = 0.
-1, 0, 1
Let q(k) = k**5 + k**4 + k - 1. Let u(z) = 12*z**5 + 2*z**4 + 2*z**3 + 20*z**2 + 2*z - 26. Let h(v) = -10*q(v) + u(v). Factor h(a).
2*(a - 2)**3*(a + 1)**2
Suppose 5*u**2 - 5*u**4 + 3*u**3 + u - 14*u**5 + 0*u + 10*u**5 = 0. What is u?
-1, -1/4, 0, 1
Let q(a) be the second derivative of 1/12*a**3 + 1/8*a**2 + 1/48*a**4 + 0 + 3*a. Factor q(d).
(