3). Factor 11*c**2 + 1/2 + 12*c**n + 4*c + 9/2*c**4.
(c + 1)**2*(3*c + 1)**2/2
Suppose 3 - 5*a + 7/3*a**2 - 1/3*a**3 = 0. What is a?
1, 3
Let k(t) be the first derivative of 0*t**2 + 2/11*t - 2 - 2/33*t**3. Find i such that k(i) = 0.
-1, 1
Suppose -5*u + 3*u + 20 = 0. Suppose -u + 2 = -4*y. Factor -2/5*t - 6/5*t**4 + 0 - 2/5*t**2 + y*t**3.
-2*t*(t - 1)**2*(3*t + 1)/5
Let q(j) = -7*j**5 + 8*j**4 + 8*j**3 - 29*j**2 + 25*j - 5. Let m(k) = 8*k**5 - 8*k**4 - 8*k**3 + 28*k**2 - 24*k + 4. Let r(i) = 3*m(i) + 4*q(i). Factor r(h).
-4*(h - 1)**4*(h + 2)
Let j(l) be the second derivative of l**5/80 - l**3/24 + 6*l. Factor j(a).
a*(a - 1)*(a + 1)/4
Let p(g) = -g**2 - 5*g - 3. Let f be p(-3). Solve y**2 + y + 2*y**4 - y**5 - f*y**2 + 0*y**2 = 0 for y.
-1, 0, 1
Let t(v) = -4*v**3 + 16*v**2 + 10*v. Let h(m) = m**3 - 5*m**2 - 3*m. Let q be (-42)/4 - (-2)/4. Let z(b) = q*h(b) - 3*t(b). Suppose z(k) = 0. Calculate k.
-1, 0
Let k(m) be the third derivative of 0*m**3 - 1/120*m**6 + 0*m + 1/105*m**7 - 1/336*m**8 + 0 + 5*m**2 + 0*m**5 + 0*m**4. Determine u so that k(u) = 0.
0, 1
Suppose -5*r + 10 + 5 = w, 0 = 2*w - 2*r - 6. Suppose -3*y = 5*z - y - 2, 0 = -w*z + 2*y + 18. Factor 6/7*j**z - 8/7 + 0*j - 2/7*j**3.
-2*(j - 2)**2*(j + 1)/7
Let p(z) be the first derivative of z**6/105 + z - 3. Let v(o) be the first derivative of p(o). Factor v(r).
2*r**4/7
Suppose 0 = -5*y + 3*b - 262, 3*y + 8 = 4*b - 147. Let a be (-4)/(-16) - y/12. Let 2/3*d - 2*d**4 + 0 + a*d**3 - 10/3*d**2 = 0. What is d?
0, 1/3, 1
Suppose -4*j + b = -2 - 3, 2*b = 2*j + 2. Factor 8*y + 2*y**2 + y + 2*y**3 - 3*y - 8*y**j - 2.
2*(y - 1)**3
Let h be 8/36 + 748/36. Let v = h - 141/7. Suppose 4/7*l**2 - 4/7 + v*l = 0. Calculate l.
-2, 1/2
Let l(m) = 1215*m**3 + 890*m**2 - 215*m - 55. Let w(j) = -45*j**3 - 33*j**2 + 8*j + 2. Let x(r) = 2*l(r) + 55*w(r). Factor x(h).
-5*h*(h + 1)*(9*h - 2)
Let z be 178/(-26) - (-12)/(-78). Let s be ((-6)/7)/(5/z). Factor s*n**2 - 2/5*n**3 - 8/5 + 0*n.
-2*(n - 2)**2*(n + 1)/5
Let z(b) be the third derivative of b**6/40 + 9*b**5/20 + 15*b**4/8 - 25*b**3/2 + 21*b**2. Factor z(l).
3*(l - 1)*(l + 5)**2
Let f be 6 + ((-9)/6)/((-1)/(-4)). Solve f*v - 4/9*v**3 - 8/9*v**2 + 2/3*v**4 + 2/9 + 4/9*v**5 = 0.
-1, 1/2, 1
Let g(p) be the second derivative of -2*p**6/35 - 4*p**5/35 + p**4/21 + 4*p**3/21 - 8*p. Factor g(o).
-4*o*(o + 1)**2*(3*o - 2)/7
Let g be (-24)/256*(-2)/6. Let h(b) be the third derivative of 0*b**3 + b**2 - 1/32*b**4 - 1/80*b**5 + 0 + g*b**6 - 3/280*b**7 + 0*b. Factor h(k).
-3*k*(k - 1)**2*(3*k + 1)/4
Let y = -1769/3 - -590. Factor -1 - 2/3*z + y*z**2.
(z - 3)*(z + 1)/3
Let u(v) be the first derivative of v**7/30 + 3*v**6/40 - v**5/12 - 3*v**4/8 - v**3/3 - v**2/2 + 1. Let t(h) be the second derivative of u(h). Solve t(w) = 0.
-1, -2/7, 1
Solve 0 + 0*d**4 + 0*d - 1/2*d**3 + 1/2*d**5 + 0*d**2 = 0.
-1, 0, 1
Let h(b) be the third derivative of -b**5/15 + 2*b**3/3 + 5*b**2. Factor h(v).
-4*(v - 1)*(v + 1)
Let s(h) = 14*h**5 - 18*h**4 + 20*h**2 - 12*h + 12. Let q(d) = d**5 - d**4 + d**2 - d + 1. Let l(t) = -12*q(t) + s(t). What is z in l(z) = 0?
-1, 0, 2
Solve -700*b**2 + b + 704*b**2 + 7*b = 0 for b.
-2, 0
Let j(z) be the first derivative of 2*z**5/5 + z**4 + 2*z**3/3 - 2. Determine n so that j(n) = 0.
-1, 0
Suppose -k = 2, 4*k - 5 = -2*n - 1. Let y(t) be the third derivative of 0*t**3 - 2*t**2 + 0*t**4 + 0 - 1/40*t**n - 1/42*t**7 + 0*t + 1/30*t**5. Factor y(i).
-i**2*(i + 1)*(5*i - 2)
Let x(y) be the second derivative of 0 - 1/12*y**3 - 1/24*y**4 - 5*y + 0*y**2 + 1/60*y**6 + 1/40*y**5. Determine n so that x(n) = 0.
-1, 0, 1
Let v(s) = s**3 - 3*s**2 + 2*s - 3. Let z be v(3). Factor 7*q**3 - 4*q**3 - 2*q**z.
q**3
Let 30 - 72*s + 920*s**2 - 155*s**2 + 337*s + 675*s**3 - 135*s**4 = 0. Calculate s.
-1/3, 6
Suppose j = -5*c + 4, 62*j - 58*j = 16. Determine b, given that 1/3*b**2 + 1/3*b + c = 0.
-1, 0
Let g(m) be the third derivative of -m**9/60480 + m**7/5040 - m**5/30 - 3*m**2. Let f(a) be the third derivative of g(a). Factor f(u).
-u*(u - 1)*(u + 1)
Let x(r) be the second derivative of 2*r**7/189 - 7*r**6/135 + 4*r**5/45 - r**4/27 - 2*r**3/27 + r**2/9 + 18*r. Determine z, given that x(z) = 0.
-1/2, 1
Suppose -5*z = -11*z + 12. Find v such that 0*v - 3/4*v**3 - 3 + 9/4*v**z = 0.
-1, 2
Let x(c) be the third derivative of 3*c**5/110 - 5*c**4/33 + 4*c**3/33 + 8*c**2. Factor x(l).
2*(l - 2)*(9*l - 2)/11
Let h(k) be the second derivative of -3*k**5/40 + k**4/2 - k**3 + 4*k. Factor h(w).
-3*w*(w - 2)**2/2
Let q = -23/4 + 25/4. Factor 1/2*a**5 - q*a + a**4 + 0*a**3 - a**2 + 0.
a*(a - 1)*(a + 1)**3/2
Let b = -14 - -14. Let a(h) be the second derivative of 3/20*h**5 + 3*h + b + 1/6*h**3 + 0*h**2 + 1/3*h**4. Solve a(z) = 0.
-1, -1/3, 0
Let u(k) be the first derivative of -k**3/3 - 3*k**2/4 + k - 5. Suppose u(g) = 0. What is g?
-2, 1/2
Let i(v) be the second derivative of v**8/36960 - v**7/13860 - v**6/3960 + v**5/660 - v**4/12 + 5*v. Let g(y) be the third derivative of i(y). Solve g(h) = 0.
-1, 1
Let a(s) = s**2 + 11*s + 12. Let i be a(-10). Let v(m) be the first derivative of 15/8*m**4 + 9/10*m**5 - 2 + 1/4*m**i + 7/6*m**3 + 0*m. Factor v(d).
d*(d + 1)*(3*d + 1)**2/2
Let p(f) be the second derivative of -5*f**9/6048 - f**8/1120 + f**7/840 + f**3/3 - 2*f. Let n(b) be the second derivative of p(b). Factor n(a).
-a**3*(a + 1)*(5*a - 2)/2
Let y(f) = f**2 - 15*f + 5. Let z be y(15). Suppose -k + 14 = 4*v, 0*k + z*k + 2 = 4*v. Find l such that 6/7*l**2 - 4/7*l + 0 - 2/7*l**v = 0.
0, 1, 2
Let j(h) = -h**3 + 8*h**2 + 2*h - 10. Let a be j(8). Let n be (0 - -3 - 2)*a. Solve -8*q + n*q**2 - 2*q + 0*q + 4 + 0*q = 0 for q.
2/3, 1
Let g(s) be the second derivative of -2*s**7/7 - 4*s**6/15 + 6*s**5/5 + 4*s**4/3 - 2*s**3 - 4*s**2 - 8*s. Determine f, given that g(f) = 0.
-1, -2/3, 1
Let j(m) be the third derivative of -m**5/15 + 2*m**4/3 - 8*m**3/3 - 3*m**2. Factor j(x).
-4*(x - 2)**2
Suppose 0 = m - 10 + 8. Solve -2/3 - 2/3*t**m + 4/3*t = 0 for t.
1
Suppose 5*w = 2*w - 2*g + 14, -3 = -3*g. Suppose -4*t = w*x - 28, 3*t = -0*x - x + 17. Solve -1/4*k + 1/4*k**3 - 1/4*k**4 + 1/4*k**x + 0 = 0.
-1, 0, 1
Let c(a) be the first derivative of -a**6/48 + a**5/20 + a**4/16 - a**3/6 - a**2/16 + a/4 + 16. Let c(k) = 0. What is k?
-1, 1, 2
Let v(k) be the second derivative of k**6/120 - 3*k**5/80 + k**4/24 - 14*k. Let v(r) = 0. What is r?
0, 1, 2
Factor -1/7*h**4 + 4/7*h**3 + 3/7 - 2/7*h**2 - 4/7*h.
-(h - 3)*(h - 1)**2*(h + 1)/7
Let b be 42/(-9) + 3 - -2. Factor 1/3*m**3 - 1/3*m + 1/3*m**2 - b*m**4 + 0.
-m*(m - 1)**2*(m + 1)/3
Let o(t) be the first derivative of -t**4 + 8*t**3/3 + 2*t**2 - 8*t - 2. Find f, given that o(f) = 0.
-1, 1, 2
Let y(c) be the third derivative of c**7/70 - c**5/10 + c**3/2 - 9*c**2. Factor y(g).
3*(g - 1)**2*(g + 1)**2
Let v be 2/7 - 360/(-63). Let i be ((-9)/v)/(9/(-12)). Factor -1/3*b + 0 + 1/3*b**i.
b*(b - 1)/3
Let b(s) be the second derivative of -s**4/12 - s**3/6 + 5*s. Suppose b(w) = 0. What is w?
-1, 0
Let d(m) = -m**3 - 6*m**2 - 6*m + 2. Let a(o) = o**2 + o - 1. Let h(x) = -3*a(x) - d(x). Find l such that h(l) = 0.
-1
Let j(h) be the second derivative of h**7/2016 - h**6/2880 + 5*h**4/12 - 7*h. Let y(g) be the third derivative of j(g). Factor y(z).
z*(5*z - 1)/4
Let d(q) = 6*q**4 + 2*q**3 + 10*q**2 - 12*q - 16. Let o(a) = -2*a**4 - a**3 - 3*a**2 + 4*a + 5. Let k(y) = -3*d(y) - 10*o(y). Find g such that k(g) = 0.
-1, 1
Let f be (2 - 0) + 26/(-39). Factor 4/3*g**3 - 1/3*g**4 - 2*g**2 + f*g - 1/3.
-(g - 1)**4/3
Let p(c) = -c**3 + 9*c**2 - 8*c + 4. Let m be p(8). Suppose m*l - 4*x - 12 = 0, l - 2 + 1 = -x. Find s, given that -l*s**2 - 3 + s**3 + 4 - s + s**2 = 0.
-1, 1
Let h = 13 + -9. Suppose -h*l + 18 = 2. Suppose 3*b - 2*b**3 + 2*b**2 + 0*b**3 - 3*b**4 + 1 - 4*b**3 - b**5 + l*b**3 = 0. Calculate b.
-1, 1
Let c(k) = k**4 - 6*k**3 + 6*k**2 - k. Let o(v) = 3*v**4 + 3*v**2 - 2*v + v - 2*v**4 - 3*v**3. Let n(q) = 4*c(q) - 7*o(q). Factor n(g).
-3*g*(g - 1)*(g + 1)**2
Let t(b) = -9*b**2 + 12*b + 4. Let s(c) = -20*c**2 + 25*c + 9. Let r(h) = 4*s(h) - 9*t(h). Solve r(g) = 0 for g.
0, 8
Let s(d) = -d + 8. Let g be (-11)/(-2) + (-3)/(-6). Let o be s(g). Solve -1 + 0*v**o + 2 - v**2 = 0 for v.
-1, 1
Let w(q) be the second derivative of -q**6/90 - q**5/30 + q**3/9 + q**2/6 + 8*q. What is n in 