b).
-(b - 1)**2*(b + 1)/2
Factor 0 + 1/4*j + 1/2*j**2 - 3/4*j**3.
-j*(j - 1)*(3*j + 1)/4
Let u(t) be the third derivative of 1/60*t**5 - 3*t**2 + 0*t + 0*t**3 + 1/630*t**7 + 1/120*t**6 + 1/72*t**4 + 0. Factor u(q).
q*(q + 1)**3/3
Let t(u) be the first derivative of 3*u**2 - 3/4*u**4 - u**3 + 0*u + 2. What is g in t(g) = 0?
-2, 0, 1
Suppose 5*w = -4*x + 8, 0 = 2*x - 3*x - 3*w + 2. Let c be 6/3 + x + 0. Factor 5*n**c - 3*n**4 - 2*n + 3*n**2 + 3*n**2 - 6*n**3.
2*n*(n - 1)**3
Find f, given that -3*f**2 + 0 + 3/2*f + 3/2*f**3 = 0.
0, 1
Factor 16*y - 107*y**2 + 204*y**2 - 101*y**2 + 20.
-4*(y - 5)*(y + 1)
Let t be 5 - 1*(-2)/(-1). Suppose t*a - 7 = -5*h, 5*h + 0*a - a - 11 = 0. Factor 0*w**2 + 0*w**2 + 2*w**h - 2.
2*(w - 1)*(w + 1)
Let m = 27/116 - -1/58. Let -1/2 - 1/4*j**3 + m*j - 1/4*j**4 + 3/4*j**2 = 0. What is j?
-2, -1, 1
Let c(o) = o + 10. Let x be c(-8). Determine r, given that 10/7*r**x + 16/7*r + 6/7 = 0.
-1, -3/5
Let h(f) = -2*f**2 - 58*f + 4. Let k be h(-29). Factor 0 - 2/3*o**2 + 1/3*o**5 - 4/3*o**k + 5/3*o**3 + 0*o.
o**2*(o - 2)*(o - 1)**2/3
Suppose 0 = -2*t + t + 4. Suppose 2 = 2*b - 6. Factor -16*w**3 + 7*w**t - w**4 + 5*w**2 + 14*w**2 - 5*w**2 - b*w.
2*w*(w - 1)**2*(3*w - 2)
Let i(c) = 0 + 2 + c + 3. Let y be i(-3). Let u**2 + 0*u**2 - 2 + u**y = 0. Calculate u.
-1, 1
Let h(i) = -i**3 + 3*i**2 + 2*i. Let q be h(3). Factor q*a**3 + 4/3*a - 14/3*a**2 + 2/3*a**5 + 0 - 10/3*a**4.
2*a*(a - 2)*(a - 1)**3/3
Let t(b) = 2*b**4 - 13*b**3 + 17*b**2 - 8*b + 7. Let m(l) = -2*l**4 + 14*l**3 - 18*l**2 + 8*l - 8. Let v(i) = 5*m(i) + 6*t(i). Suppose v(h) = 0. Calculate h.
1
Let z(g) = 24*g**2 - 2*g + 1. Let n be z(1). Let p(w) = n*w + w**3 - 23*w. Let k(b) = 4*b**3. Let i(d) = -k(d) + 6*p(d). Factor i(t).
2*t**3
Let l(a) = -a**2 + 6*a - 5. Let g be l(4). Let z be (2 - 7/g)*-6. Factor -d**4 + 2*d**2 - d**3 - d**z + d**5 + 0*d**5.
d**2*(d - 1)**2*(d + 1)
Let -20/9 + 2/3*z**4 - 38/9*z**3 + 14/9*z + 38/9*z**2 = 0. What is z?
-2/3, 1, 5
Let h(f) be the second derivative of f**7/42 + f**6/15 - 3*f**5/20 - f**4/3 + 2*f**3/3 + 20*f. Factor h(l).
l*(l - 1)**2*(l + 2)**2
Let y = 5236 - 183201/35. Let k = y - 7/5. Factor 2/7*x - k*x**3 + 0 + 0*x**2.
-2*x*(x - 1)*(x + 1)/7
Let s(k) = 3*k. Let m be s(7). Suppose m + 3 = 3*u. Find c, given that u*c**4 - c**4 - 4*c**3 - c**4 = 0.
0, 2/3
Solve -2*v - 4*v**3 + 71*v**4 + 2*v**2 + 3*v**2 - 70*v**4 = 0 for v.
0, 1, 2
Let w be ((-13)/338)/(2/(-16)). Factor 2/13*g**2 + 0 - w*g.
2*g*(g - 2)/13
Suppose 2/3*z + 4/9 - 4/9*z**2 - 2/3*z**3 = 0. What is z?
-1, -2/3, 1
Suppose 13*c**2 + 110*c + 605 + 4*c**2 - 12*c**2 = 0. What is c?
-11
Let u(k) = 4*k**2 - 4*k + 1. Let x(g) = -3*g**2 + 3*g. Let h(z) = -2*u(z) - 3*x(z). Determine c so that h(c) = 0.
-1, 2
Let x(r) be the first derivative of 5*r**4/11 - 2*r**3/11 - 10*r**2/11 + 6*r/11 - 4. Solve x(o) = 0 for o.
-1, 3/10, 1
Let f = 2 - -1. Let m be (-14)/(-8) + f/12. Find y such that -2*y**m + 1 + 4*y**2 - 5 + 2*y = 0.
-2, 1
Suppose 6/5*x**4 + 0 + 2/5*x**5 + 0*x + 2/5*x**2 + 6/5*x**3 = 0. Calculate x.
-1, 0
Suppose -3*l + 13 = 2*u + 4, 3*l + 4*u = 3. Factor -3 + c**4 - 1 + 2*c - 2*c**4 + l - 2*c**3.
-(c - 1)*(c + 1)**3
Let d be (-145)/150 - 3/(-3). Let j(a) be the second derivative of -1/6*a**3 - 1/5*a**2 + a - d*a**4 + 0. Let j(m) = 0. Calculate m.
-2, -1/2
Let q(i) be the first derivative of i**8/1008 + i**7/315 + i**6/360 - i**2/2 + 2. Let y(g) be the second derivative of q(g). Determine f so that y(f) = 0.
-1, 0
Suppose -465*o = -468*o. Find v, given that 2/5*v**2 + 0 + 2/5*v**3 + o*v = 0.
-1, 0
Let f be 5 + 8/(4/(-1)). Let k(b) be the third derivative of -b**2 + 0*b**f + 0 - 1/180*b**5 + 0*b - 1/72*b**4. Suppose k(z) = 0. What is z?
-1, 0
Let i(f) be the first derivative of 4*f**3/3 - 2*f**2 - 24*f - 5. Solve i(x) = 0 for x.
-2, 3
Factor 1/4*v**5 - 1/4*v - 1/2*v**2 + 1/2*v**4 + 0 + 0*v**3.
v*(v - 1)*(v + 1)**3/4
Suppose -3*c + q + 4 = 0, 3*c - 34 = 5*q - 14. Let s = 18 - 29/2. Factor s*t**2 + c + t.
t*(7*t + 2)/2
Let r = -6 + 9. Suppose r*k - 4 = k. Factor -10*d**3 - 3*d**k + d**2 - 16*d**4 - d**3 - 7*d**5.
-d**2*(d + 1)**2*(7*d + 2)
Factor -10*h**3 - 3*h**4 - 2*h**5 + 9*h - 9*h + 4*h**2 + 11*h**4.
-2*h**2*(h - 2)*(h - 1)**2
Let t = -17 + 33. Let c be (12/t*2)/6. Factor 0*o - 1/4*o**2 - c*o**3 + 0.
-o**2*(o + 1)/4
Let y(i) be the third derivative of 1/35*i**7 - 1/15*i**5 - 1/30*i**6 + 0*i + 1/4*i**4 - 1/168*i**8 + i**2 - 1/3*i**3 + 0. Factor y(j).
-2*(j - 1)**4*(j + 1)
Let g(d) be the first derivative of 1 - 1/5*d**5 + 0*d + 1/3*d**3 + 1/6*d**6 + 0*d**2 - 1/4*d**4. Factor g(k).
k**2*(k - 1)**2*(k + 1)
Let s = 0 - -1. Let j = s - -2. Solve -8 - 12*f - f**3 + 0*f**3 - 6*f**2 + 0*f**j = 0 for f.
-2
Let v(i) be the second derivative of 1/48*i**4 + 2*i - 1/8*i**2 + 0*i**3 + 0. Determine d, given that v(d) = 0.
-1, 1
Let t(y) be the first derivative of -1/20*y**5 + 0*y + 0*y**2 + 0*y**3 - 4 + 0*y**4. Factor t(i).
-i**4/4
Let d be (-47)/(-282)*(-1 + 2). Determine l so that 0*l + d*l**4 + 0*l**2 - 1/6*l**3 + 0 = 0.
0, 1
Let q(f) be the second derivative of 3*f - 1/180*f**6 + 1/120*f**5 - 1/6*f**2 + 0 - 1/36*f**3 + 1/24*f**4. Solve q(p) = 0.
-1, 1, 2
Let v = -41 + 71. Let u be 4*((-9)/v)/(-3). Suppose -2/5*p**3 + 0*p + 0 + u*p**5 + 2/5*p**2 - 2/5*p**4 = 0. What is p?
-1, 0, 1
Let o(l) be the first derivative of 3*l**5/25 + 9*l**4/20 + l**3/5 - 9*l**2/10 - 6*l/5 + 13. Determine h so that o(h) = 0.
-2, -1, 1
Let q = 36 + -107/3. Let p(l) be the first derivative of -2*l**2 - 4*l + 2 - q*l**3. Factor p(c).
-(c + 2)**2
Let p be 0/2 + -1 - -8. Suppose -p - 8 = -5*t. Factor q - q**2 + 0*q**t + 2*q**3 + q**3 - 2*q**2 - q**4.
-q*(q - 1)**3
Suppose 3*l - 3 = 4*q, -2*q + 23 = -q + 4*l. Suppose -4*u + 9*u = 3*r - 6, -6 = -3*r - u. Factor -r*b**2 - q*b + 3*b.
-2*b**2
Let g(p) be the second derivative of 3*p**5/20 - 5*p**4/2 + 17*p**3/2 - 12*p**2 + 3*p. What is t in g(t) = 0?
1, 8
Let q = -4 + 7. Suppose -3*m = -4*z + 19, 4*m = -4*z + q*z. Factor -2/3*i**z + 0*i**2 + 1/3*i**3 + 0*i + 0 + 1/3*i**5.
i**3*(i - 1)**2/3
Suppose -11*o + 44 = -15*o. Let s be 3 - (-2)/(8/o). Let -1/4*w**2 + 1/4 + s*w - 1/4*w**3 = 0. What is w?
-1, 1
Let s be ((-2)/2)/((-2)/24). Let g be s + -14 - 14/(-6). Let g*c**2 + 2/3*c + 1/3 = 0. Calculate c.
-1
Suppose 12 + 4 = 4*y. Suppose y*m = -2*r + 6*m + 2, -2*r = m - 5. Factor r*d**2 + 2 + d**3 + d**3 - 2*d - 4*d**2.
2*(d - 1)**2*(d + 1)
Let q(v) be the first derivative of -v**5/25 - v**4/20 + v**3/15 + v**2/10 - 5. Find i, given that q(i) = 0.
-1, 0, 1
Let i(o) = o - 1. Let p(y) = y**3 + 8*y**2 - y + 6. Let u be p(-8). Let z(n) = -2*n**2 - n - 13. Let v(j) = u*i(j) - 2*z(j). Determine r so that v(r) = 0.
-3, -1
Factor -15188*k + 40*k**2 + 20*k**3 + 32 + 15300*k + 48*k**2.
4*(k + 2)**2*(5*k + 2)
Determine c so that -4/11*c - 2/11*c**2 + 6/11 = 0.
-3, 1
Let u(d) be the first derivative of -2*d**5/85 - 3*d**4/34 - 4*d**3/51 + 5. Let u(m) = 0. Calculate m.
-2, -1, 0
Let h be (-5 - -7)/(-2) - (-16)/4. Find s, given that -4/5*s**2 - 2/5*s + 3/5*s**4 + 1/5 + 2/5*s**h = 0.
-1, 1/3, 1
Let v(y) be the first derivative of y**3/2 - 3*y**2/2 - 9*y/2 + 11. What is c in v(c) = 0?
-1, 3
Let 2/5*c - 2/5 + 2/5*c**2 - 2/5*c**3 = 0. What is c?
-1, 1
Suppose t = -4*t + 5. Suppose -7 = -2*i + t. Factor -4*l - i*l**4 + 3*l - 15*l**3 - 4*l**4 + 8*l**2 + 16*l**5.
l*(l - 1)*(l + 1)*(4*l - 1)**2
Suppose 4*g - 3 = -23. Let m be 0 - (3 + g/1). Factor 1/2 + s**m + 3/2*s - 1/2*s**5 - s**3 - 3/2*s**4.
-(s - 1)*(s + 1)**4/2
Let a(r) be the second derivative of r**6/10 - 3*r**5/10 - 3*r**4/4 + 2*r**3 + 6*r**2 + 6*r. Factor a(m).
3*(m - 2)**2*(m + 1)**2
Suppose -5*u + 48 = -u. Suppose 0 = -v - 3*v + u. Solve 0 + 0*q**2 + 2/9*q - 2/9*q**v = 0.
-1, 0, 1
Let i(h) be the second derivative of -4*h + 1/18*h**4 + 0*h**3 + 0*h**2 + 0 + 1/30*h**5. Solve i(d) = 0 for d.
-1, 0
Let a(y) = -3*y**3 - 16*y**2 + 48*y - 68. Let k(h) = -2*h**3 - 15*h**2 + 48*h - 67. Let u(s) = -3*a(s) + 4*k(s). Factor u(z).
(z - 4)**3
Let a = -5 - -8. Let 3*l**4 + a*l + 3*l - 9*l**2 + 0*l = 0. What is l?
-2, 0, 1
Let q(p) be the first derivative of -p**7/1260 + p**6/90 - p**5/15 + 2*p**4/9 + 2*p**3/3 - 3. Let m(h) be the third derivative of q(h). Factor m(j).
-2*(j - 2)**3/3
Let s(w) be the first derivative of -w**6/180 + w**5/30 - w**4/12 +