 b.
-1, 0, 1/3
Let d(p) be the second derivative of 0 + 5/12*p**4 - 13/18*p**3 + p - 1/3*p**2. Factor d(f).
(f - 1)*(15*f + 2)/3
Factor 3 + 51/8*h + 15/4*h**2 + 3/8*h**3.
3*(h + 1)**2*(h + 8)/8
Find d such that 2*d**5 + 68/7*d**3 + 4/7 - 32/7*d**2 - 2/7*d - 52/7*d**4 = 0.
-2/7, 1
Suppose -2*k = 4*k - 3*k. Suppose -69/4*v**4 + k - 21/4*v**5 - 81/4*v**3 - 3/2*v - 39/4*v**2 = 0. Calculate v.
-1, -2/7, 0
Factor 1/3*q + 2*q**2 - 1/3*q**3 - 2.
-(q - 6)*(q - 1)*(q + 1)/3
Suppose 3/4 - q + 1/4*q**2 = 0. What is q?
1, 3
Suppose 8*k + 12 = 11*k. Let y(g) be the third derivative of 0 + 0*g**k + 2/105*g**7 + 5/168*g**8 + 0*g**3 + 0*g + 2*g**2 + 0*g**6 + 0*g**5. Factor y(a).
2*a**4*(5*a + 2)
What is w in -10/7*w**3 + 0 + 3/7*w**4 + 9/7*w**2 - 2/7*w = 0?
0, 1/3, 1, 2
Let j(h) = -8*h**5 + 13*h**4 - 5*h**3 - 5*h + 5. Let n(w) = -20*w**5 + 32*w**4 - 12*w**3 - 12*w + 12. Let a(v) = 12*j(v) - 5*n(v). Let a(l) = 0. Calculate l.
0, 1
Suppose -11 = -4*n - 4*h + 17, 0 = 3*n - 5*h - 61. Let b = n + -12. Suppose 0*o + 0 + 2/5*o**4 + 0*o**2 + b*o**3 = 0. What is o?
0
Let d(n) be the first derivative of n**6/21 - 2*n**5/35 - 3*n**4/14 + 2*n**3/21 + 2*n**2/7 - 5. Find p, given that d(p) = 0.
-1, 0, 1, 2
Let i(m) = 2*m - 5. Let v(g) = g**2 + 6*g + 4. Let r be v(-6). Let l be i(r). Factor -2 + 2 + l*h**2 - 2*h**4 - 2*h**3 + 2*h - h**2.
-2*h*(h - 1)*(h + 1)**2
Let 3*m**2 - 2 - 5*m**2 + 3 - 2*m + 3 = 0. Calculate m.
-2, 1
Let i(h) be the first derivative of 0*h**2 + 0*h + 3 - 1/48*h**4 + 0*h**5 + 1/3*h**3 + 1/720*h**6. Let t(u) be the third derivative of i(u). Factor t(w).
(w - 1)*(w + 1)/2
Suppose 3*r + 2*w + 57 = -32, -42 = 2*r - 3*w. Let g be -3 - 3/(r/33). Factor 2/3*h + 2/9 + g*h**2 + 2/9*h**3.
2*(h + 1)**3/9
Let -14*r**3 + 25*r**3 - 13*r**3 - 6*r + 8*r**2 = 0. What is r?
0, 1, 3
Suppose 0 = -q - 8 - 8. Let y be (4/q)/((-9)/24). Factor 0*n**3 + 0*n - 2/3*n**4 + y*n**2 + 0.
-2*n**2*(n - 1)*(n + 1)/3
Let y(g) be the third derivative of -g**5/60 + 5*g**4/24 - 2*g**3/3 - 3*g**2. Let y(t) = 0. What is t?
1, 4
Suppose -q - 3 = 1. Let i = q + 7. Factor -2*t + 0*t + i*t - 2*t**2 + t**2.
-t*(t - 1)
Find n, given that -24*n - 8*n**2 - 4*n**3 + 4*n**4 + 24*n = 0.
-1, 0, 2
Suppose 3/2*p**4 - 21/2*p**2 - 6*p**3 + 15*p + 0 = 0. What is p?
-2, 0, 1, 5
Suppose 0 - 2/3*k - 8/3*k**2 = 0. Calculate k.
-1/4, 0
Let l(x) be the second derivative of -1/6*x**4 + 1/42*x**7 + 0*x**2 - x + 1/15*x**6 - 1/6*x**3 + 0*x**5 + 0. Factor l(c).
c*(c - 1)*(c + 1)**3
Suppose -w + 15 = -5*c - 6*w, -4*w - 4 = -4*c. Let a = 1 - c. Solve -f + f**3 + 2*f - a*f = 0 for f.
-1, 0, 1
Let v be 0 + 0 + 56/4. Factor -v*g**3 - 2 + 8*g**4 - 6*g**2 + 4*g**3 - 2*g + 12*g.
2*(g - 1)**2*(g + 1)*(4*g - 1)
Let z be ((-8)/(-20))/((-2)/(-10)). Determine x so that 11*x**z - 2 + 8*x**2 - 9*x**2 - 4*x - 8*x**4 + 3*x**5 + x = 0.
-1, -1/3, 1, 2
Suppose u = -2*i + 4*u, 3*u = 5*i - 9. Suppose i*y = 2*y. Determine p, given that -1/4*p**5 - 1/2*p**2 + 1/4*p + y + 0*p**3 + 1/2*p**4 = 0.
-1, 0, 1
Let q be (-1 + 2)/(3/(-9)). Let o be (-1)/((q/12)/1). Suppose 4*l**o + 2*l**4 - 2*l**5 + l**3 + 2*l**2 - 7*l**3 = 0. What is l?
0, 1
Let i(q) be the first derivative of -2*q**5/25 - 4*q**4/5 - 32*q**3/15 - 7. Solve i(g) = 0.
-4, 0
Suppose 0 = -2*p + 3*l + 2 - 20, 4*p + 3*l = 0. Let f = -1 - p. Factor t**f + t**3 - t**4 + 2*t + 0*t**2 - 3*t.
-t*(t - 1)**2*(t + 1)
Let b(r) be the second derivative of -r**5/50 + 21*r. Find l such that b(l) = 0.
0
Let q = -9 + 9. Suppose -u - 3*k + 15 = 0, -3*u + 6*u + 4*k - 25 = q. Let -1/3*d**u - d + d**2 + 1/3 = 0. Calculate d.
1
Let c(r) be the third derivative of -r**5/510 - r**4/204 - 2*r**2. Factor c(h).
-2*h*(h + 1)/17
Let y(o) be the third derivative of o**5/10 - 27*o**4/20 + 2*o**3 - 29*o**2. Suppose y(n) = 0. What is n?
2/5, 5
Let q = 4 + -4. Let i(t) be the second derivative of 1/18*t**4 - 1/30*t**5 + 1/126*t**7 - t - 1/6*t**2 + 1/18*t**3 - 1/90*t**6 + q. Solve i(r) = 0 for r.
-1, 1
Suppose -3*u + 2*h + 94 = -0*u, -u - 3*h = -13. Suppose 3*a - 22 = 2*a - 5*o, 4*a + 5*o - u = 0. Factor -2/5*j**a + 0 + 0*j.
-2*j**2/5
Suppose 3 = 2*g - 1. Suppose 3*p - p**g - 5 + 6*p + 8 + 7*p**2 = 0. Calculate p.
-1, -1/2
Let u = -1837/36 + 205/4. Determine p, given that -2/3*p + 0 - u*p**2 = 0.
-3, 0
Let m = 17 - 14. Let q = m + 1. Factor -2/3*b**q - 2/3 + 8/3*b**3 - 4*b**2 + 8/3*b.
-2*(b - 1)**4/3
Let q be (-3498)/(-252) + 1/(-6). Let 128/7*r**4 + 0 + q*r**3 + 2/7*r + 24/7*r**2 = 0. Calculate r.
-1/4, 0
Solve -8/9*k - 16/9 - 1/9*k**2 = 0 for k.
-4
Let -128*m**3 - 3*m**4 - 3*m**2 + 239*m**3 + 9*m + 6 - 120*m**3 = 0. What is m?
-2, -1, 1
Let y(p) be the second derivative of -1/5*p**5 + 0 + 8*p + 0*p**2 + 4/3*p**3 + 1/3*p**4. Find a, given that y(a) = 0.
-1, 0, 2
Let o(w) be the second derivative of -w**4/28 - w**3/7 + 12*w. Determine q so that o(q) = 0.
-2, 0
Let u(v) be the third derivative of 0 + 0*v + v**2 + 1/600*v**6 - 1/300*v**5 + 0*v**3 - 1/60*v**4. Factor u(n).
n*(n - 2)*(n + 1)/5
Suppose 0 = 4*r + 3*k - 2, -3*r = -4*r - 2*k - 2. Let l be r/6 + 1*3. Factor -l*w + 8/3*w**2 + 2/3.
2*(w - 1)*(4*w - 1)/3
Suppose 0 = -4*k + 4*z + 16, -4*z - 6 - 6 = -2*k. Factor 3/2*a**3 - 3/2*a - 3/2*a**k + 3/2.
3*(a - 1)**2*(a + 1)/2
Let x(y) be the first derivative of -y**5/40 + y**4/24 + y**3/6 + 5*y - 3. Let b(z) be the first derivative of x(z). Let b(f) = 0. Calculate f.
-1, 0, 2
Let v(w) = 2*w + 3. Let m(n) = 5*n + 7. Let f(c) = -3*m(c) + 7*v(c). Let g(h) = 4*h**2 - 13*h. Let b(l) = 5*f(l) - g(l). Factor b(z).
-4*z*(z - 2)
Let i be (8/12)/((-4)/(-6)). Suppose -2 - i = -y. Factor 3*p**y + 5*p**2 + p + 3*p**4 - p**3 + 5*p**3.
p*(p + 1)**2*(3*p + 1)
Let k(a) be the first derivative of a**6/42 - a**4/7 - 2*a**3/21 + 3*a**2/14 + 2*a/7 + 2. Factor k(u).
(u - 2)*(u - 1)*(u + 1)**3/7
Let v(i) be the third derivative of -i**7/735 - i**6/210 + i**5/70 + 2*i**4/21 + 4*i**3/21 - 14*i**2. Suppose v(t) = 0. Calculate t.
-2, -1, 2
Let c be 0/1 + 1/(-1). Let j be 5/5 + (0 - c). Suppose -4 + 1 - 2*l + l**j + 4*l + 4 = 0. Calculate l.
-1
Let q(d) be the first derivative of 0*d - 2/9*d**3 + 1/3*d**2 - 3. Suppose q(i) = 0. Calculate i.
0, 1
Let a(n) be the second derivative of n**4/9 + 8*n**3/9 + 8*n**2/3 - 3*n. Factor a(h).
4*(h + 2)**2/3
Let s(c) = -20*c**2 + 102*c + 115. Let f(u) = 11*u**2 - 51*u - 58. Let m(n) = -7*f(n) - 4*s(n). Factor m(i).
3*(i - 18)*(i + 1)
Suppose -3*v + 0*v - 3*j = -24, 4*v - 5*j = -13. Suppose -s + 1 = -2. Factor -u**s + 2*u**3 - 2*u**4 - 3*u**v.
-2*u**3*(u + 1)
Let k = -160011/7 - -22737. Let m = k - -122. Factor -m*l**2 + 0*l + 2/7*l**3 + 0.
2*l**2*(l - 1)/7
Let u be (-2)/(2 - 6)*0. What is j in u*j**4 + 3*j**4 - 2*j**2 - j**4 = 0?
-1, 0, 1
Suppose 5*v + 8 = 4*b, -5 = -b + 2*v - 3. Let s(m) = m**2 + 7*m + 8. Let l be s(-6). Find w such that -w**2 + 3*w**3 + 0*w**2 + b*w**l = 0.
-1/3, 0
Suppose -5*p + q = -6 - 4, 3*p + 5*q + 22 = 0. Let l be 3*6/14 - p. Factor 0 + l*n**2 - 4/7*n.
2*n*(n - 2)/7
Let w = 267 + -265. Factor -2*b + w - 3/2*b**2.
-(b + 2)*(3*b - 2)/2
Let j = 1 - -2. Factor -5*q**j + 4 + 2*q + 8*q**3 - 8*q - q**3.
2*(q - 1)**2*(q + 2)
Suppose s = 3*s + 3*y - 7, 5*s = -4*y + 14. Determine t, given that 0*t**2 - 2*t + 2*t**s + t**4 - 5*t**2 = 0.
-1, 0, 2
Let c = 120 + -358/3. Let k(y) be the first derivative of 1/6*y**4 + c*y**3 + 0*y - 4 + 0*y**2. Solve k(h) = 0 for h.
-3, 0
Let y(a) be the third derivative of 7*a**6/30 + 3*a**5/5 + a**4/3 + 12*a**2. Factor y(q).
4*q*(q + 1)*(7*q + 2)
Let c(x) be the first derivative of x**3/9 + x**2 + 3*x + 14. Determine w so that c(w) = 0.
-3
Find d, given that -140*d**4 - 34*d**5 - 29*d + 89*d**2 - 4 - 249*d**2 - 21*d - 69*d**3 - 151*d**3 = 0.
-1, -2/17
Let b = 0 + 3. Let o = -13 + 16. Factor b*w**3 - 3*w**2 - 3*w**4 + w - o*w**4 + 5*w**4.
-w*(w - 1)**3
Let i(v) be the first derivative of v**4 - 4*v**3 - 8*v**2 - 35. What is q in i(q) = 0?
-1, 0, 4
Factor 3/2 + 1/2*o**3 + 7/2*o + 5/2*o**2.
(o + 1)**2*(o + 3)/2
Let q(n) be the second derivative of n**6/140 + n**5/70 + n**4/84 - n**3/2 + n. Let v(g) be the second derivative of q(g). Determine r so that v(r) = 0.
-1/3
Suppose 13 = 4*f + 1, -2*f + 14 = 4*m. Let q(r) = -r**3 - r. Let s(y) = -4*y. Let l(v) = m*q(v) - s(v). Factor l(g).
-2*g*(g - 1)*(g + 1)
Let f(j) be the second derivative of 3*j**5/4 + 5*j**4/12 - 21*j. Factor 