 = 17*j**4 - 27*j**3 + 17*j**2 + 27*j - 18. Let b(n) = -3*d(n) - 8*h(n). Factor b(y).
-3*(y - 2)*(y - 1)**2*(y + 1)
Let q be -6 - (-192)/(-90)*-3. Find t such that -q - 3/5*t - 1/5*t**2 = 0.
-2, -1
Suppose o - 31 = -3*o - d, o = 3*d - 2. Factor -4*p + 2*p + 2 + p**2 - 2*p + o*p.
(p + 1)*(p + 2)
Let s(x) = x**2 + x. Let o be s(-4). Factor -o*v - 4*v**2 - 18 - v**2 + 3*v**2.
-2*(v + 3)**2
Let f = -293/6 + 49. Let a(z) be the second derivative of 0 + 1/20*z**5 - z - f*z**3 + 1/12*z**4 - 1/2*z**2. Factor a(g).
(g - 1)*(g + 1)**2
Let y(n) be the third derivative of -1/6*n**4 - n**2 - 1/60*n**6 + 0*n**3 + 0 - 1/10*n**5 + 0*n. Factor y(q).
-2*q*(q + 1)*(q + 2)
Let q(j) = j**2 + 2*j + 1. Let m be q(-1). Suppose k = -m*k. Factor -1/2*h**2 + h**3 + k + 0*h - 1/2*h**4.
-h**2*(h - 1)**2/2
Let l = 7 - 9. Let n(j) = -3*j - 2. Let c be n(l). Factor 0*g - 2/3*g**c - 2/3*g**5 + 0 + 2/3*g**3 + 2/3*g**2.
-2*g**2*(g - 1)*(g + 1)**2/3
Let i(w) = -10*w**3 + 26*w. Let r(z) = -2*z**3 + 5*z. Let g(a) = -3*i(a) + 16*r(a). Factor g(u).
-2*u*(u - 1)*(u + 1)
Factor -1/3*r**3 + 1/3*r**2 + 0*r - 1/3*r**4 + 1/3*r**5 + 0.
r**2*(r - 1)**2*(r + 1)/3
Let n(b) be the first derivative of 147*b**4/32 + 35*b**3/4 - 39*b**2/4 + 3*b - 2. Suppose n(y) = 0. Calculate y.
-2, 2/7
Let u(y) be the third derivative of -y**6/120 + y**4/24 + 10*y**2. Find v such that u(v) = 0.
-1, 0, 1
Solve -30/7*r - 4/7*r**2 + 16/7 = 0.
-8, 1/2
Let b(s) be the second derivative of 0*s**3 + 3*s - 1/20*s**6 + 0*s**4 + 0*s**2 - 1/20*s**5 + 0. Determine t, given that b(t) = 0.
-2/3, 0
Let l = -1 + 0. Let r be (-2 - l)*18/(-6). Factor -2*v + v**r - 4*v**2 - 2*v - 2*v**3.
-v*(v + 2)**2
Factor 8*w**2 + 2 - 4*w - 3*w**3 + 4*w - 3*w - 4.
-(w - 2)*(w - 1)*(3*w + 1)
Suppose 3 = 2*j - 7*j + 3*v, -3*j - 2 = -2*v. Let d(x) be the third derivative of j*x**4 + 2*x**2 + 0*x**3 + 0*x + 0 + 1/30*x**5. Find l, given that d(l) = 0.
0
Let j(g) be the first derivative of -g**5/180 + g**3/18 - g**2 - 1. Let t(u) be the second derivative of j(u). Let t(z) = 0. Calculate z.
-1, 1
Factor 24/5*w**2 - 4*w**3 + 16/5*w + 4/5*w**4 - 32/5.
4*(w - 2)**3*(w + 1)/5
Let c(f) be the first derivative of f**7/3780 - f**5/180 - f**4/54 + 2*f**3/3 - 1. Let z(i) be the third derivative of c(i). Factor z(d).
2*(d - 2)*(d + 1)**2/9
Suppose 0 = -l - 4, -2*t + 5*l + 34 = 6. Factor 5*p**3 - t*p**3 + 4*p**3 + 8*p**2 - 5*p + p.
p*(p + 2)*(5*p - 2)
Let m(u) be the third derivative of 0*u**7 - 2*u**2 + 0*u**5 - 1/24*u**4 + 0*u + 0*u**3 - 1/336*u**8 + 0 + 1/60*u**6. Find g, given that m(g) = 0.
-1, 0, 1
Let s = 16 - 23. Let m(a) = a + 7. Let i be m(s). Factor -4/3*q + i + 14/3*q**2 + 2*q**4 - 16/3*q**3.
2*q*(q - 1)**2*(3*q - 2)/3
Let i(g) be the first derivative of -g**3/18 + g**2/3 - 2*g/3 - 8. Suppose i(d) = 0. What is d?
2
Let m be 6*(11/(-18))/(-11). Suppose 0 + m*k**2 + 0*k = 0. Calculate k.
0
Let k = 71 - 39. Let a = -32 + k. Find q such that -2/3*q**2 + 4/3*q + a = 0.
0, 2
Factor -3*v**3 + 4*v**2 + 2*v**5 + 0*v**3 - 4*v**4 + v**3.
2*v**2*(v - 2)*(v - 1)*(v + 1)
Let g(n) be the second derivative of -1/10*n**5 - 1/2*n**2 - 1/6*n**4 - 1/42*n**7 + 0 + 1/10*n**6 - 4*n + 1/2*n**3. Suppose g(t) = 0. What is t?
-1, 1
Let q = -6/275 + 293/825. Factor 2/3 + q*b**2 + b.
(b + 1)*(b + 2)/3
Let o(g) be the third derivative of g**6/10 + 13*g**5/20 + 3*g**4/8 - 3*g**2. Factor o(s).
3*s*(s + 3)*(4*s + 1)
Let t(f) be the first derivative of -3*f**5/100 + f**4/10 - f**3/10 + 3*f + 4. Let a(l) be the first derivative of t(l). Factor a(s).
-3*s*(s - 1)**2/5
Let z(u) be the first derivative of u**6/15 - u**4/5 + u**2/5 - 4. Let z(l) = 0. What is l?
-1, 0, 1
Let z be 88/14 + 4/(-14). Let h be 4 + (-3)/(9/z). Find a such that 4 - 2*a**3 - 4 + h*a = 0.
-1, 0, 1
Let g = 967 - 1933/2. Factor 1/2*s**3 - g*s**4 + 0 + s**2 + 0*s.
-s**2*(s - 2)*(s + 1)/2
Let q = 7 + 4. Suppose 0 = 4*b - q - 1. Factor 5/6*h**b + 8/3*h + 2/3 + 17/6*h**2.
(h + 1)*(h + 2)*(5*h + 2)/6
Suppose -5*g = -2*f - 53, g + 2*f - 1 + 0 = 0. Let a = g - 6. Factor -2*v**5 - 2*v**4 + 7*v**a - v**3 + 10*v**2 + 5*v - v.
-2*v*(v - 2)*(v + 1)**3
Let d(r) = -12*r**3 - 3*r**2 + 15*r. Let c(t) = t**4 - 11*t**3 - 2*t**2 + 14*t. Let z(o) = -3*c(o) + 2*d(o). Factor z(j).
-3*j*(j - 2)**2*(j + 1)
Let q(t) be the first derivative of t**6/42 - 2*t**5/35 - 3*t**4/7 + 6*t**3/7 + 27*t**2/14 + 59. Factor q(b).
b*(b - 3)**2*(b + 1)*(b + 3)/7
Let t(q) be the third derivative of -q**5/270 + q**4/36 - 2*q**3/27 - 10*q**2. Factor t(u).
-2*(u - 2)*(u - 1)/9
Determine a, given that -18*a + 10*a**3 + 0*a**2 + 6*a**2 + 4*a**4 - 2*a**4 = 0.
-3, 0, 1
Let p = -3415/42 + 267/7. Let w = p - -89/2. Suppose 8/3*s + w*s**3 + 2/3 + 10/3*s**2 = 0. What is s?
-1, -1/2
Let u = -54 + 58. Let f(s) be the second derivative of -s + 1/20*s**5 + 0 - 1/6*s**3 + 0*s**2 + 0*s**u. Factor f(a).
a*(a - 1)*(a + 1)
Let b(m) be the third derivative of -m**8/84 + 16*m**7/315 - m**6/90 - 8*m**5/45 + 2*m**4/9 - 10*m**2. Solve b(i) = 0.
-1, 0, 2/3, 1, 2
Let x(q) = q**3 + q**2 - 4*q - 4. Let t(v) = -v**2 + 5*v - 5. Let w be t(5). Let i(c) = 2*c**3 + 2*c**2 - 7*c - 7. Let n(b) = w*x(b) + 3*i(b). Factor n(l).
(l - 1)*(l + 1)**2
Let m = -10 - -12. Suppose 5*g**4 + 4*g**3 + 10*g**4 - m*g**2 + 5*g**3 - 4*g**2 = 0. Calculate g.
-1, 0, 2/5
Suppose -38 = v - 40. Let b = 22/7 - 52/21. Factor -m - 1/3*m**v - b.
-(m + 1)*(m + 2)/3
Let t(i) be the second derivative of 0*i**2 + 1/4*i**4 + 3/20*i**5 + 0 - 5*i - i**3. Determine r, given that t(r) = 0.
-2, 0, 1
Let d(y) be the second derivative of y**5/20 - 7*y**4/48 - y**3/12 + 5*y. Factor d(z).
z*(z - 2)*(4*z + 1)/4
Suppose -5*j - 118 + 3 = 0. Let g = -65/3 - j. Determine z so that -g*z + 0 + 2/3*z**2 = 0.
0, 2
Let -2*x + 4*x**4 - 3*x**2 + x**4 - 3*x**4 - x**4 = 0. What is x?
-1, 0, 2
Let p(s) be the first derivative of 5*s**3/3 - 5*s**2 + 5*s + 18. Find r, given that p(r) = 0.
1
Let a(d) be the first derivative of 3*d**5/20 - d**4/2 - 2*d - 3. Let v(b) be the first derivative of a(b). Factor v(c).
3*c**2*(c - 2)
Let q be 2 + 42/(-9) + 12/4. Let c be 18/(-45) - (-44)/10. Factor -q*g - 1/3*g**c + 0 - g**3 - g**2.
-g*(g + 1)**3/3
Let c(s) = s**2 + 3*s. Let n be c(-4). Let u be (2/n)/(-4 - -6). Determine d, given that 0*d + 0 + 1/4*d**2 - u*d**3 = 0.
0, 1
Let y = 27/7 + -101/28. Let i be (-14)/8 - (-1 + -1). Factor -y*m**4 - 3/4*m**3 + 0 - i*m - 3/4*m**2.
-m*(m + 1)**3/4
Let z(c) be the third derivative of -c**5/690 - c**4/138 + 44*c**2 + 2. Find q such that z(q) = 0.
-2, 0
Let h(i) be the third derivative of i**7/840 - i**6/480 - i**5/80 + i**4/96 + i**3/12 + 6*i**2. Let h(w) = 0. What is w?
-1, 1, 2
Let s(f) be the second derivative of 2*f**6/45 - 23*f**5/60 + 7*f**4/6 - 10*f**3/9 - 4*f**2/3 + 5*f. Factor s(i).
(i - 2)**3*(4*i + 1)/3
Let u(l) be the third derivative of -l**6/60 - 4*l**5/45 - 7*l**4/36 - 2*l**3/9 - l**2 - 6. Factor u(g).
-2*(g + 1)**2*(3*g + 2)/3
Let b(h) be the third derivative of h**8/50400 - h**7/12600 - h**5/30 + 4*h**2. Let x(r) be the third derivative of b(r). Factor x(m).
2*m*(m - 1)/5
Let s(u) be the third derivative of 1/270*u**5 + 0*u + 2/27*u**3 - 1/36*u**4 - u**2 + 0. Factor s(o).
2*(o - 2)*(o - 1)/9
Let 5*p**2 - 5/4*p**5 + 0 - 15/2*p**3 - 5/4*p + 5*p**4 = 0. Calculate p.
0, 1
Let m(h) be the first derivative of h**6/15 + h**5/5 - 2*h**3/3 - h**2 + 2*h + 4. Let x(j) be the first derivative of m(j). What is z in x(z) = 0?
-1, 1
Let r(p) be the first derivative of -p**4/6 - 2*p**3/3 - p**2 - 6*p - 2. Let l(y) be the first derivative of r(y). Solve l(u) = 0.
-1
Let o be (4/(-6))/((-4)/87). Let a = o + -12. Factor -a*r - 1/2*r**3 + 2*r**2 + 1.
-(r - 2)*(r - 1)**2/2
Let j(a) be the third derivative of a**7/1260 - a**6/180 + a**5/60 + a**4/24 + 2*a**2. Let h(o) be the second derivative of j(o). Suppose h(x) = 0. What is x?
1
Let j(t) be the first derivative of 7/9*t**3 + 3/5*t**5 + 0*t - 3 + 5/4*t**4 + 1/6*t**2. Determine f so that j(f) = 0.
-1, -1/3, 0
Let o(b) be the second derivative of 1/14*b**7 + 0 + 0*b**3 + 7/20*b**5 + 0*b**2 + b + 4/15*b**6 + 1/6*b**4. Factor o(t).
t**2*(t + 1)**2*(3*t + 2)
Suppose 5*v = -0*v. Let f(c) be the third derivative of 1/240*c**5 + v + 0*c + 0*c**4 + c**2 - 1/24*c**3. Factor f(s).
(s - 1)*(s + 1)/4
Let u(r) be the second derivative of r**4/36 + 13*r**3/9 + 169*r**2/6 + r + 6. Let