-153). Find n such that -b + 2/9*n**3 + 2/9*n**2 - 2/9*n = 0.
-1, 1
Let z(d) = -37*d**2 - 2304*d - 55309. Let f(y) = 6*y**2 + 384*y + 9218. Let c(k) = 13*f(k) + 2*z(k). Factor c(a).
4*(a + 48)**2
Let t(a) be the first derivative of 0*a**2 + 0*a - 1/9*a**4 + 0*a**3 + 6 - 2/45*a**5. Factor t(r).
-2*r**3*(r + 2)/9
Let m be ((-170)/(-136))/((-110)/(-16)). Factor m*y + 6/11*y**2 + 0 + 6/11*y**3 + 2/11*y**4.
2*y*(y + 1)**3/11
Determine i, given that 0 + 33/7*i**2 - 34/7*i + 1/7*i**3 = 0.
-34, 0, 1
Let z(g) be the third derivative of -4/9*g**3 + 0*g + 13/36*g**4 + 0 - 1/6*g**5 - 1/315*g**7 + 7/180*g**6 + 11*g**2. Let z(w) = 0. Calculate w.
1, 4
Let n be ((-978)/108 + 13 + -4)*-6. Let w = -2 + 5. Factor 1/3*j**4 + 1/3*j - 1/3*j**2 - n*j**w + 0.
j*(j - 1)**2*(j + 1)/3
Factor -1/6*g**4 + 1/6*g**2 + 1/6*g + 0 - 1/6*g**3.
-g*(g - 1)*(g + 1)**2/6
Let w be ((-24)/3)/(-16)*0. Let k(r) be the second derivative of w - 3/20*r**5 - r**2 + 7/6*r**3 - 1/6*r**4 - 4*r. What is l in k(l) = 0?
-2, 1/3, 1
Let v(k) be the second derivative of k**8/1680 - k**7/630 + k**4/2 - 4*k. Let t(m) be the third derivative of v(m). Factor t(n).
4*n**2*(n - 1)
Let h(a) = -2*a. Let z(x) = x**2 + 0*x**2 + 0*x - x. Let r(m) = -h(m) - z(m). Suppose r(c) = 0. What is c?
0, 3
Let h(q) be the first derivative of -2*q**3 + 117*q**2/2 - 57*q + 244. Factor h(k).
-3*(k - 19)*(2*k - 1)
Let i(x) be the third derivative of 0 - x**2 + 0*x - 1/120*x**4 - 23/600*x**6 + 1/12*x**5 - 1/5*x**3 + 1/210*x**7. Factor i(w).
(w - 3)*(w - 1)**2*(5*w + 2)/5
Let i(a) be the second derivative of -a**7/10 - 51*a**6/50 - 63*a**5/50 + 19*a**4/5 + 12*a**3/5 + 3*a - 20. Solve i(w) = 0 for w.
-6, -2, -2/7, 0, 1
Let c be (-4200)/(-2352) + (-3)/2. Factor 4/7*b + 2/7*b**2 + c.
2*(b + 1)**2/7
Let v(r) = -4*r**5 + 35*r**4 + 23*r**3 - 21*r**2 + 5*r. Let k(g) = 4*g**5 - 36*g**4 - 24*g**3 + 22*g**2 - 6*g. Let u(b) = 5*k(b) + 6*v(b). Solve u(z) = 0.
-1, 0, 1/2, 8
Let m(p) = p - 2. Let v(t) = -7*t + 8. Let o(q) = -4*m(q) - v(q). Let j be o(1). Factor -6/5*s**2 + 4/5*s + 0 + 2/5*s**j.
2*s*(s - 2)*(s - 1)/5
Suppose -4*m = -4*q - 5*m - 305, -3*q - 250 = 5*m. Let t = 153/2 + q. Factor 0*f**2 - t*f + 0 + 3/2*f**3.
3*f*(f - 1)*(f + 1)/2
Let l(z) be the third derivative of 0 - 1/3*z**3 + 1/8*z**4 - 1/40*z**5 + 1/480*z**6 + 6*z**2 + 0*z. Solve l(w) = 0.
2
Factor 286 - 30*o - 7*o - 286 - o + 2*o**2.
2*o*(o - 19)
Suppose 8*a - 126 = -a. Factor -8 + 0*x**3 - 6*x**3 - 4*x**2 + 12*x**4 - a*x**3 + 20*x.
4*(x - 1)**2*(x + 1)*(3*x - 2)
Let f(a) be the second derivative of 19*a**4/6 + 12*a**3 - 4*a**2 - 71*a. Factor f(s).
2*(s + 2)*(19*s - 2)
Let b = 387/520 - 15/104. Factor 0*p - 3/5*p**4 + 6/5*p**3 + 0 - b*p**2.
-3*p**2*(p - 1)**2/5
Let w(o) be the first derivative of o**5/10 - 3*o**4/4 - o**3/6 + 3*o**2/2 + 73. Factor w(d).
d*(d - 6)*(d - 1)*(d + 1)/2
Suppose -9*h + 72 - 54 = 0. Let a(j) be the second derivative of 7*j + 7/3*j**4 + 2/15*j**6 + 9/10*j**5 + 3*j**3 + h*j**2 + 0. Suppose a(q) = 0. What is q?
-2, -1, -1/2
Let h(l) = -8*l + 1. Let y(q) = -12*q + 1. Let a(x) = -8*h(x) + 5*y(x). Let g be a(11). Factor 0 + 12 + 44*d**3 - 9*d**2 - g*d**3.
3*(d - 2)**2*(d + 1)
Let h be 4/19 - (-185)/(-17575). Factor h*x**2 + 1/5 + 2/5*x.
(x + 1)**2/5
Let m(x) be the third derivative of x**6/180 + 7*x**5/30 - 2*x**4/3 - 44*x**3/9 - 307*x**2. Solve m(b) = 0.
-22, -1, 2
Factor 21*v**2 + 2*v**5 + v**5 + 8*v + 15*v**3 - 21*v**4 - 26*v.
3*v*(v - 6)*(v - 1)**2*(v + 1)
Factor 9*z**3 + 3*z**2 + 82*z**4 + 3*z**5 + 73*z**4 - 146*z**4.
3*z**2*(z + 1)**3
Factor -1/2*l**2 + 3 - 1/2*l.
-(l - 2)*(l + 3)/2
Let y = 16 + -16. Suppose -24 + 41*a + 3*a + y*a + 200*a**2 + 32*a**3 = 0. Calculate a.
-6, -1/2, 1/4
Let d(r) be the second derivative of -4*r**7/105 - 19*r**6/75 - 23*r**5/50 - r**4/6 + r**3/5 - 85*r. Let d(v) = 0. Calculate v.
-3, -1, 0, 1/4
Factor 5/2*b**2 + 14*b - 22 - 2*b**3.
-(b - 2)**2*(4*b + 11)/2
Let x be -3*1 + (-1 - 6). Let d be ((-12)/(-24))/((-1)/x). Factor -4*p + 2*p**3 - p**2 + 2*p**d + 6*p**2 + p**2 - 6*p**4.
2*p*(p - 2)*(p - 1)**2*(p + 1)
Let p(u) be the second derivative of u**7/42 - u**6/15 - u**5/10 + u**4/3 + u**3/6 - u**2 + 86*u. Determine n so that p(n) = 0.
-1, 1, 2
Let -10 + 4/3*z + 2/3*z**2 = 0. Calculate z.
-5, 3
Solve 2/5*t**4 - 4/15*t**3 - 32/15*t**2 - 2/5 - 28/15*t = 0 for t.
-1, -1/3, 3
Suppose 53*u - 249 = -37. Factor -2/5*v**u - 2/5*v**3 + 0*v + 4/5*v**2 + 0.
-2*v**2*(v - 1)*(v + 2)/5
Let u = 114 - 67. Factor -8 + 7*h**3 - 9*h**2 + 3*h**3 + 0*h**3 + u*h**2 + 32*h.
2*(h + 2)**2*(5*h - 1)
Let g(s) be the second derivative of s**4/32 - 5*s**3/16 - 9*s**2/8 + 439*s. Factor g(r).
3*(r - 6)*(r + 1)/8
Let y(i) be the first derivative of -2*i**6/3 + 24*i**5/5 - 12*i**4 + 32*i**3/3 + 87. Factor y(x).
-4*x**2*(x - 2)**3
Let g(i) = -i**2 - 13*i - 20. Let v be g(-11). Factor 5*l**2 - 10*l**3 - 2*l**2 + v*l**2 + 5*l**4.
5*l**2*(l - 1)**2
Suppose -33*j - 42 + 141 = 0. Let n(w) be the third derivative of 0*w + 1/24*w**4 - 2*w**2 + 0 - 1/120*w**5 + 0*w**j. What is m in n(m) = 0?
0, 2
Let y(c) be the second derivative of -4*c**7/147 - 4*c**6/21 - 37*c**5/70 - 5*c**4/7 - 3*c**3/7 - 79*c. Factor y(n).
-2*n*(n + 1)**2*(2*n + 3)**2/7
Let r(g) be the first derivative of g**9/672 + g**8/160 + g**7/105 + g**6/180 - g**3 + 4. Let x(m) be the third derivative of r(m). Find z such that x(z) = 0.
-1, -2/3, 0
Let f = 21 - 17. Let j(m) = 5*m**4 + 4*m**3 - 5*m**2 - 4*m + 4. Let c(v) = -4*v**4 - 3*v**3 + 4*v**2 + 3*v - 3. Let q(b) = f*c(b) + 3*j(b). Factor q(l).
-l**2*(l - 1)*(l + 1)
Let a(x) be the second derivative of -x**7/42 + x**6/15 + 2*x**5/5 - 4*x**4/3 - 8*x**3/3 + 16*x**2 - 42*x. Find p, given that a(p) = 0.
-2, 2
Let k(z) = 2 + 16*z + 2 - 17*z. Let l be k(0). Solve 21*d - l*d**2 + 4*d**3 - 21*d - d**4 = 0 for d.
0, 2
Let z = -16 - -22. Suppose 0 = 5*b - 8*b + 9. Factor 3*v**b + 3*v - 11*v**4 + 9*v**5 - 13*v**4 + 15*v**3 - z*v.
3*v*(v - 1)**3*(3*v + 1)
Find s, given that 8/7*s + 20/7*s**2 + 4/7*s**3 - 32/7 = 0.
-4, -2, 1
Suppose -5*y - 8 = 4*b, -4*y + 3*b - 4 = -10. Let w(h) be the second derivative of 1/15*h**3 + 0*h**2 + y + 1/100*h**5 + 2*h + 1/20*h**4. Factor w(o).
o*(o + 1)*(o + 2)/5
Factor -9/4 - 3/8*c**3 + 3/2*c**2 - 3/8*c.
-3*(c - 3)*(c - 2)*(c + 1)/8
Let c(w) be the third derivative of -w**7/70 - 21*w**6/20 - 22*w**5 + 21*w**4/4 + 441*w**3/2 + 77*w**2. Factor c(r).
-3*(r - 1)*(r + 1)*(r + 21)**2
Let i(g) = 4*g**3 + 8*g**2. Let f = -37 - -42. Let m(j) = 8*j**3 + 17*j**2 + 1. Let d(w) = f*i(w) - 2*m(w). What is x in d(x) = 0?
-1, 1/2
Let m = -803/5 + 161. Let y = -24 - -27. Factor 0 - 2/5*n**y - 4/5*n**2 - m*n.
-2*n*(n + 1)**2/5
Let r(s) = -48*s - 139. Let m be r(-3). Let d(y) be the second derivative of -1/80*y**m - 1/48*y**4 + 0 - 7*y + 0*y**2 + 0*y**3. Factor d(v).
-v**2*(v + 1)/4
Let y = 105 + -99. Let h(f) be the third derivative of 1/3*f**3 + 5*f**2 - 1/30*f**5 + 0 + 1/12*f**4 + 0*f - 1/60*f**y. Determine l so that h(l) = 0.
-1, 1
Let q(o) = -7*o**5 + 15*o**3 + 45*o**2 + 30*o + 3. Let a(x) = -3*x**5 + 8*x**3 + 22*x**2 + 15*x + 2. Let l(g) = -5*a(g) + 2*q(g). What is h in l(h) = 0?
-1, 4
Solve 21*m - 46*m**2 - 392*m**3 + 193*m**3 + 67*m + 200*m**3 = 0 for m.
0, 2, 44
Let f be (-39)/10 - (-8 - -4). Let c(b) be the second derivative of -1/3*b**4 + 0*b**2 + f*b**5 - b + 0 + 1/3*b**3. Solve c(j) = 0.
0, 1
Suppose -21 = -3*w + 4*l, 4*l - 6 = 2*w - 24. Suppose -2*f = -15 + w. Solve -p**3 + p**3 + 6*p**5 + 15*p**4 + f*p**3 + 3*p**5 = 0.
-1, -2/3, 0
Let y(z) be the third derivative of z**8/110880 + z**7/13860 - z**6/1320 + z**5/5 - z**2. Let n(t) be the third derivative of y(t). Suppose n(g) = 0. What is g?
-3, 1
Let m(d) = 2*d**3 + 30*d**2 + 42*d + 54. Let i(o) = 3*o - o**2 - 2*o + 0*o. Let z(n) = 4*n**2 + 2*n. Let s be z(-2). Let f(t) = s*i(t) + m(t). Factor f(w).
2*(w + 3)**3
Let o(w) be the first derivative of 0*w + 4/15*w**2 - 1/3*w**6 + 6 + 8/9*w**3 - 52/75*w**5 + 17/30*w**4. Suppose o(h) = 0. What is h?
-2, -2/5, -1/3, 0, 1
Let i(l) be the first derivative of 2*l**3/3 - 32*l**2 - 136*l - 456. Factor i(u).
2*(u - 34)*(u + 2)
Let i be 2/30*-2*-10. Let a be 0/(((-300)/(-10))/(-5)). Solve 2/3*p + a + i*p**2 + 0*p**3 - 2/3*p**5 - 4/3*p**4 = 0 for p.
-1, 0, 1
Let m(z) be the second derivative of 2/3*z**2 + 0 + z + 1/120*z**5 - 1/9*z**3 - 1/36*z**