2*v**3/5 + 4*v**2 + 3. Factor k(y).
(y + 1)*(7*y - 2)*(11*y + 6)/5
Suppose 0 = -3*x + 22 + 23. Let g = x + -12. Factor -8*v + 0*v**4 + 32*v**2 - 12*v**2 + g*v**4 + v**4 - 16*v**3.
4*v*(v - 2)*(v - 1)**2
Let f(m) = 2 - 85*m**3 + 84*m**3 - 10*m**2 + 0 + 4 - 4*m. Let u(j) = -j**2 + 1. Let z(k) = f(k) - 6*u(k). What is h in z(h) = 0?
-2, 0
Let a be (-14467)/(-17612) + 4/6 + (-78)/63. Factor f**3 + a*f**4 + 1/2*f**2 - f - 3/4.
(f - 1)*(f + 1)**2*(f + 3)/4
Let p(j) be the third derivative of j**8/252 + 2*j**7/105 + j**6/45 - 19*j**2. Factor p(q).
4*q**3*(q + 1)*(q + 2)/3
Suppose -4*j + 3*h - 188 = -h, 0 = 2*j + 3*h + 69. Let i be 14/j - 34/(-6). Factor -1/3*t**5 + 4/3*t**4 + 0 + i*t + 0*t**3 - 16/3*t**2.
-t*(t - 2)**3*(t + 2)/3
Let h(c) be the first derivative of -35*c**4/12 - 5*c**3/3 - 4*c + 1. Let u(m) be the first derivative of h(m). Find r, given that u(r) = 0.
-2/7, 0
Factor 0*x - 4/3*x**3 + 0 - 2/9*x**5 + 0*x**2 - 10/9*x**4.
-2*x**3*(x + 2)*(x + 3)/9
Let v(g) be the third derivative of 1/8*g**4 - 3/20*g**5 - 1/70*g**7 + 0*g**3 + 0 + 3/40*g**6 + 0*g - 16*g**2. What is k in v(k) = 0?
0, 1
Let g(m) be the second derivative of -m**7/630 + m**6/36 - 5*m**4/3 - 3*m - 12. Let z(d) be the third derivative of g(d). Solve z(y) = 0.
0, 5
Let a(s) = -63*s**2 + s. Let l be a(1). Let u = -121/2 - l. Suppose 0*j**2 + 3*j - 3*j**3 + u - 3/2*j**4 = 0. What is j?
-1, 1
Let l(z) be the first derivative of 2*z**3/9 + 20*z**2/3 + 200*z/3 + 36. Factor l(y).
2*(y + 10)**2/3
Let f(k) be the second derivative of -k**6/30 - k**5/5 + k**4/12 + 2*k**3/3 + 26*k. Factor f(t).
-t*(t - 1)*(t + 1)*(t + 4)
Let t = 95342 - 7627467/80. Let g = -15/16 - t. Let 2/5*n - 4/5*n**2 + 0 + g*n**3 = 0. Calculate n.
0, 1
Suppose -5*s = j + 7 + 9, 25 = 5*s. Let a be j/(-12) - (-30)/(-40). Factor 2/3*r**3 + 2*r**2 - a + 0*r.
2*(r - 1)*(r + 2)**2/3
Factor 3/4*u + 0 - 3/4*u**3 + 1/4*u**4 - 1/4*u**2.
u*(u - 3)*(u - 1)*(u + 1)/4
Let n(m) be the second derivative of -m**4/4 - 11*m**3/6 + 10*m. Let c(d) = d**2 + 4*d. Let w(v) = -8*c(v) - 3*n(v). Factor w(r).
r*(r + 1)
Let b(v) be the first derivative of 10/3*v**3 + 2 + 25/2*v**2 - 5/4*v**4 - 30*v. Factor b(h).
-5*(h - 3)*(h - 1)*(h + 2)
Let z(j) be the first derivative of j**4/4 - 16*j**3/3 + 42*j**2 - 144*j - 175. Factor z(t).
(t - 6)**2*(t - 4)
Let n(r) = -r**5 - 5*r**4 - 7*r**3 - 3*r**2 + 4*r. Let z(a) = a**5 + 5*a**4 + 7*a**3 + 3*a**2 - 5*a. Let b(f) = -5*n(f) - 4*z(f). Factor b(d).
d**2*(d + 1)**2*(d + 3)
Let d be ((-49)/(-42) + (-1510)/1500)/((-4)/(-10)). Suppose 14/5*n**2 - d*n**3 - 32/5 - 16/5*n = 0. What is n?
-1, 4
Let u(d) be the third derivative of 3*d**8/112 - d**7/10 + 3*d**6/40 + 3*d**5/20 - d**4/4 + 49*d**2. Factor u(p).
3*p*(p - 1)**3*(3*p + 2)
Let y(m) be the second derivative of 16/3*m**2 - 4/3*m**3 - 1/120*m**5 + 0 - 27*m + 1/6*m**4. Factor y(r).
-(r - 4)**3/6
Let s(j) = -163*j**4 + 343*j**3 + 923*j**2 + 565*j + 122. Let u(p) = 27*p**4 - 57*p**3 - 154*p**2 - 94*p - 20. Let z(g) = -2*s(g) - 13*u(g). Factor z(h).
-(h - 4)*(h + 1)*(5*h + 2)**2
Let a be (2/(-1))/(42/(-28)). Let x(u) be the second derivative of -1/5*u**5 + 0 - 8/3*u**3 + 4*u + 0*u**2 - a*u**4. Factor x(v).
-4*v*(v + 2)**2
Let r be (-3)/(-5) + 454/10. Let q = r - 44. Factor -14/11*g - 6/11*g**3 - 4/11 - 16/11*g**q.
-2*(g + 1)**2*(3*g + 2)/11
Suppose -4*o - 8 = -8*o. Let -3*i**o - 9*i + 20 + 3*i**3 - 3*i - 8 = 0. What is i?
-2, 1, 2
Let p(c) be the third derivative of -1/240*c**5 + 0 + 1/192*c**4 - 1/480*c**6 - 10*c**2 + 1/48*c**3 + 0*c + 1/1680*c**7 + 1/2688*c**8. Factor p(l).
(l - 1)**2*(l + 1)**3/8
Let l(p) be the second derivative of -p**4/6 - 8*p**3/3 - 12*p**2 + 2*p - 24. Let l(k) = 0. Calculate k.
-6, -2
Let c(x) be the third derivative of 3*x**8/112 + 29*x**7/35 - 103*x**6/40 + 21*x**5/10 + 259*x**2. Let c(f) = 0. What is f?
-21, 0, 2/3, 1
Let b(g) be the first derivative of -2*g**3/9 + 218*g**2/3 - 23762*g/3 - 312. Factor b(p).
-2*(p - 109)**2/3
Suppose -7*x - 5*b = -28 - 13, -2*x + 4*b = 10. Let u(j) be the first derivative of -2/15*j**x + 0*j**2 + 0*j - 2 + 1/30*j**4. Determine m so that u(m) = 0.
0, 3
Let f(q) be the second derivative of q**4/32 + q**3/8 + 629*q. Determine d so that f(d) = 0.
-2, 0
Let k(m) be the third derivative of 1/525*m**7 + 0*m**6 + 0*m - 2/225*m**5 + 0 - 1/2520*m**8 + 30*m**2 + 0*m**4 + 0*m**3. Factor k(q).
-2*q**2*(q - 2)**2*(q + 1)/15
Suppose 34*v = -30*v + 256. Let d(k) be the third derivative of 0*k**3 + 0 + 8*k**2 - 1/540*k**6 + 0*k**5 + 1/108*k**v + 0*k. Find m, given that d(m) = 0.
-1, 0, 1
Let y(s) = -9*s - 17. Let j(p) = -p - 1. Let h(v) = -6*j(v) + y(v). Let n be h(-5). Factor 2*r**4 + 4*r + 1 + 1 + 0*r**4 - 4*r**4 - n*r**3.
-2*(r - 1)*(r + 1)**3
Let 15 - 5/6*b**2 - 35/6*b = 0. What is b?
-9, 2
Suppose 4761/7*o + 3/7*o**3 - 207/7*o**2 - 36501/7 = 0. Calculate o.
23
Factor 17/8*y - 17/8*y**3 + 19/8*y**2 - 1/8*y**4 - 9/4.
-(y - 1)**2*(y + 1)*(y + 18)/8
Let r(f) be the third derivative of 4*f**2 + 1/24*f**4 + 0 + 0*f + 0*f**3 + 1/60*f**5. Factor r(z).
z*(z + 1)
Let r(l) be the third derivative of -l**6/30 - l**5/5 + 12*l**2 + 1. Factor r(i).
-4*i**2*(i + 3)
Let r(l) be the second derivative of l**5/40 - 17*l**4/3 + 1156*l**3/3 - 374*l. Factor r(k).
k*(k - 68)**2/2
Let d = 423/842 + -1/421. Factor 1/3 + 1/6*j**2 - d*j.
(j - 2)*(j - 1)/6
Let d(v) = -2*v + 14. Let r be d(6). Let h = -4 - -6. Let -1 + 1 + y**r + 0*y**h = 0. What is y?
0
Let j = -2 + -20. Let c = j + 24. What is v in 0*v**c - 3/2*v + 1/2*v**3 - 1 = 0?
-1, 2
Let j = -500 - -2547/5. Let s = j + -136/15. Factor 0 - 1/3*p + s*p**3 - p**4 + p**2.
-p*(p - 1)*(p + 1)*(3*p - 1)/3
Factor 0 + 0*z - 2/3*z**4 - 52/3*z**3 - 338/3*z**2.
-2*z**2*(z + 13)**2/3
Let t(w) be the first derivative of -w**6/39 + 8*w**5/65 - 3*w**4/13 + 8*w**3/39 - w**2/13 + 126. Factor t(x).
-2*x*(x - 1)**4/13
Let h(i) = -i**4 + i**3 + i**2 - 1. Let j(g) = 4*g**4 - 12*g**3 - 20*g**2 - 13*g + 1. Let f(w) = 5*h(w) + j(w). Factor f(p).
-(p + 1)**3*(p + 4)
Let n(r) be the first derivative of r**3/3 - r**2 - 8*r - 245. Factor n(o).
(o - 4)*(o + 2)
Let x be 3/((-6)/(-4)) + -14. Let l = x + 17. Factor 60*g**2 - l + 4*g + 1 - 61*g**2.
-(g - 2)**2
Let p(u) be the second derivative of -u**5/40 - 3*u**4/8 - 5*u**3/4 + 2*u**2 - 25*u. Let v(g) be the first derivative of p(g). Factor v(z).
-3*(z + 1)*(z + 5)/2
Let i(f) be the third derivative of 0*f**3 - 1/72*f**4 + 1/45*f**5 + 0 + 1/72*f**6 - 13*f**2 + 0*f. Factor i(n).
n*(n + 1)*(5*n - 1)/3
Suppose 2*t + n + n = 24, 3*n = 6. Suppose 0*a = 5*a - t. Let -4*c**3 + 5*c**3 - 3*c**3 + a*c**4 = 0. Calculate c.
0, 1
Let k(j) be the second derivative of -j**4/4 + 2*j**3/3 + 15*j**2/2 - 2*j + 18. Factor k(g).
-(g - 3)*(3*g + 5)
Let f(t) be the second derivative of -t**5/25 - 4*t**4/15 + 2*t**3/5 + 36*t**2/5 - 2*t - 18. Factor f(n).
-4*(n - 2)*(n + 3)**2/5
Let w be 11 - (1591/333 + 6/27). Find s, given that 10*s - 1/2*s**4 + 7/2*s**2 - s**3 + w = 0.
-2, -1, 3
Let k(x) be the third derivative of 0*x + 23*x**2 - x**4 - 6*x**3 + 0 - 1/15*x**5. Factor k(w).
-4*(w + 3)**2
Let u(s) be the first derivative of s**6/42 - 4*s**5/35 + 3*s**4/14 - 4*s**3/21 + s**2/14 - 8. Solve u(y) = 0 for y.
0, 1
What is o in -8*o**5 + 2*o**2 - o**2 + 12*o**5 - 16*o - 5*o**2 + 12*o**3 + 16*o**4 - 12*o**2 = 0?
-2, -1, 0, 1
Let z(f) be the third derivative of f**7/840 - f**6/240 - f**5/240 + f**4/48 + 108*f**2. Solve z(r) = 0 for r.
-1, 0, 1, 2
Let m(g) = -8*g**3 - g - 2. Let a be m(-1). Factor -13 - a - 5*i**2 - 6*i - 21*i + 7*i.
-5*(i + 2)**2
Let y(c) = c**3 + 5*c**2 + 2*c + 12. Let x be y(-5). Determine d, given that -28*d**4 - 16 - 76*d**3 + 1519*d**x - 64*d + 0*d**5 - 1619*d**2 - 4*d**5 = 0.
-2, -1
Let k(c) be the second derivative of c**5/100 - c**3/30 + 114*c. Factor k(v).
v*(v - 1)*(v + 1)/5
Let f(t) be the third derivative of -t**8/672 - t**7/70 - t**6/30 + t**5/60 + 3*t**4/16 + t**3/3 - 62*t**2 + 2*t. Let f(i) = 0. Calculate i.
-4, -1, 1
Let u(m) = m**3 + 28*m**2 + 54*m + 57. Let j be u(-26). Suppose -2/11*v**j + 4/11*v**4 + 2/11*v + 0 - 4/11*v**2 + 0*v**3 = 0. What is v?
-1, 0, 1
Suppose 2*h - 2 = -4*l, 7*h - 10 = 4*h + l. Factor -25 + h*j**2 + 6*j**2 - 10*j**2 - 10*j.
-(j + 5)**2
Let z(i) = i**2 - i + 3. Let y be z(0). Suppose 0*n + y = n. Factor -n*b + b + 0*b - b**2 + b.
-b*(b + 1)
