). Factor 0 + 4/9*f - 2/9*f**c.
-2*f*(f - 2)/9
Let w(b) = -b**3 - 4*b**2 - 2*b - 5. Let x be w(-4). Factor 21 + 81*p - 5*p**x + 27*p**2 + 5*p**3 + 3*p**3 + 60.
3*(p + 3)**3
Let a(z) = 19*z - 7*z**2 + 5 - 19*z. Let c(v) = -3*v**2 + 2. Let s(p) = -2*a(p) + 5*c(p). What is w in s(w) = 0?
0
Let w(d) be the third derivative of -1/15*d**5 + 0*d**3 + 0*d**4 + 0*d - 1/105*d**7 + 0 - 4*d**2 + 1/20*d**6. Suppose w(i) = 0. What is i?
0, 1, 2
Let u(x) be the first derivative of -6*x**5/5 + x**4/14 + 4*x**3/21 + 18. Let u(y) = 0. Calculate y.
-2/7, 0, 1/3
Let m(w) be the first derivative of w**3/3 - w**2 + w - 24. Factor m(p).
(p - 1)**2
Let l(u) = 68*u**2 + 20*u + 6. Let f(k) = -67*k**2 - 19*k - 7. Let m(y) = -4*f(y) - 5*l(y). Factor m(z).
-2*(6*z + 1)**2
Let y(t) be the first derivative of -t**3/3 + t + 10. Find k such that y(k) = 0.
-1, 1
Let u(w) be the third derivative of -w**9/60480 + w**8/5040 - w**7/1260 + w**5/60 - 3*w**2. Let n(j) be the third derivative of u(j). Let n(k) = 0. Calculate k.
0, 2
Suppose -8/5*g - 4/5*g**2 + 0 = 0. Calculate g.
-2, 0
Suppose 2/5 + 1/5*b - 1/5*b**2 = 0. Calculate b.
-1, 2
Let i be (-10)/(-45) + (-193)/180 - -1. Let d(t) be the first derivative of -1 + i*t**4 + 3/5*t**3 - 3/25*t**5 - 6/5*t - 3/10*t**2. What is c in d(c) = 0?
-1, 1, 2
Factor 16/7*a**3 + 4/7*a**2 - 12/7*a**4 - 18/7*a + 2/7*a**5 + 8/7.
2*(a - 4)*(a - 1)**3*(a + 1)/7
Let y be (-3 + 108/32)/(14/56). Determine q so that -y*q**5 + 0*q**3 + 3/2*q + 3*q**2 - 3*q**4 + 0 = 0.
-1, 0, 1
Let f(a) = -a**3 - a**2 + 1. Let d be f(-1). Factor -3 - d + 3*l + l**3 - 2*l**3 + 2.
-(l - 1)**2*(l + 2)
Let p(h) = h**3 + 3*h**2 + 2*h + 2. Let l be p(-3). Let m be 2*(-1)/2*l. Factor 3 + 2*i**2 - i - 7 + 3*i - m*i.
2*(i - 2)*(i + 1)
Let o(w) be the first derivative of w**4/16 - w**3/12 - 5*w**2/8 - 3*w/4 - 10. Factor o(h).
(h - 3)*(h + 1)**2/4
Factor -2/5*y - 6/5*y**3 + 6/5*y**2 + 2/5*y**4 + 0.
2*y*(y - 1)**3/5
Let t(d) be the third derivative of d**6/120 - d**5/80 - d**4/96 - 3*d**2. Factor t(c).
c*(c - 1)*(4*c + 1)/4
Solve 6 + 2*l + l**2 - 3 + l - 1 = 0 for l.
-2, -1
Let x(w) be the first derivative of -w - 1 + 3/2*w**2 + 4/3*w**3. Factor x(h).
(h + 1)*(4*h - 1)
Let s(c) = 2*c**3 + 2*c + 4. Let o(l) = -2*l**3 - l**2 - 3*l - 4. Let j(d) = -4*o(d) - 5*s(d). Factor j(x).
-2*(x - 2)*(x - 1)*(x + 1)
Let n(s) = -2*s**5 - 14*s**4 + 14*s**2 - 8*s + 10. Let j(x) = x**4 - x**2 + x - 1. Suppose 3 = -5*h - 2. Let m(f) = h*n(f) - 10*j(f). Factor m(y).
2*y*(y - 1)*(y + 1)**3
Suppose i = -2*i + 33. Let w(j) = -j**2 + 11*j. Let k be w(i). Factor 0 - 2/7*h**2 + k*h - 2/7*h**3.
-2*h**2*(h + 1)/7
Let p be (-3)/2*(-16)/6. Suppose p + 2 = 3*f. Find g such that 0*g**2 - g**f - 5*g + 4*g = 0.
-1, 0
Let l = -145/7 + 153/7. Suppose 4/7 - 18/7*y + 36/7*y**3 - 18/7*y**5 + 4/7*y**4 - l*y**2 = 0. Calculate y.
-1, 2/9, 1
Let w = 4 + -2. Factor 0*p**2 - 12*p**2 - 8*p - w - 2*p**3 - 6*p**3 - 2*p**4.
-2*(p + 1)**4
Let n(q) be the second derivative of q**4/48 - q**3/6 + q**2/2 - 12*q. Factor n(z).
(z - 2)**2/4
Let k(x) = -2*x. Let d be k(-5). Suppose 24*p + p**2 + 8*p**2 - 30*p + d*p**3 + 5*p**3 = 0. What is p?
-1, 0, 2/5
Suppose 4 = -w + 3*w. Let b = w - -2. Solve 5*s**b + 2*s + 3*s**5 + s**3 - 5*s**2 - 3*s**5 - 3*s**5 = 0.
-1, 0, 2/3, 1
Let d be 0 - (0 - -1*2). Let w be ((-9)/(-12))/(d/(-8)). Factor 2*h**w + 4*h**2 - 3*h**3 - 3*h**2.
-h**2*(h - 1)
Let v be 2*4*1/2. Suppose 0 = c - v*c. Factor c + 0*o + 1/2*o**3 + 1/2*o**2.
o**2*(o + 1)/2
Let w(q) be the second derivative of 1/3*q**3 + 1/2*q**2 - 1/10*q**5 + 0 + 0*q**4 + 2*q - 1/30*q**6. Factor w(c).
-(c - 1)*(c + 1)**3
Let k(v) = -8*v**2 - 12*v - 6. Let f(j) = -24*j**2 - 36*j - 19. Let s(p) = -2*f(p) + 7*k(p). Let s(b) = 0. What is b?
-1, -1/2
Let y(z) be the first derivative of z**6/11 - 6*z**5/55 - 3*z**4/22 + 2*z**3/11 + 14. Factor y(n).
6*n**2*(n - 1)**2*(n + 1)/11
Let c = -18 - -20. Let f(i) be the third derivative of -2*i**c + 0*i + 1/105*i**7 + 0*i**3 + 0*i**4 - 1/60*i**6 - 1/30*i**5 + 0 + 1/168*i**8. Factor f(l).
2*l**2*(l - 1)*(l + 1)**2
Suppose -3*n = -0*n - 3. Suppose -5*l + 15 = 5*x, -l + n = x - 2*l. Find j such that 9*j**x + 16 - 22*j - 12 + 23*j**2 - 14*j**3 = 0.
2/7, 1
Let 0 + 2/7*i**2 + 2/7*i = 0. What is i?
-1, 0
Let 2 + 0*i + 2*i**2 - 6*i - 2*i + 4 = 0. What is i?
1, 3
Let o(z) be the third derivative of -z**8/1512 + z**7/945 + z**6/540 - z**5/270 + 14*z**2. Factor o(g).
-2*g**2*(g - 1)**2*(g + 1)/9
Solve 0 - 2/9*i**2 + 4/9*i - 4*i**3 + 2*i**4 = 0.
-1/3, 0, 1/3, 2
Let j(i) = i**5 - i**4 - 4*i**3 + 4*i**2 + 3*i. Let d(l) = -l**3 + l**2 + l. Let h(c) = -3*d(c) + j(c). Factor h(t).
t**2*(t - 1)**2*(t + 1)
Let x(o) be the third derivative of -o**8/147 + 10*o**7/147 - 13*o**6/105 + o**5/21 - o**2. Find i such that x(i) = 0.
0, 1/4, 1, 5
What is z in 0 + 0*z - z**3 - 5/3*z**4 + 2/3*z**2 = 0?
-1, 0, 2/5
Let o(i) be the third derivative of 0 + 1/40*i**6 + 1/210*i**7 + 1/24*i**4 + 0*i + 0*i**3 + 1/20*i**5 + 5*i**2. Suppose o(v) = 0. Calculate v.
-1, 0
Let w(u) be the first derivative of -u**4 + 8*u**3/3 + 2*u**2 - 8*u - 31. Factor w(g).
-4*(g - 2)*(g - 1)*(g + 1)
Suppose 4*t = 5 - 1. Let o = 1 + t. Factor -8*a + 0*a**2 + 5*a**3 + 18*a**o - 8 + 13*a**3.
2*(a + 1)*(3*a - 2)*(3*a + 2)
Let u(f) = -f - 4. Let b be u(-12). Let g be 2/b*(17 + -9). What is s in -10/7*s**3 - 18/7*s**g - 2/7*s**4 - 2*s - 4/7 = 0?
-2, -1
Let m = -25 - -10. Let w be 1/m*(-10 - -4). Suppose -w*r**3 + 2/5*r + 4/5*r**4 - 4/5*r**2 + 0 = 0. Calculate r.
-1, 0, 1/2, 1
Let f(o) = o**5 + o**3 - o**2. Let b(v) be the third derivative of v**8/112 - v**5/30 + v**4/24 + 5*v**2. Let i(r) = b(r) - 2*f(r). Let i(j) = 0. Calculate j.
-1, 0, 1
Let t(n) be the second derivative of -n**5/200 + n**3/20 + n**2/10 + 25*n. Factor t(d).
-(d - 2)*(d + 1)**2/10
Let v(q) be the first derivative of 2*q**5/25 + q**4/10 - 4*q**3/5 + 17. Find i, given that v(i) = 0.
-3, 0, 2
Factor -5*a**2 + 12*a + 2*a**2 - 9*a.
-3*a*(a - 1)
Let z be 4 - 2 - (-3 - -5 - 0). Let b(m) be the first derivative of 0*m**2 + 2/5*m**5 + z*m**4 + 3 + 0*m - 2/3*m**3. Determine x so that b(x) = 0.
-1, 0, 1
Let o(y) be the second derivative of -y**6/40 - 3*y**5/80 + y**4/16 + y**3/8 - 5*y. Factor o(k).
-3*k*(k - 1)*(k + 1)**2/4
Let s(a) be the first derivative of -10*a**6/3 - 8*a**5/5 + 3. Factor s(p).
-4*p**4*(5*p + 2)
Suppose -g = -4*p - 20, 20 = 2*g - 2*p - p. Let m(l) be the first derivative of -l**2 + 3 + 0*l + 15/4*l**g + 1/3*l**3. Factor m(a).
a*(3*a - 1)*(5*a + 2)
Suppose -19*k + 21*k = 0. Let t(a) be the third derivative of 0*a**4 + 0 - 1/60*a**6 + 1/15*a**5 + 2*a**2 + k*a + 0*a**3. Solve t(i) = 0 for i.
0, 2
Let p(w) = 3*w**2 + 12*w - 23. Let k(i) = -22 + 8*i + 0*i + 4*i + 2*i**2. Let o(v) = 5*k(v) - 4*p(v). Factor o(n).
-2*(n - 3)**2
Factor -2/9*o**4 + 2/9*o**2 + 2/9*o**5 + 0 + 0*o - 2/9*o**3.
2*o**2*(o - 1)**2*(o + 1)/9
Let h(u) be the second derivative of u**6/30 - 13*u**5/60 + 19*u**4/36 - 11*u**3/18 + u**2/3 - 7*u. Solve h(c) = 0.
1/3, 1, 2
Let t be (-9)/(-6) + 1/2. Suppose 2*u**3 - u**5 - 3*u**4 - 2*u**2 + u**3 + t*u**5 + u**2 = 0. What is u?
0, 1
Let j(l) be the second derivative of -l**5/60 - l**4/18 + 2*l**3/9 + 4*l**2/3 - 18*l. Factor j(d).
-(d - 2)*(d + 2)**2/3
Let v = 20 - 18. Let t(o) be the third derivative of v*o**2 + 0 + 0*o + 1/8*o**4 + 1/6*o**3 + 1/120*o**6 + 1/20*o**5. Find k such that t(k) = 0.
-1
Suppose 4*r - 2*r + 8 = 0. Let t = 6 + r. Factor 2/3*y**t + 0*y + 2/9*y**3 - 8/9.
2*(y - 1)*(y + 2)**2/9
Let 6/5*o**2 + 2/5*o + 0 = 0. What is o?
-1/3, 0
Let -4*v**3 + 13*v**2 - 4*v**2 - 4*v - v**2 = 0. What is v?
0, 1
Let x(q) be the first derivative of -q**9/3024 + q**7/420 - q**5/120 + 2*q**3/3 + 1. Let y(p) be the third derivative of x(p). Solve y(k) = 0 for k.
-1, 0, 1
Suppose 5*g - 2*k + k - 31 = 0, -g - 4*k = -2. Factor -g*v**2 + 10 - 140*v**3 - 2 - 15*v**4 - 25*v + 113*v**4 + 65*v.
2*(v - 1)**2*(7*v + 2)**2
Let b be (-1 - 0)*0/(-1). Let f(w) be the third derivative of b*w**3 + 0 + 0*w**4 - 1/240*w**5 + 0*w + 3*w**2. Factor f(p).
-p**2/4
Let d(o) be the third derivative of -o**7/5040 - o**6/1440 + o**5/120 - o**4/24 + o**2. Let c(y) be the second derivative of d(y). Factor c(n).
-(n - 1)*(n + 2)/2
Let k(j) be the third derivative of 0*j**4 - 2*j**2 - 1/140*j**6 + 0*j**3 + 1/105*j**5 + 0 + 1/735*j**7 + 