et z(f) = -40 - f**2 - 3*f**2 + 54*f - 6*f**2. Let y(k) = n*z(k) - 14*p(k). Factor y(u).
2*(u - 2)**2
Let d(q) = 10*q**3 + 32*q**2 - 62*q + 20. Let f(h) = 20*h**3 + 63*h**2 - 123*h + 40. Let g(j) = 9*d(j) - 4*f(j). Factor g(i).
2*(i - 1)*(i + 5)*(5*i - 2)
Let z(l) = l + 11. Let q be z(-8). Factor t**3 - t - 8*t**2 - q*t - 3*t**3 + 14*t**2.
-2*t*(t - 2)*(t - 1)
Let o(d) = -5*d**3 + 10*d**2 - 16*d + 5. Let y(k) = -k**3 - 1. Let u(s) = -2*o(s) + 6*y(s). Let u(m) = 0. What is m?
1, 2
Suppose 0 = -2*s - 2*s + 24. Let c(a) = -a**3 - a**2 + a + 1. Let j(t) = -4*t**3 - 3*t**2 + 4*t + 3. Let v(r) = s*c(r) - 2*j(r). What is w in v(w) = 0?
-1, 0, 1
Suppose 8*p = -12*p. Solve p + 2/15*f - 4/15*f**2 + 2/15*f**3 = 0.
0, 1
Solve 0 - 20/7*b + 4/7*b**2 = 0 for b.
0, 5
Let p(v) be the first derivative of -1 + 4/3*v - 7/3*v**2 + 16/9*v**3 + 1/9*v**6 - 4/15*v**5 - 1/3*v**4. Solve p(f) = 0.
-2, 1
Let j(c) be the first derivative of 2*c**3/45 + 4*c**2/15 - 7. Determine g so that j(g) = 0.
-4, 0
Let s(u) = -u + 8. Let g be s(6). Let v be ((-12)/16)/((-6)/20)*2. Factor -w - v*w**2 + w**g + 3*w**2.
-w*(w + 1)
Let l(d) be the third derivative of -d**6/1080 + d**5/360 - d**3/6 + d**2. Let t(n) be the first derivative of l(n). Factor t(h).
-h*(h - 1)/3
Let i(x) = x**2 - 2. Let o be i(2). Let -2*c**3 - 2*c**4 + c**o + c**2 + 0*c**4 + 2*c = 0. What is c?
-1, 0, 1
Let v(t) be the second derivative of -t**4/32 - t**3/8 - 3*t**2/16 - 6*t. Factor v(w).
-3*(w + 1)**2/8
Let u(b) be the third derivative of b**5/40 - b**4/16 - b**3/2 - 2*b**2. Find x such that u(x) = 0.
-1, 2
Let -4/7*i**4 - 4/7*i + 0 + 4/7*i**2 + 4/7*i**3 = 0. What is i?
-1, 0, 1
Factor -2/9*o + 4/9*o**2 - 4/9 + 2/9*o**3.
2*(o - 1)*(o + 1)*(o + 2)/9
Let s = -9 + 13. Let x(p) be the first derivative of -1/5*p**5 + 0*p**2 - 1 + 0*p + 0*p**3 + 1/4*p**s. Let x(o) = 0. What is o?
0, 1
Let v = -259 + 2333/9. Factor -2/9*g**3 + v*g**2 + 0 + 4/9*g.
-2*g*(g - 2)*(g + 1)/9
Let c(u) be the second derivative of 1/12*u**4 - 1/3*u**3 + 0 + 1/2*u**2 + 3*u. Factor c(v).
(v - 1)**2
Let g be ((-34)/153)/(2/46) + 6. Factor -2/3 - 2/9*n**2 + g*n.
-2*(n - 3)*(n - 1)/9
Suppose 4*x - 4*x + 46*x**3 - 45*x**3 = 0. What is x?
0
Let r = -23/7 + 33/7. Let z be (-2 - (0 + 0))/((-3)/6). Suppose 2/7*w + r*w**3 + 0 + 8/7*w**2 + 4/7*w**z = 0. Calculate w.
-1, -1/2, 0
Let b(m) be the second derivative of -m**5/60 - m**4/8 - m**3/3 + 5*m**2/2 + 5*m. Let i(r) be the first derivative of b(r). Let i(u) = 0. Calculate u.
-2, -1
Factor 4/7*w + 2/7*w**2 - 6/7.
2*(w - 1)*(w + 3)/7
Let q be ((-4)/3)/((-4)/6). Suppose 2 = 4*l + 2*x, q*l - 20 = -2*l + 4*x. Find p, given that 2 + 12*p**l + 4*p**4 + p**4 + 8*p - 3*p**4 + 8*p**3 = 0.
-1
Suppose 0 = g - 0*g. Suppose -3*b + 3*c = 0, -6 = -g*b - b - c. Determine d, given that d - 15*d**4 + 3*d**2 + 0*d**3 + b*d**3 + 16*d**4 = 0.
-1, 0
Let h = -99/2 - -513/10. Find c, given that -4/5*c**3 - 1/5 - h*c**2 - 6/5*c = 0.
-1, -1/4
Let 2/3*r**2 + 0 + 2/3*r = 0. What is r?
-1, 0
Let f(a) be the second derivative of 5*a**4/12 - a**3/6 - 2*a**2 - 2*a. Let w(j) = -9*j**2 + 2*j + 7. Let b(d) = 11*f(d) + 6*w(d). Solve b(g) = 0 for g.
-2, 1
Find o such that -27/5*o + 3/5*o**3 - 81/5 + 9/5*o**2 = 0.
-3, 3
Let m(o) be the third derivative of 0 - 1/6*o**3 + 0*o - 7/720*o**6 - 3*o**2 - 1/24*o**4 + 3/80*o**5. Let p(l) be the first derivative of m(l). Factor p(u).
-(u - 1)*(7*u - 2)/2
Factor 2/5*d**2 + 2/5*d + 0.
2*d*(d + 1)/5
Let a = 13/8 + -37/24. Let m(b) be the second derivative of -1/20*b**5 - a*b**4 + 1/30*b**6 + 0 + 3*b + 1/6*b**3 + 0*b**2. Factor m(x).
x*(x - 1)**2*(x + 1)
Let w = 2/33 + 16/99. Let r be -1 + (-94)/(-18) - 4. Factor -w*x**4 + 0*x + r*x**2 + 0*x**3 + 0.
-2*x**2*(x - 1)*(x + 1)/9
Let k(b) be the first derivative of 0*b**2 + 2/15*b**5 - 2/9*b**3 + 0*b + 5 - 1/6*b**4 + 1/9*b**6. Let k(d) = 0. What is d?
-1, 0, 1
Let l(f) = -3*f + 4. Let c be l(0). Let t(x) be the third derivative of -2*x**2 + 1/6*x**3 + 0 + 1/24*x**c + 1/240*x**5 + 0*x. Determine m so that t(m) = 0.
-2
Suppose 5 = -3*w + 14. Factor -2*d**3 + d**3 - 3*d**3 + w*d**3.
-d**3
Let k(d) = -25*d**3 + 145*d**2 - 80*d + 5. Let u(s) = -37*s**3 + 218*s**2 - 120*s + 8. Let c(t) = 8*k(t) - 5*u(t). Determine y so that c(y) = 0.
0, 2/3, 4
Let z(j) be the first derivative of j**6/33 - 2*j**5/55 - j**4/11 + 4*j**3/33 + j**2/11 - 2*j/11 + 48. Factor z(i).
2*(i - 1)**3*(i + 1)**2/11
Let w(l) be the second derivative of 0*l**2 + 1/60*l**6 - 1/40*l**5 - 1/24*l**4 - 2*l + 0*l**3 + 1/84*l**7 + 0. Determine o, given that w(o) = 0.
-1, 0, 1
Suppose 0 = -26*w + 5*w + 5*w. Factor 5/3*q**3 + 1/3*q + w - 2/3*q**4 - 4/3*q**2.
-q*(q - 1)**2*(2*q - 1)/3
What is m in 2/5*m - 2/5 - 2/5*m**3 + 2/5*m**2 = 0?
-1, 1
Let z(p) be the second derivative of -2/3*p**3 - p**2 + 1/15*p**6 + 0 + 0*p**4 + 3*p + 1/5*p**5. Solve z(s) = 0 for s.
-1, 1
Let w(h) = -2*h**3 + 4*h - 2*h**4 + 2*h**3. Let f(v) = -4*v**4 + v**3 - v**2 + 9*v. Let b = 1 + 4. Let c(x) = b*w(x) - 2*f(x). Suppose c(s) = 0. Calculate s.
-1, 0, 1
Factor -3/7*o**3 + 1/7*o**4 + 0 + 1/7*o**5 + 2/7*o - 1/7*o**2.
o*(o - 1)**2*(o + 1)*(o + 2)/7
Let n = -21 - -21. Let r = -2 + 4. Factor -r*g**2 + g**3 + g**3 + n*g**2 + g**5 + 3*g**4 - 3*g - 1.
(g - 1)*(g + 1)**4
Let o be 0*(12 + -6)/(-6). Factor 0 + 0*q - 1/4*q**5 - 1/4*q**3 - 1/2*q**4 + o*q**2.
-q**3*(q + 1)**2/4
Solve 2187/7 - 3/7*x**3 - 729/7*x + 81/7*x**2 = 0 for x.
9
Let m(t) = 8*t**2 + 9*t + 8. Let w(v) = -4*v**2 - 5*v - 4. Suppose -6 = 3*d - d. Let j(p) = d*m(p) - 7*w(p). Factor j(x).
4*(x + 1)**2
Factor -5*a - 5/2*a**2 + 0.
-5*a*(a + 2)/2
Factor -4/3*u + 4/9 - 2/3*u**3 + 1/9*u**4 + 13/9*u**2.
(u - 2)**2*(u - 1)**2/9
Let o be 6/(-18) - (-8)/(-3). Let t be o/18*2*-12. Factor 1/2*j**t - 1/2*j**3 + 0 + 1/2*j - 1/2*j**2.
j*(j - 1)**2*(j + 1)/2
Let v be ((-3)/(-6))/((-1)/(-4)). Suppose 3*o = v + 4. Suppose -10/3*x**o + 4/3 - 2*x = 0. Calculate x.
-1, 2/5
Let g(k) = 45*k**2 + 397*k + 101. Let y(f) = 11*f**2 + 99*f + 25. Let w(v) = -6*g(v) + 22*y(v). Factor w(l).
-4*(l + 7)*(7*l + 2)
Factor 0*s + 0 + 2/3*s**2 + 2/3*s**3.
2*s**2*(s + 1)/3
Let m = 1 - -4. Suppose 4*l = m*s - 6, -4*s + 5*l - 1 = -4. Let u(p) = p**2 + p. Let c(q) = 3*q**2 + 3*q - 1. Let k(t) = s*c(t) - 5*u(t). Factor k(w).
(w - 1)*(w + 2)
Let t(w) = 18*w**2 + w + 1. Let l be t(1). Let h be -4 - (-4)/(l/21). Let -h*b**5 + 1/5 + b**4 + 2*b**2 - b - 2*b**3 = 0. What is b?
1
Factor 1/2*q**3 - 1/2*q - 1/2*q**2 + 1/2.
(q - 1)**2*(q + 1)/2
Factor 5*q**5 + 5*q + 59*q**3 - 17*q**4 - 20*q**2 - 20*q**3 - 9*q**3 - 3*q**4.
5*q*(q - 1)**4
Let q(o) be the first derivative of 1/4*o**2 - 1/6*o**3 - 1/8*o**4 - 4 + 1/2*o. Factor q(b).
-(b - 1)*(b + 1)**2/2
Let m(c) be the second derivative of -c**4/72 - 7*c**3/36 - c**2/2 + 31*c. Solve m(x) = 0.
-6, -1
Let h(d) = d**3 + 6*d**2 - 5*d - 27. Let b be h(-6). Find q, given that 0*q - 8/5*q**b - 2/5*q**4 + 0 - 8/5*q**2 = 0.
-2, 0
Determine k, given that -3/2*k + 1/2*k**2 + 1 = 0.
1, 2
Let z(q) be the first derivative of 0*q - 2*q**4 + 7 + 0*q**3 - 24/5*q**5 + 0*q**2 - 3*q**6. Let z(c) = 0. Calculate c.
-2/3, 0
Let m(k) be the first derivative of -4/27*k**3 - 2 + 2/45*k**5 + 1/9*k**2 + 1/27*k**6 + 2/9*k - 1/9*k**4. Factor m(s).
2*(s - 1)**2*(s + 1)**3/9
Let p(t) = t**5 + t**4 - t**3 + t**2 + t + 1. Let k(o) = -7*o**5 - 34*o**4 - 85*o**3 - 107*o**2 - 35*o + 13. Let d(w) = -4*k(w) - 12*p(w). Factor d(f).
4*(f + 2)**4*(4*f - 1)
Let p(u) = u**2 - 8*u + 3. Let a be p(9). Solve -15*n**4 - 24*n**3 - 56*n + 56*n + a*n**2 = 0.
-2, 0, 2/5
Let p(d) be the first derivative of -d**6/27 + d**4/6 - 4*d**3/27 - 9. Factor p(y).
-2*y**2*(y - 1)**2*(y + 2)/9
Let g(h) = 3*h**5 - 8*h**4 - 8*h**3 + 5*h**2. Let o(i) = 4*i**5 - 8*i**4 - 8*i**3 + 6*i**2. Suppose 24 = 4*y + 4. Let d(w) = y*o(w) - 6*g(w). Factor d(r).
2*r**3*(r + 2)**2
Let x(s) = -s**3 - 5*s**2 - s - 3. Let b be x(-5). Determine p so that -3*p**3 + p**4 + 4*p + 3*p**2 + 0*p**b - 5*p = 0.
0, 1
Suppose -3*s - 2*h = -19, 7*s - 29 = 4*s - 4*h. Suppose s*c = -c. Find i such that -2*i + 2*i**3 - 2*i**2 + 2 + i**2 + c*i**2 - i**2 = 0.
-1, 1
Let a(u) be the first derivative of -169*u**4 + 104*u**3/3 - 2*u**2 - 40. Factor a(x).
-4*x*(13*x - 1)**2
Let n = 169/5 + -33. Factor -n*x - 2/5 - 2/5*x**2.
-2*(x + 1)**2/5
Let z = 461 - 325. Let x = z - 1222/9. Factor x*h -