
Let w(a) = -14*a + 2. Let k be w(-3). Factor 2*u**5 - 2*u**4 - k*u + 40*u - 6*u**3 + 15*u**2 - 5*u**2.
2*u*(u - 1)**3*(u + 2)
Let z = -25 - 0. Let y be (z/20)/((-2)/8). Factor 0 + p**2 + 0*p**3 - 1/2*p**y + 1/2*p - p**4.
-p*(p - 1)*(p + 1)**3/2
Suppose 0*a - l - 3 = -5*a, l = 2*a - 3. Let f(c) be the first derivative of 0*c + 1/8*c**4 + 3 + a*c**3 + 0*c**2. What is k in f(k) = 0?
0
Suppose 4*n + 8 = 0, -2*n - 7 = 5*y - 33. Suppose -30 = -11*c + y*c. Factor -4*s**2 + s - c*s**3 - 4*s**4 - s**5 + 0*s - 2*s.
-s*(s + 1)**4
Let n(x) be the second derivative of 4/21*x**4 + 2/21*x**3 + 0 - 4/147*x**7 - 1/7*x**2 + 1/35*x**5 + 6*x - 1/15*x**6. Solve n(b) = 0.
-1, 1/4, 1
Let a = -19 - -21. Factor -2/7*g - 2/7*g**3 - 4/7*g**a + 0.
-2*g*(g + 1)**2/7
Factor -3/4*t**2 + 1/2*t**3 + 0 + 1/4*t.
t*(t - 1)*(2*t - 1)/4
Let f(d) be the first derivative of d**3 + 6*d**2 + 12*d + 19. Determine y so that f(y) = 0.
-2
Let f(v) = -v**2. Let a(q) = 12*q - 8. Let x(k) = a(k) + 4*f(k). Factor x(u).
-4*(u - 2)*(u - 1)
Factor 0*x**2 - 3/4*x**4 + 0*x + 3/2*x**3 + 0.
-3*x**3*(x - 2)/4
Solve -39 - 8*a**3 - 8*a**5 + 16*a - 21*a**4 - 7*a**4 + 23 + 44*a**2 = 0.
-2, -1, 1/2, 1
Find o such that 0*o - 12/5*o**4 + 0 + 6/5*o**5 - 6/5*o**3 + 12/5*o**2 = 0.
-1, 0, 1, 2
Let i = 26 + -17. Let s = 9 - i. Factor s - 2/3*t + 1/3*t**2.
t*(t - 2)/3
Determine y, given that 2*y + 34 - 7*y - 15*y + 2*y**2 + 16 = 0.
5
Let j(s) = s**4 + 2*s**3 + 1. Let b(r) = -r. Let y(d) = -d**3 - d**2 - 3*d - 1. Let l(i) = -2*b(i) + y(i). Let x(a) = -j(a) - l(a). Solve x(w) = 0 for w.
-1, 0, 1
Let b = -7 - -1. Let o be 1 - ((-3)/b + 0). Find t such that 1/4*t + 0*t**3 + 1/2*t**2 - 1/4*t**5 - o*t**4 + 0 = 0.
-1, 0, 1
Let c = -43 + 43. Let k(i) be the third derivative of c*i + 0*i**3 + 1/36*i**4 + i**2 + 0 - 1/90*i**5. Factor k(w).
-2*w*(w - 1)/3
Suppose -5*z + 14 = -1. What is k in 19*k**z + 8*k**3 - 4 + 30*k + 25*k**3 - 18*k**5 - 72*k**2 + 12*k**4 = 0?
-2, 1/3, 1
Let f = -19 + 21. Factor -f*n**5 + 0*n**4 - 2*n - 4*n**4 + 4*n**5 + 4*n**2.
2*n*(n - 1)**3*(n + 1)
Suppose -5*y = 3*p - y - 227, 5*y + 344 = 4*p. Factor -28*s + p*s**4 + 123*s**3 + 4 + 14*s**2 + 3*s**3 - s**2.
(s + 1)**2*(9*s - 2)**2
Let c(b) be the second derivative of -b**7/1680 + b**6/720 + b**5/240 - b**4/48 - b**3/2 + 3*b. Let o(k) be the second derivative of c(k). Factor o(r).
-(r - 1)**2*(r + 1)/2
Suppose -p = -5*t + 45, p = -2*t + 4*p + 18. Let u(x) = -x**3 + 8*x**2 + 10*x - 7. Let h be u(t). Factor 1/3*d - d**h + 0 - 1/3*d**4 + d**3.
-d*(d - 1)**3/3
Let f = 81 - 134. Let t = 266/5 + f. Factor 1/5*n**2 + 1/5*n**3 - 1/5 - t*n.
(n - 1)*(n + 1)**2/5
Let s(m) be the second derivative of -4*m - 1/90*m**5 - 1/54*m**4 + 0*m**3 + 0*m**2 + 1/189*m**7 + 0 + 1/135*m**6. Factor s(x).
2*x**2*(x - 1)*(x + 1)**2/9
Let f(h) = -2*h**3 + 10*h**2 - 14*h + 12. Let u(g) = 2*g**3 - 10*g**2 + 14*g - 13. Let d(t) = 7*f(t) + 6*u(t). Factor d(w).
-2*(w - 3)*(w - 1)**2
Let q(z) be the second derivative of z**9/3024 + z**8/1680 - z**7/840 - z**6/360 + z**3/2 - z. Let w(y) be the second derivative of q(y). Factor w(j).
j**2*(j - 1)*(j + 1)**2
Let r(a) be the third derivative of a**7/735 - 2*a**6/105 + 4*a**5/35 - 8*a**4/21 + 16*a**3/21 + 15*a**2. Suppose r(d) = 0. What is d?
2
Factor 1/8*q**3 - 1/4 + 1/4*q**2 - 1/8*q.
(q - 1)*(q + 1)*(q + 2)/8
Let m be (3*1)/((-33)/(-110)). Let k be m/55 - 6/33. Factor 0*x**2 + k*x + 2/3*x**4 - 2/3*x**3 + 0.
2*x**3*(x - 1)/3
Let i be 3/12 + (-4)/16. Let -2/3*h**2 + i + 0*h = 0. Calculate h.
0
Suppose -4*t = -2*p, 2*p = 2*t - t + 6. Suppose 4*b + 2*f - 28 = 6*f, 2*f - 2 = -2*b. Factor -u**2 + 3*u - 20*u**3 + 4*u**2 + 3*u**t + 12*u**b - u**3.
3*u*(u - 1)**2*(4*u + 1)
Factor 7*n + 167*n**3 - 2*n - 25*n**2 - 328*n**3 + 5 + 176*n**3.
5*(n - 1)**2*(3*n + 1)
Factor n**3 - 4*n**2 + n**5 - 4*n**4 - 7*n**3 - n - 4*n**5 + 2*n**5.
-n*(n + 1)**4
Let l(p) = -3*p**2 - p**2 + p**3 - 6 + 7*p**2 - 6*p. Let t be l(-4). Find y such that 5/2*y**3 - 11*y**t + 14*y - 4 = 0.
2/5, 2
Let x(s) = s**2 + 6*s - 2. Let b be x(-6). Let r be 57/11 + b/11. Determine l, given that l**3 + 2*l**4 - 7*l**2 + 1 + l**4 - l**r + 3 = 0.
-1, 1, 2
Let 2/3*s**4 - 4/9*s**2 - 2/9 + 2/9*s**5 + 4/9*s**3 - 2/3*s = 0. Calculate s.
-1, 1
Let w(s) be the first derivative of -s**5/100 + s**4/30 - s**3/30 - 4*s + 2. Let u(o) be the first derivative of w(o). Let u(j) = 0. Calculate j.
0, 1
Let h(d) be the first derivative of -d**5 + 5*d**4/2 + 20*d**3/3 - 20*d**2 - 14. Factor h(a).
-5*a*(a - 2)**2*(a + 2)
Let n(d) be the first derivative of -d**7/1470 + d**6/315 - d**3/3 + 6. Let y(s) be the third derivative of n(s). Factor y(c).
-4*c**2*(c - 2)/7
Let y(x) = -x**3 - 7*x**2 + x + 7. Let u be y(-7). Let h = 4 + u. Let -3*s**4 + 2*s**h - s**5 + 0*s**5 = 0. What is s?
-1, 0
Let i(p) be the first derivative of -2*p**6/3 + 4*p**5/5 + 14. Factor i(d).
-4*d**4*(d - 1)
Let n(f) be the first derivative of 2*f**5/5 - 3*f**4/2 + 2*f**3 - f**2 + 20. Factor n(g).
2*g*(g - 1)**3
Find o, given that 6*o**2 + 16/3 + 76/3*o = 0.
-4, -2/9
Let c(w) = 9*w**2 - 5. Let j(q) = 5*q**2 - 3. Let r(f) = -3*c(f) + 5*j(f). What is t in r(t) = 0?
0
Factor 0*s**2 - 6/13*s + 4/13 + 2/13*s**3.
2*(s - 1)**2*(s + 2)/13
Suppose -l = -6*l + 15. Suppose 2*p + 4 = p + 3*d, 2*d = -l*p + 10. Solve 1 - 2*h**4 + 6*h**3 + 6*h**4 - 3 - p*h**2 - 6*h = 0.
-1, -1/2, 1
Suppose 4*v - 4 + 4 = 0. Let j(i) be the third derivative of 0*i + v*i**4 + 1/75*i**5 + 0*i**3 + 7/300*i**6 + 0 + 3*i**2. Let j(d) = 0. What is d?
-2/7, 0
Let v be -4 - (-2 + -1 - -1). Let y be 4*(3/v)/(-3). Factor 7*r**2 - 2*r**4 + 4*r**4 - 9*r**2 - 2*r**3 + y*r.
2*r*(r - 1)**2*(r + 1)
Let c be 0 + -3 + 20/6. Let p(w) be the first derivative of 0*w**2 - 1/5*w**5 + 0*w**4 + 2 + 0*w + c*w**3. Factor p(y).
-y**2*(y - 1)*(y + 1)
Find g such that 1/4 + 1/4*g**3 + 3/4*g + 3/4*g**2 = 0.
-1
Let v(f) = -6*f + 15. Let d be v(2). Let q = -10 + 12. Find h, given that -q*h**2 + 2/3*h**4 + 0*h**d + 0 - 4/3*h = 0.
-1, 0, 2
Suppose -5*n + 6*c - 2*c + 241 = 0, 3*n + 3*c - 150 = 0. Suppose n*g**5 - 4*g**2 + 4*g**5 + 52*g**4 - 5*g**5 = 0. Calculate g.
-1, -1/3, 0, 1/4
Factor 5/3*g**5 + 11/3*g**2 + 0 + 7*g**3 + 2/3*g + 17/3*g**4.
g*(g + 1)**3*(5*g + 2)/3
Suppose 0 = 5*k - 4*j - 22, 4*k - k + 4*j = -6. Solve 5*r**k - 4*r**3 + 7*r**2 - 20*r + 12*r = 0.
0, 1, 2
Let i(g) = -45*g**2 - 21*g. Let p be -2 - 0 - (11 + -15). Let c(j) = -11*j**2 - 5*j. Let y(m) = p*i(m) - 9*c(m). Factor y(w).
3*w*(3*w + 1)
Let s(l) be the third derivative of l**6/24 + 23*l**5/180 + l**4/8 + l**3/18 + 48*l**2 - 1. Suppose s(r) = 0. Calculate r.
-1, -1/3, -1/5
Factor -16*m**2 + 8*m**2 + 3*m + 2*m**3 - 1 + 5*m**2 - m**3.
(m - 1)**3
Let i(o) be the second derivative of o**5/90 - o**4/18 + o**3/9 - o**2/9 + 4*o + 1. Factor i(n).
2*(n - 1)**3/9
Suppose 0 = l - 0 - 2. Factor l*t + t + 2*t**5 + t**5 - 6*t**3 + 0*t.
3*t*(t - 1)**2*(t + 1)**2
Let a(h) be the first derivative of h**6/21 - h**5/5 + h**4/4 - 2*h**3/21 - 5. Determine i, given that a(i) = 0.
0, 1/2, 1, 2
Solve 5 - 171*c**2 + 0 - 5*c + 166*c**2 + 5*c**3 = 0 for c.
-1, 1
Let v be 35/(-15)*2/3 - -2. Factor -2/9 + v*i - 2/9*i**2.
-2*(i - 1)**2/9
Factor 5*c**3 - 229 - 2*c - 15*c**2 + 239 - 3*c + 5*c**4.
5*(c - 1)**2*(c + 1)*(c + 2)
Let c(m) be the second derivative of m**9/12096 - m**8/2240 + m**7/1120 - m**6/1440 - 2*m**3/3 - 4*m. Let g(b) be the second derivative of c(b). Factor g(f).
f**2*(f - 1)**3/4
Let h(c) = 3*c**5 - 8*c**4 + 7*c**3 - 2*c**2 - 2*c + 2. Let i(w) = 15*w**5 - 40*w**4 + 35*w**3 - 10*w**2 - 11*w + 11. Let p(v) = 11*h(v) - 2*i(v). Factor p(y).
y**2*(y - 1)**2*(3*y - 2)
Let p(l) be the third derivative of 0*l + 0 + 0*l**3 + 2*l**2 - 1/30*l**5 + 0*l**4. Factor p(i).
-2*i**2
Let l = -3 + 5. What is t in -3*t**5 - 18*t**l - 2*t**4 - 24 + 48*t**2 + t**4 + 12*t - 11*t**4 - 3*t**3 = 0?
-2, 1
Solve -49 - 487*s + 2*s**2 + 473*s - 3*s**2 = 0.
-7
Let l(h) be the third derivative of -h**6/180 + h**5/120 + h**4/144 - h**2. Solve l(g) = 0.
-1/4, 0, 1
Suppose 8*i + 20 = 3*i. Let f = -1 - i. What is l in 4*l**f + 10*l + 64/3*l**2 + 4/3 - 14*l**5 - 68/3*l**4 = 0?
-1, -1/3, -2/7, 1
Suppose 0 = -y - 0*n - n - 5, 0 = -y + 2*n - 2. Let x(h) = 4*h - 4 - 5*h**2 + 7*h**2 + 2*h. Let c(t) = -t + 1. Let j(p) = y*c(p) - x(p). Factor j(k).
-2*k*(k + 1)
Find o such that -28*o**3 - 46*o*