- 1)*(u + 1)**2
Let q be (-1)/(-4) - (-14)/8. Let a(f) = f**3 - f + 3. Let d be a(0). Factor 2*b + b**d - b - 3*b**2 - b**4 + q*b**3.
-b*(b - 1)**3
Let v = -42 - -128/3. Factor 1/6*q**4 - 2*q - q**3 + 13/6*q**2 + v.
(q - 2)**2*(q - 1)**2/6
Suppose 453 - 432 = 7*l. Factor -2/13*r - 2/13*r**4 - 2/13 + 4/13*r**2 + 4/13*r**l - 2/13*r**5.
-2*(r - 1)**2*(r + 1)**3/13
Let p be (-7)/265*(21 - 8). Let a = 3/53 - p. What is n in 0 + 2/5*n + a*n**2 = 0?
-1, 0
Let q be -5*(24/(-5) + 4). Solve 3/2*r**2 + 15/2*r**5 - r - 31/2*r**q + 15/2*r**3 + 0 = 0.
-1/3, 0, 2/5, 1
Let l(k) be the first derivative of -6/5*k**5 - 1 + 5/2*k**4 - 2/3*k**3 - k**2 + 0*k. Factor l(f).
-2*f*(f - 1)**2*(3*f + 1)
Factor 0*a + 1/8*a**3 - 1/8*a**5 - 1/8*a**4 + 0 + 1/8*a**2.
-a**2*(a - 1)*(a + 1)**2/8
Let m be (5 - 5)/(1 - 0). Let s(b) be the second derivative of -2*b - 1/40*b**5 + 0 + 1/12*b**4 + m*b**2 - 1/12*b**3. Factor s(u).
-u*(u - 1)**2/2
Suppose -3*n - 111 = -5*h - 12, h + 132 = -4*n. Let u be n/(-9) + 2/(-3). Factor -r**3 + 2*r**u - 2 - 4*r**2 + 0*r**3 + 5*r.
(r - 2)*(r - 1)**2
Suppose -3*d + 4 = -x, -5*d - 1 = x - 21. Factor -2*k**4 - k**3 + d*k**3 - 2*k**3 + 4*k**2 - 2.
-2*(k - 1)**2*(k + 1)**2
Let p(u) = u**3 - u**2 + 4. Let v be p(0). Suppose -v*q + 1 = -5*f + 3, -3*q + 6 = 0. Let -3*g**f + g**2 - 4 + 6*g + 0*g**2 = 0. What is g?
1, 2
Let x be 1 + 3 + 0 - 0. Let r(g) be the third derivative of 1/12*g**3 - 2*g**2 + 0 + 1/8*g**5 + 13/240*g**6 + 0*g + 1/105*g**7 + 7/48*g**x. Factor r(z).
(z + 1)**3*(4*z + 1)/2
Suppose -8 = -4*p - 4*j - 0, -2*p - 4*j - 6 = 0. Let s = p + -5. Factor -2/7*y**4 + 0*y**3 + 0*y + 0 + 2/7*y**s.
-2*y**2*(y - 1)*(y + 1)/7
Let z(a) be the second derivative of a**5/240 - a**4/24 + a**3/6 - 4*a**2 - 7*a. Let v(b) be the first derivative of z(b). Suppose v(c) = 0. Calculate c.
2
Let f(s) = 23*s**2 + 5*s + 23. Let n(i) = 4*i**2 + i + 4. Let l(d) = 6*f(d) - 34*n(d). Find k, given that l(k) = 0.
1
Let x(h) = -10*h**2 - 55*h. Let p(m) = -5*m**2 - 28*m. Let c(g) = 5*p(g) - 3*x(g). Factor c(w).
5*w*(w + 5)
Let o(k) be the second derivative of -k**4/28 - k**3/7 - 3*k**2/14 + 23*k. Determine t so that o(t) = 0.
-1
Solve -4*u**2 - 18*u**3 + 4 + 17*u**3 + u**2 = 0 for u.
-2, 1
Let z(l) be the second derivative of -l**9/75600 + l**4/4 - 3*l. Let d(g) be the third derivative of z(g). Factor d(n).
-n**4/5
Let j(x) = -x**3 + 2*x**2 + 3*x. Let t be j(3). Suppose 4*u + 4*c - 24 = t, -5*c + c + 26 = 5*u. Factor -1/2 + 1/4*o + 3/4*o**u.
(o + 1)*(3*o - 2)/4
Let p(h) be the first derivative of h**4/48 - h**3/24 - 3*h - 4. Let s(i) be the first derivative of p(i). Factor s(f).
f*(f - 1)/4
Let a(s) be the third derivative of -s**5/15 - s**4/6 - 22*s**2. Factor a(o).
-4*o*(o + 1)
Let u(l) = -2*l. Let r be u(0). Let k(p) be the first derivative of 0*p + r*p**5 + 2 + 1/30*p**6 - 1/20*p**4 + 0*p**2 + 0*p**3. Find g such that k(g) = 0.
-1, 0, 1
Let b = -12 - -16. Let r(m) be the first derivative of -2 + 0*m + 2/21*m**3 + 0*m**2 + 1/14*m**b. Solve r(p) = 0 for p.
-1, 0
Suppose 6*a + 25 - 55 = 0. Factor 0*y**4 + 0 + 0*y + 0*y**3 + 0*y**2 - 2/3*y**a.
-2*y**5/3
Let c(p) = p**3 - 2*p**2 - 2*p - 1. Let j be c(3). Find k, given that k**3 - 2*k**j + 3*k**3 - 5*k**3 + k**2 = 0.
-1, 0
Let x = -4 + 8. Let t be x/(-10) + 85/25. Factor 2/11*s**4 + 6/11*s**2 + 6/11*s**t + 2/11*s + 0.
2*s*(s + 1)**3/11
Determine h, given that -16 - h**2 + 32 - 3*h**2 = 0.
-2, 2
Suppose -3*p - 2 + 11 = 0. Let z(d) be the second derivative of 1/12*d**4 + 0*d**p + 0 + 0*d**2 + 3*d. Factor z(g).
g**2
Factor -11/2*z - 3 + 1/2*z**3 - 2*z**2.
(z - 6)*(z + 1)**2/2
Let s(w) be the first derivative of -w**5/240 + w**3/24 - 9*w**2/2 - 6. Let j(u) be the second derivative of s(u). Factor j(d).
-(d - 1)*(d + 1)/4
Let d(k) be the second derivative of k**5/10 - 2*k**4/3 + k**3 + 4*k. Let d(v) = 0. Calculate v.
0, 1, 3
Let y(h) = -h**3 - 12*h**2 - 12*h - 12. Let w be y(-11). Let g be 6/8*2 + w. Factor 0*r + g*r**2 - 1/2.
(r - 1)*(r + 1)/2
Factor -2/9*i**2 + 0 + 2/3*i.
-2*i*(i - 3)/9
Let g(l) be the second derivative of 8/3*l**3 - 1/15*l**6 + 0*l**2 + l + 3/5*l**5 + 0 - 2*l**4. Factor g(y).
-2*y*(y - 2)**3
Let w(n) = -2*n**2 + 15*n - 3. Let v be w(10). Let t = 373/7 + v. Suppose -4/7 + 6/7*o - t*o**2 = 0. What is o?
1, 2
Let v(f) be the second derivative of f**5/34 - 31*f**4/51 + 4*f**3 - 72*f**2/17 - f - 6. Factor v(k).
2*(k - 6)**2*(5*k - 2)/17
Let j = 17 + -7. Let t be (-14)/35 + 9/j. Factor 1/2*u**3 + 0*u + 0 - t*u**4 - 1/2*u**5 + 1/2*u**2.
-u**2*(u - 1)*(u + 1)**2/2
Let v(u) be the second derivative of 0 - 1/5*u**5 + u**4 - 1/3*u**6 - 2*u - u**2 - 1/3*u**3 + 1/7*u**7. Solve v(m) = 0.
-1, -1/3, 1
Let g be (-3)/(-18)*(-9)/(-30). Let l(s) be the first derivative of 1 - g*s**5 + 0*s**2 - 1/24*s**6 + 0*s + 1/16*s**4 + 1/12*s**3. Factor l(j).
-j**2*(j - 1)*(j + 1)**2/4
Suppose 19 = 2*k + 5*m - 3, 5*m = 3*k + 17. Factor -2*d + 4*d - d**2 + k + 0*d - 2.
-(d - 1)**2
Factor 1/5*j**5 - 1/5*j**3 - 11/5*j**2 + 3/5*j**4 - 12/5*j - 4/5.
(j - 2)*(j + 1)**3*(j + 2)/5
Find q such that -1/5*q**4 + 0*q + 0*q**2 + 0 - 1/5*q**3 = 0.
-1, 0
Let r(q) be the second derivative of 1/12*q**3 + 0 - 1/240*q**6 + 1/40*q**5 - 2*q - 1/2*q**2 - 1/16*q**4. Let d(c) be the first derivative of r(c). Factor d(l).
-(l - 1)**3/2
Find m, given that -3/4*m**2 - 3/8*m**3 + 3/4*m**4 + 0 + 3/8*m**5 + 0*m = 0.
-2, -1, 0, 1
Suppose 28*w + 33 = 39*w. What is f in -2/5*f**w + 4/5*f + 0 + 2/5*f**2 = 0?
-1, 0, 2
Let h be 1 - -1 - (2 + -2). What is v in v - 5 + 8 + 1 - 7*v + h*v**2 = 0?
1, 2
Let g(s) be the first derivative of -1/120*s**6 - s + 0*s**2 + 1/80*s**5 + 0*s**4 - 2 + 0*s**3. Let o(n) be the first derivative of g(n). Factor o(x).
-x**3*(x - 1)/4
Let q be (-12)/21 - 24/(-42). Factor 1/4*m**2 + q + 1/4*m.
m*(m + 1)/4
Let b(t) = -20*t**4 - 29*t**3 + 108*t**2 - 126*t + 34. Let v(n) = 7*n**4 + 10*n**3 - 36*n**2 + 42*n - 11. Let g(k) = -4*b(k) - 11*v(k). Factor g(j).
3*(j - 1)**3*(j + 5)
Let y(n) be the first derivative of -n**4/6 - 4*n**3/9 - n**2/3 + 10. Factor y(x).
-2*x*(x + 1)**2/3
Let f = 529 + -527. Factor 0*u + 0 + 1/7*u**f.
u**2/7
Let u(b) = -14*b - 26. Let r be u(-2). Factor 1/2*p**4 - 4 + 5/2*p**3 - 2*p + 3*p**r.
(p - 1)*(p + 2)**3/2
Suppose -1/3*n**4 + 0*n + 0*n**2 + 0 - 1/9*n**5 + 4/9*n**3 = 0. Calculate n.
-4, 0, 1
Suppose -h - 5 = 4*c, 3*c + h = -0 - 3. Let b be 2/6*0 - c. Factor 0 - 1/2*v**b - 1/2*v**3 + v.
-v*(v - 1)*(v + 2)/2
Let n(t) be the first derivative of t**4/6 + 2*t**3/3 + 2*t**2/3 - 2. Determine i, given that n(i) = 0.
-2, -1, 0
Let o(k) be the first derivative of 2 + 4/3*k**3 + 0*k**2 + 0*k. Let o(z) = 0. Calculate z.
0
Let n = 12/59 - 206/1593. Let q(o) be the second derivative of 0*o**2 - n*o**3 - 8/45*o**5 - 2*o + 11/54*o**4 + 7/135*o**6 + 0. Let q(b) = 0. What is b?
0, 2/7, 1
Let u(p) = p**3 - 4*p**2 - 3*p. Let x(h) = -13*h - 14*h**2 + 6*h**2 - 9*h**2 + 5*h**3. Let d(m) = 9*u(m) - 2*x(m). Determine z so that d(z) = 0.
-1, 0
Let z(q) be the first derivative of q**7/630 + q**6/360 - q**5/180 - q**4/72 + q**2/2 + 3. Let n(k) be the second derivative of z(k). What is j in n(j) = 0?
-1, 0, 1
Let d be (-1 + 0)/(3/(-2)). Factor -d - 2/3*n - 1/6*n**2.
-(n + 2)**2/6
Let -10/3 + 5*y - 5/3*y**3 + 0*y**2 = 0. Calculate y.
-2, 1
Let i = 15/2 + -7. Let s be ((-10)/30)/((-2)/3). Factor -s*b**2 + 1/2 - 1/2*b + i*b**3.
(b - 1)**2*(b + 1)/2
Let b(s) = 8*s**2 - 48*s + 67. Let o(l) = -12*l**2 + 72*l - 100. Let m(q) = 8*b(q) + 5*o(q). Factor m(p).
4*(p - 3)**2
Let c be (-6 - 516/(-84))*(-2)/(-1). Factor 0 - 2/7*m**2 + c*m.
-2*m*(m - 1)/7
Let s(x) be the third derivative of x**8/56 + x**7/21 - 7*x**6/60 - 3*x**5/10 + x**4/3 + 4*x**3/3 - 43*x**2. Solve s(q) = 0 for q.
-2, -1, -2/3, 1
Suppose -2*q + 5*q = 0. Suppose -5*g + g = q. Factor 4*z**3 + g*z - z - z**3 + 2*z**4.
z*(z + 1)**2*(2*z - 1)
Suppose 131*h + 2 = 132*h. Solve 2/7 + 4/7*u**h + 2/7*u**5 - 6/7*u + 4/7*u**3 - 6/7*u**4 = 0.
-1, 1
Let u(h) be the third derivative of -h**5/240 - h**4/48 - h**3/24 + 4*h**2. Suppose u(i) = 0. Calculate i.
-1
Factor -3757 + 12*f + 0*f**2 - f**2 + 3737.
-(f - 10)*(f - 2)
Let x(s) be the first derivative of s**6/360 - s**4/24 - s**3/9 - 3*s**2/2 + 1. Let i(c) be the second derivative of x(c). Factor i(y).
(y - 2)*(y + 1)**2/3
Let w(s) = -s**3 - s**2 + s + 1. Let m(j) = 2