n(b) = 0.
-1, 1, 3
Suppose -2*c = 2*c - 12. Let y be (16/20)/(4/10). Factor -1/2 - 3/2*x - 3/2*x**y - 1/2*x**c.
-(x + 1)**3/2
Let h(u) be the first derivative of u**5 - 5*u**4/2 - 8. Factor h(j).
5*j**3*(j - 2)
Suppose -3*z - 6 = -v - 5*z, v - 5 = -z. Suppose v*f + 0*f**3 + f**2 + 8*f**3 + 2*f**4 + 9*f**2 = 0. Calculate f.
-2, -1, 0
Suppose 3*o = -x + 15, -5*x - 20 = 2*o - 6*o. Factor -f**5 + 1 + 2*f**2 + x*f**2 + 3*f - 3*f**4 + 0*f**2 - 2*f**3.
-(f - 1)*(f + 1)**4
Suppose -5*j = 5 + 10. Let b = j + 5. Factor -u + 2 - 3 - 3*u**2 - u + 2*u**b.
-(u + 1)**2
Factor 4*w**3 - 10*w**2 + 10*w**2 - 2*w**5 - 2*w.
-2*w*(w - 1)**2*(w + 1)**2
Let l(u) be the third derivative of -u**8/336 + u**7/35 - 13*u**6/120 + u**5/5 - u**4/6 + 31*u**2. Suppose l(a) = 0. What is a?
0, 1, 2
Suppose 2*v + 3/4 + 3/2*v**2 + 0*v**3 - 1/4*v**4 = 0. Calculate v.
-1, 3
Let w(j) = 2*j**2 - 4*j + 12. Suppose 0 = -2*c + 6, 3*n + 6*c = 2*c + 15. Let p(d) = d + 1. Let i(b) = n*w(b) - 4*p(b). Factor i(m).
2*(m - 2)**2
Let u = 130 - 386/3. Let y(l) be the first derivative of 10/9*l**3 + 2/3*l + 1 - 1/3*l**4 - u*l**2. Factor y(p).
-2*(p - 1)**2*(2*p - 1)/3
Let m(k) be the first derivative of 0*k**2 - 1 + 4/9*k**3 + 7/6*k**4 + 2/3*k**5 + 0*k. Factor m(l).
2*l**2*(l + 1)*(5*l + 2)/3
Let t be -2*4/(-48)*4. Factor 4/3*k**2 + 2/3*k**3 + 0 + t*k.
2*k*(k + 1)**2/3
Let o(a) be the second derivative of -a**6/60 + a**5/30 + 3*a**2/2 - a. Let x(f) be the first derivative of o(f). Factor x(p).
-2*p**2*(p - 1)
Let w(b) be the first derivative of b**7/42 - b**6/15 + b**4/6 - b**3/6 - b - 3. Let f(n) be the first derivative of w(n). Factor f(s).
s*(s - 1)**3*(s + 1)
Let v(w) = -w - 3. Let l be v(-7). Suppose 4*j**l - 3*j**5 - j**4 + 6*j**5 = 0. Calculate j.
-1, 0
Let u(x) be the first derivative of 0*x**2 + 1/14*x**4 - 2/21*x**3 + 0*x + 1. Determine i, given that u(i) = 0.
0, 1
Let l(f) be the second derivative of -f**7/3360 - f**6/720 - f**5/480 - f**3/2 + 3*f. Let m(t) be the second derivative of l(t). Factor m(d).
-d*(d + 1)**2/4
Let p(y) be the first derivative of y**4/26 + 4*y**3/39 + y**2/13 - 4. Factor p(g).
2*g*(g + 1)**2/13
Suppose -2*r - 2*v + 8 = 0, v - 11 = -3*r - v. Factor 3 + 3*g**2 + 0*g**2 - 3 - 3*g**r.
-3*g**2*(g - 1)
Let y = 1 + 2. Factor -35*x**3 - 3*x**2 + 33*x**y + 0*x**4 + 3*x**4 + 2*x.
x*(x - 1)*(x + 1)*(3*x - 2)
Let g = 81/20 - 33/10. Determine y, given that -9/4*y + 3/2*y**2 + 3/2*y**3 + 3/4*y**5 + g - 9/4*y**4 = 0.
-1, 1
Let g(u) be the first derivative of u**3/3 - u**2/2 - 2*u + 6. Let n be g(-2). Factor 4/3*f**3 - 4/3*f + f**2 - 4/3 + 1/3*f**n.
(f - 1)*(f + 1)*(f + 2)**2/3
Suppose -5*q + 312 = 267. Factor -27/2 - 3/2*s**2 + q*s.
-3*(s - 3)**2/2
Suppose 0 - 9/2*j - 21/4*j**3 + 69/4*j**2 = 0. Calculate j.
0, 2/7, 3
Let f(i) be the first derivative of -i**3/3 - i**2/2 + 3. Find x such that f(x) = 0.
-1, 0
Let k(i) be the second derivative of 2*i**6/15 - 3*i**5/5 + i**4 - 2*i**3/3 + 5*i. Determine t, given that k(t) = 0.
0, 1
Let q(o) be the first derivative of -4 - 9/4*o**4 + 0*o - 1/2*o**6 - 9/5*o**5 - o**3 + 0*o**2. Let q(s) = 0. What is s?
-1, 0
Let -16/5 + 2/5*q**4 + 24/5*q - 4/5*q**2 - 6/5*q**3 = 0. Calculate q.
-2, 1, 2
Let q(z) be the second derivative of -z**5/20 - z**4/3 - 5*z**3/6 - z**2 + 2*z. Factor q(u).
-(u + 1)**2*(u + 2)
Let f(v) = 2*v**2 - 4. Let y be f(-2). Let w(m) be the third derivative of 0*m**3 + 0 - 1/24*m**y + 1/60*m**5 + 0*m - 3*m**2. Factor w(j).
j*(j - 1)
Let o(x) be the second derivative of x**6/120 + x**5/80 - x**4/48 - x**3/24 - 9*x. Factor o(b).
b*(b - 1)*(b + 1)**2/4
Let h(c) be the second derivative of -c**4/15 + 18*c**2/5 + 43*c. Factor h(u).
-4*(u - 3)*(u + 3)/5
Let o(q) be the third derivative of -1/18*q**3 + 0 - 1/36*q**4 + 0*q + 2*q**2 - 1/180*q**5. Find b, given that o(b) = 0.
-1
Let b = 758 + -50027/66. Let r(p) be the second derivative of b*p**4 - p - 1/55*p**5 + 0 + 0*p**2 + 0*p**3 + 1/165*p**6. Solve r(i) = 0.
0, 1
Let w(a) be the second derivative of 5*a**4/12 - 25*a**3/6 + 13*a. Determine u so that w(u) = 0.
0, 5
Let x be (-1976)/(-912) + 2/(-3) + 0. Factor 0 - 3/4*f**2 - x*f.
-3*f*(f + 2)/4
Let p(i) = -i**2 + 4*i + 7. Let y be p(5). Factor a + 4*a**2 - 4*a**y + 0*a - a**2.
-a*(a - 1)
Let z(o) = o**3 - o + 1. Let m(q) = 3*q**4 + 6*q**3 + q**2 - 2*q + 2. Let s(p) = 2*m(p) - 4*z(p). Solve s(b) = 0.
-1, -1/3, 0
Let l(c) be the second derivative of -c**6/360 - c**5/90 - c**4/72 - 3*c**2/2 + 2*c. Let d(k) be the first derivative of l(k). Factor d(v).
-v*(v + 1)**2/3
Suppose -2*f = f + 3*f. Determine y, given that -3/5*y - 3/5*y**2 + f = 0.
-1, 0
Let y(b) = -b**2 + 7*b - 4. Let g(h) = -2*h**2 + 6*h - 4. Let k(s) = 6*g(s) - 5*y(s). Let d(m) = -20*m**2 + 4*m - 12. Let l(x) = -5*d(x) + 14*k(x). Factor l(v).
2*(v - 2)*(v - 1)
Let x be ((-144)/80)/(3/(-10)). Let -201/8*q**2 - 1/2 - 355/8*q**3 - 81/8*q**5 - 279/8*q**4 - x*q = 0. Calculate q.
-1, -2/9
Let r be 3 + 2 - (0 + 0). Suppose -12 = -r*m + m. Let -i**3 + 0*i**3 - 3*i + m*i**2 + 0 + 1 = 0. What is i?
1
Factor 0 + 3/2*p - 3/4*p**2.
-3*p*(p - 2)/4
Let m = 4 + -1. Factor v**2 - v**2 - m*v**2 + v + 0*v**2.
-v*(3*v - 1)
Let j(h) be the second derivative of -2/15*h**6 - 1/5*h**5 - 1/42*h**7 - 7*h + 1/6*h**4 + 5/6*h**3 + 0 + h**2. Factor j(t).
-(t - 1)*(t + 1)**3*(t + 2)
Determine k, given that 14/9*k**4 + 2/3*k**3 - 22/9*k**2 - 8/9*k**5 + 0 + 10/9*k = 0.
-5/4, 0, 1
Let k = 610 + -45749/75. Let m(d) be the second derivative of k*d**6 + 0 + 0*d**2 - 1/30*d**4 + 1/50*d**5 + 3*d - 1/15*d**3. Factor m(n).
2*n*(n - 1)*(n + 1)**2/5
Let k = 53/112 + -3/16. Factor 0 + 2/7*t + k*t**2.
2*t*(t + 1)/7
Let -4/5*f**2 - 8/5*f + 0 = 0. Calculate f.
-2, 0
Solve -d + 15*d**2 - 7*d**2 + 2*d**3 - d**5 - 8*d**2 = 0 for d.
-1, 0, 1
Suppose 0 = 2*r - 0*r - 4. Find f such that 0*f - 3*f**r + 2*f + f**2 = 0.
0, 1
Let r(q) be the third derivative of -q**8/168 - 2*q**7/35 - 13*q**6/60 - 2*q**5/5 - q**4/3 - 16*q**2. Factor r(w).
-2*w*(w + 1)**2*(w + 2)**2
Suppose 0 = 2*p + 7 - 17. What is y in 12*y**2 - 12*y**2 + 3*y**4 + 3*y**p - 9*y**3 - 3*y**2 + 6*y = 0?
-2, -1, 0, 1
Let l(g) = 2*g**4 - 8*g**3 + 6*g**2 - 8*g. Let h(t) = -t**4 + 3*t**3 - 2*t**2 + 3*t. Let b = 12 - 4. Let f(m) = b*h(m) + 3*l(m). Let f(v) = 0. What is v?
-1, 0, 1
Let g(a) be the first derivative of -a**6/14 + 3*a**5/7 - 3*a**4/7 + 32. Find z such that g(z) = 0.
0, 1, 4
Solve -1/2*r**2 + 3/4*r**4 + 0 - 5/4*r**3 + 0*r = 0 for r.
-1/3, 0, 2
Let f(x) be the first derivative of -x**5 + 5*x**4/2 + 20*x**3/3 - 5*x**2 - 15*x - 10. Determine h, given that f(h) = 0.
-1, 1, 3
Let c(r) be the third derivative of -r**7/1890 + r**6/1080 + r**5/540 - r**4/216 - 8*r**2. Factor c(w).
-w*(w - 1)**2*(w + 1)/9
Let s(w) = -33*w. Let k be s(1). Let a(n) = 9*n**4 + 9*n**3 + 33*n**2 - 33*n. Let j(m) = -m**4 - m**3 - 4*m**2 + 4*m. Let u(p) = k*j(p) - 4*a(p). Factor u(f).
-3*f**3*(f + 1)
Let k = -44 + 44. Let w(s) be the third derivative of 0*s**5 + 1/60*s**6 + 0*s**3 - 3*s**2 + 0 + 0*s**4 + k*s. Factor w(b).
2*b**3
Let l(c) be the third derivative of -c**7/1995 - c**6/570 + c**5/570 + c**4/114 - 4*c**2. What is a in l(a) = 0?
-2, -1, 0, 1
Let y(r) be the first derivative of -r**5 + 5*r**4 - 25*r**3/3 + 5*r**2 + 12. Solve y(c) = 0.
0, 1, 2
Factor 2 + 13*v**3 - 2*v**4 - 3*v - v - 5*v**3 - 4*v**3.
-2*(v - 1)**3*(v + 1)
Let q(i) be the first derivative of 0*i**3 - i**2 + 0*i**4 + 3 + 0*i - 1/480*i**6 + 1/240*i**5. Let z(t) be the second derivative of q(t). Factor z(h).
-h**2*(h - 1)/4
Suppose 288 = -4*m - 4*z, 3*m = -m - 5*z - 290. Let y be (-6)/m - (-2)/10. Factor -6/7*p + y - 8/7*p**2.
-2*(p + 1)*(4*p - 1)/7
Let z(s) = s**3 - s**2 + s + 3. Let n(t) = -6*t**3 + 4*t**2 - 6*t - 16. Let f(v) = 3*n(v) + 16*z(v). Suppose f(i) = 0. What is i?
-1, 0
Let h(t) = t**2 - 4*t. Let a(s) = -4*s + 3*s + 0*s. Let p = 5 - -1. Let n(v) = p*a(v) - 2*h(v). Let n(k) = 0. Calculate k.
0, 1
Let n(w) = w**3 - 4*w**2 - 3*w - 8. Let m be n(5). Factor -1/4 + 3/4*v + v**m.
(v + 1)*(4*v - 1)/4
Let w(v) be the second derivative of v**8/1008 - v**6/360 + 3*v**2/2 + v. Let q(x) be the first derivative of w(x). Factor q(f).
f**3*(f - 1)*(f + 1)/3
Let 11*p**3 + 0*p**4 - 3*p**5 - 14*p**3 - 6*p**4 = 0. What is p?
-1, 0
Solve 95*c**2 + 67 + 225*c**3 - 675*c**2 - 80*c - 52 - 135*c**5 + 270*c**4 + 305 = 0.
-1, 4/3
