ose k = -2*u - 3*u. Factor -1/2 + u*x + 1/2*x**2.
(x - 1)*(x + 1)/2
Suppose -4*d = 1 - 9. Solve -30 + 38 - 14*n + d*n**2 + 4*n = 0 for n.
1, 4
Let c(w) = 5*w**3 + 8*w**2 - 3*w - 3. Let h(b) = -10*b**3 - 15*b**2 + 5*b + 5. Let q(f) = 5*c(f) + 3*h(f). Factor q(l).
-5*l**2*(l + 1)
Let v(u) = 11*u**2 + 17*u + 23. Let c(l) = 4*l**2 + 6*l + 8. Let i(q) = -17*c(q) + 6*v(q). Determine p so that i(p) = 0.
-1, 1
Solve 0 + 1/3*m**2 - 2/3*m + 1/3*m**3 = 0 for m.
-2, 0, 1
Factor 4*p**3 - 4*p**3 - 12*p**2 + 4*p**3 + 8*p.
4*p*(p - 2)*(p - 1)
Suppose -20 = -5*w - x, w - 4*x - 28 = -3. Let t(r) = -r + 5. Let d be t(w). Factor 2/9*n**2 - 2/9*n**3 - 2/9*n**4 + 2/9*n + d.
-2*n*(n - 1)*(n + 1)**2/9
Let n(a) = -4*a**3 + a + 1. Let w be n(-1). Let u be (-1)/w - (-7)/12. Let -2/3 + 1/3*f + f**2 - 1/3*f**4 - u*f**3 = 0. Calculate f.
-2, -1, 1
Let x be -46*(0 - 3 - -2). Suppose -2*v + 72 = 2*v. What is z in -24*z**4 + 108*z**2 - 27*z + 16 + 79*z + x*z**3 + 20*z - v*z**5 = 0?
-1, -2/3, 2
Let j(a) be the second derivative of 0 - 1/6*a**4 + 1/15*a**6 + 0*a**5 - 1/42*a**7 + 3*a + 1/6*a**3 + 0*a**2. Factor j(o).
-o*(o - 1)**3*(o + 1)
Let c = 209/21 - 29/3. Factor 2/7*f**3 - c - 2/7*f + 2/7*f**2.
2*(f - 1)*(f + 1)**2/7
Let w(b) be the second derivative of 1/4*b**4 - 1/6*b**3 - 3/20*b**5 + 1/30*b**6 + 0*b**2 + 4*b + 0. What is n in w(n) = 0?
0, 1
Let q be 2/(-1)*(-4 + 3). Suppose 5*a = g + 13, -3*g + 16 = 2*g + 2*a. Factor 4*s - g*s**2 - 6 + 2 + s**q.
-(s - 2)**2
Determine c so that 5/2*c**3 - 5/4*c + 0 + 5/4*c**2 = 0.
-1, 0, 1/2
Let g(p) be the second derivative of p**4/21 + 10*p**3/21 + 8*p**2/7 - 5*p. Find w, given that g(w) = 0.
-4, -1
Let p(k) be the first derivative of k**7/3360 - k**5/160 + k**4/48 + k**3 + 7. Let m(z) be the third derivative of p(z). Let m(l) = 0. Calculate l.
-2, 1
Let y(x) be the second derivative of 0 + 1/60*x**5 + 0*x**2 - 2*x + 0*x**3 - 1/18*x**4. Factor y(r).
r**2*(r - 2)/3
Let x be 27/36*(-32)/2. Let j = x - -14. Factor -3/4*k + 3/4*k**3 + 0 + 0*k**j.
3*k*(k - 1)*(k + 1)/4
Let p = -11 + 19. Let y be 0 + -1 + -2 - -7. Factor -2*d**2 - p + y*d + 8.
-2*d*(d - 2)
Let -10/13*f**2 + 2/13*f**3 + 10/13 - 2/13*f = 0. Calculate f.
-1, 1, 5
Let b(p) = -11*p + 14*p - 1 + 18*p. Let i be b(1). Factor -6*q - i*q**2 + 0*q + 23*q**2.
3*q*(q - 2)
Let q(j) = j**2 - 34*j. Let b be q(34). Let y = 1703/28 + -241/4. Solve 2*x**4 - 10/7*x**3 + 0*x - y*x**2 + b = 0 for x.
-2/7, 0, 1
Let j(z) be the first derivative of -3*z**4/22 - 8*z**3/33 + z**2/11 + 4*z/11 + 2. Suppose j(d) = 0. Calculate d.
-1, 2/3
Determine n, given that -36/7*n**2 - 24/7*n**3 - 4/7*n**4 + 0*n + 0 = 0.
-3, 0
Suppose -5*u = -5, u = -0*m - m - 3. Let i be m*(-5)/80 + 0. Factor -i*c**4 - 1/2*c + 0*c**3 + 3/4*c**2 + 0.
-c*(c - 1)**2*(c + 2)/4
Let v(g) = 2*g**2 + 2*g. Let z(j) = -3*j**2 - 3*j. Let s(u) = -4*v(u) - 3*z(u). Factor s(t).
t*(t + 1)
Let d = 59/159 + -2/53. Let j(h) be the second derivative of 1/24*h**4 - d*h**3 + h + 0 + h**2. Solve j(u) = 0.
2
Let b be (15/24)/(54/432). Factor 0*q + 3/4*q**3 - 3/4*q**4 + 0 + 1/4*q**b - 1/4*q**2.
q**2*(q - 1)**3/4
Let u be (6/(-15)*-5)/1. Let c be (-16)/12*(-3)/u. Find o, given that 0 + 0*o**c + 2/3*o**3 - 2/3*o = 0.
-1, 0, 1
Let h(x) be the second derivative of 3*x + 3/140*x**5 + 0 + 1/7*x**2 - 1/14*x**3 - 1/42*x**4. Factor h(i).
(i - 1)*(i + 1)*(3*i - 2)/7
Let o be (0 + -2)*(-1 - 0). Factor u**2 - 2 + 2*u - o + u**2.
2*(u - 1)*(u + 2)
Let n(i) = i**2 + i - 1. Let r be (2 + -3)*15/3. Let k(g) = -2*g**3 - 7*g**2 - 5*g + 5. Let d(x) = r*n(x) - k(x). Factor d(f).
2*f**2*(f + 1)
Let v(c) be the first derivative of c**3/12 - c**2/2 + 3*c/4 - 5. Factor v(m).
(m - 3)*(m - 1)/4
Let k = 5/21 + 2/21. Solve -1/3*s**2 - k*s**4 + 0*s - 2/3*s**3 + 0 = 0.
-1, 0
Solve 4 - 6*i**2 - 1 + 2*i**4 + i**4 = 0 for i.
-1, 1
Let a = 157 + -469/3. Factor 0 + a*o - 1/3*o**2.
-o*(o - 2)/3
Let i(d) be the third derivative of -d**9/12096 + d**7/3360 + d**3/6 + d**2. Let x(l) be the first derivative of i(l). Let x(n) = 0. Calculate n.
-1, 0, 1
Factor 3*j**3 - 8*j**3 + 3*j**3 + 12*j**2 + 6*j**3 + 8*j.
4*j*(j + 1)*(j + 2)
Let y = 7 + -5. What is f in -11*f**2 + 16*f**y - f**2 = 0?
0
Let b(l) be the third derivative of -l**7/168 - l**6/48 + l**5/48 + 5*l**4/48 - 7*l**2. Factor b(f).
-5*f*(f - 1)*(f + 1)*(f + 2)/4
Suppose 0 - 4/15*j**2 + 2/15*j + 2/15*j**3 = 0. What is j?
0, 1
Let y = 29 - 26. Let o(v) be the second derivative of -v + 0*v**2 + 0 + 0*v**y - 1/24*v**4. Determine f so that o(f) = 0.
0
Suppose -n = n + 5*p + 14, -2*p = 4*n - 4. Determine q, given that 2 - 2 + q**2 + 3*q**n + q**3 = 0.
-1/4, 0
Let c(x) be the second derivative of x**6/65 + 11*x**5/130 + 4*x**4/39 - 4*x**3/39 - x + 6. Suppose c(m) = 0. Calculate m.
-2, 0, 1/3
Let y = 9 + -13. Let t(r) = -3 + 5*r**3 + 3*r**5 + r + r**5 - 4*r**3 - 3*r**5. Let z(h) = -2*h**5 - 2*h + 4. Let v(o) = y*t(o) - 3*z(o). Solve v(d) = 0 for d.
-1, 0, 1
Suppose -58 = 4*u + 5*j, 28 = u - 3*u - 3*j. Let y = -17 - u. Factor 64/7*h**3 + y + 0*h + 14*h**5 + 22*h**4 + 8/7*h**2.
2*h**2*(h + 1)*(7*h + 2)**2/7
Let q(f) be the first derivative of 4*f**3/3 - 20*f**2 + 100*f - 13. Factor q(r).
4*(r - 5)**2
Factor 2/3 - p + 1/3*p**2.
(p - 2)*(p - 1)/3
Let y(d) = -d + 21. Let h be y(12). Suppose -4*v - 1 = 4*o - h, -5*o + 4 = 3*v. Factor 1/6*z**v - 5/6*z + 1/6*z**4 - 1/3 - 1/2*z**2.
(z - 2)*(z + 1)**3/6
Let l = -298/5 + 60. Let l - 4/5*g + 2/5*g**2 = 0. What is g?
1
Let c(t) be the third derivative of 2/3*t**4 + 0 - t**2 + 2/3*t**3 + 1/30*t**7 + 1/336*t**8 + 19/120*t**6 + 5/12*t**5 + 0*t. Factor c(n).
(n + 1)**3*(n + 2)**2
Suppose 3*g - 2*g - 24 = 0. Factor -5*x**2 + 2*x**3 + g*x + 12 + 5*x**2 + 12*x**2 + 4.
2*(x + 2)**3
Let j(o) be the second derivative of o**5/80 - o**4/16 + o**3/12 + 4*o. Determine r, given that j(r) = 0.
0, 1, 2
Solve 0 + 0*k**2 - 2/3*k**3 + 1/3*k**5 + 0*k**4 + 1/3*k = 0 for k.
-1, 0, 1
Let r(u) be the first derivative of 6/55*u**5 + 1/11*u**4 + 0*u - 2/33*u**3 + 0*u**2 - 1. Factor r(z).
2*z**2*(z + 1)*(3*z - 1)/11
Let h = 7/22 - -2/11. Determine m, given that 5/4*m + m**2 + h + 1/4*m**3 = 0.
-2, -1
Let k(b) be the third derivative of -b**7/21 - 5*b**6/24 - b**5/4 + 5*b**4/24 + 5*b**3/6 - 18*b**2. Factor k(m).
-5*(m + 1)**3*(2*m - 1)
Suppose 0 = -c - c. Let m(r) be the second derivative of 1/3*r**3 + 0*r**4 + 2*r + 0 - 1/10*r**5 + c*r**2. Solve m(y) = 0.
-1, 0, 1
Suppose a**4 + 0*a**2 + 0*a - 1/2*a**3 + 0 - 1/2*a**5 = 0. What is a?
0, 1
Suppose 16 = 4*u, 4*u - 3*u + 4 = 4*i. Let -21*b**2 - 75*b**4 + 37*b**i - 65*b**3 + 20*b - 8 + 22*b**2 = 0. Calculate b.
-1, -2/3, 2/5
Let u be (-1)/18 - (-598)/828. Find s such that -u*s + 1/3 + 1/3*s**2 = 0.
1
Let w be 1/4*6*2. Factor r**2 + w*r - 3 + 2 + 1.
r*(r + 3)
Let u be (-429)/315 - (-8)/(-20). Let o = 17/7 + u. Factor -2/3*z + o*z**2 + 0.
2*z*(z - 1)/3
Let b(n) be the third derivative of n**8/20160 - n**6/2160 + n**4/8 - n**2. Let r(o) be the second derivative of b(o). Factor r(a).
a*(a - 1)*(a + 1)/3
Let f be (-7)/(-4) + (-1)/(-4). Let h(p) be the second derivative of 1/12*p**3 + 1/2*p**f - p - 1/24*p**4 + 0. Factor h(s).
-(s - 2)*(s + 1)/2
Let c be 6248/3885 - (-14)/(-49). Let r = c - -2/185. Factor -2*a - 2/3*a**2 - r.
-2*(a + 1)*(a + 2)/3
Let v be 9/(18/8) + -1. Let g(d) be the second derivative of -1/9*d**3 + 0*d**2 - 1/6*d**4 + 0 - 1/45*d**6 - 1/10*d**5 - v*d. What is r in g(r) = 0?
-1, 0
Let i(z) = 7*z**3 + 16*z**2 - 17*z - 8. Let t(k) = 17 - 14*k**3 - 39*k**2 + 13*k + 21*k + 7*k**2. Let r(o) = -5*i(o) - 2*t(o). Factor r(n).
-(n - 1)*(n + 3)*(7*n + 2)
Let x be 15 - ((-1)/(-1) + 2). Factor 5 + s**3 + x*s - 13*s - s**2 - 4.
(s - 1)**2*(s + 1)
Let v(u) = u**3 + u**2 - 1. Let x be v(2). Let y be (-1)/(-3)*(x + -2). Factor q**2 + 2*q**3 + 2*q**4 - 4*q**3 + 2*q - y*q**2.
2*q*(q - 1)**2*(q + 1)
Let x be (21/(-12) - -1)/(15/(-80)). Let 0 + 7/4*d**5 + 11/4*d**3 + 4*d**x + 0*d + 1/2*d**2 = 0. Calculate d.
-1, -2/7, 0
Let t(u) = 2. Let s(j) = 2*j**2 + j**2 - 2*j**2. Let m(r) = 2*s(r) - t(r). Factor m(b).
2*(b - 1)*(b + 1)
Let x(v) be the second derivative of v**5/5 + 7*v**4/3 + 4*v**3 + 2*v. Factor x(i).
4*i*(i + 1)*(i + 6)
Suppose -4*t + 3 - 27 = -2*a, -a = 3*t + 13. Let 3*h - h - 2*h**a + h**2 + h = 0. What is h?
0, 3
Factor 2*y**2 - 5 - 31*y**2 - 69*y**2 - 230*y**3 - 45*y**5 - 165*y**4 - 52