20*q**5 + v*q**3 + q - 1/6*q**4. Determine l so that f(l) = 0.
-2, 0
Let g(m) = -m + 16. Let z be g(11). Factor -2/7*c**z - 2/7 - 2/7*c - 2/7*c**4 + 4/7*c**3 + 4/7*c**2.
-2*(c - 1)**2*(c + 1)**3/7
Let k = 590 + -7660/13. Suppose -6/13*a**2 - k*a + 2/13*a**3 + 2/13*a**4 - 4/13 = 0. What is a?
-1, 2
Let t = -35 - -26. Let o = t + 9. Factor -q**2 + o - 1/2*q**3 + 0*q.
-q**2*(q + 2)/2
Let k(s) = -19*s**3 + 19*s**2 - 7*s - 6. Let t(f) = 3*f**3 - 3*f**2 + f + 1. Let o(p) = 6*k(p) + 39*t(p). Factor o(u).
3*(u - 1)**2*(u + 1)
Let w = 10 - 8. Suppose -w*o = o. Find n such that 0 - 2*n**3 + o*n + 2/3*n**2 = 0.
0, 1/3
Let t = -902 + 10831/12. Let z(b) be the first derivative of -5/9*b**3 + 1/6*b**2 - 1/5*b**5 - 2 + t*b**4 + 0*b. Factor z(o).
-o*(o - 1)**2*(3*o - 1)/3
Let s(n) be the second derivative of 4*n**6/165 - n**4/6 + 3*n**3/11 - 2*n**2/11 - 8*n. Determine d so that s(d) = 0.
-2, 1/2, 1
Let d(t) = 5*t**4 - t**3 - 6*t**2 - 6. Let b(k) = k**4 - k**2 - 1. Let j(w) = 30*b(w) - 5*d(w). Find f, given that j(f) = 0.
-1, 0
Factor 3/7*a - 10/7 + 1/7*a**3 + 6/7*a**2.
(a - 1)*(a + 2)*(a + 5)/7
Factor 50/11 + 24/11*r**3 + 120/11*r + 92/11*r**2 + 2/11*r**4.
2*(r + 1)**2*(r + 5)**2/11
Suppose 3 - 13 = -2*j. Let y(w) = -w + 8. Let g be y(j). What is r in 3*r**5 - 3*r**4 + 3*r**4 + 2*r**2 + 6*r**g + 6*r**4 - r**5 = 0?
-1, 0
Let u(a) be the second derivative of 1/30*a**6 + 0 - 1/10*a**5 + 6*a + 2/3*a**3 - 1/4*a**4 + 2*a**2. Factor u(n).
(n - 2)**2*(n + 1)**2
Determine f, given that -2/3 + 2/3*f**3 + 2/3*f**2 - 2/3*f = 0.
-1, 1
Let y(q) be the third derivative of 1/735*q**7 - 6*q**2 + 0*q**3 + 0*q + 0 - 1/840*q**6 - 1/2352*q**8 + 0*q**4 + 0*q**5. Factor y(t).
-t**3*(t - 1)**2/7
Let v be (-10 + 10)/(1*-1). Let a(n) be the third derivative of -1/12*n**4 - 3*n**2 + 0*n + 0*n**5 + v + 1/60*n**6 + 0*n**3. Solve a(r) = 0.
-1, 0, 1
Let y(r) be the third derivative of -1/60*r**6 - 4/525*r**7 - 1/840*r**8 + 0 + 0*r**3 + 0*r - 1/75*r**5 + 5*r**2 + 0*r**4. Factor y(k).
-2*k**2*(k + 1)**2*(k + 2)/5
Find d such that 1/2*d**2 - d - 3/2 = 0.
-1, 3
Factor -2/3*q + 0*q**3 + 4/3*q**4 - 4/3*q**2 + 2/3*q**5 + 0.
2*q*(q - 1)*(q + 1)**3/3
Let l(g) = g**3 + 10*g**2 + 8*g - 7. Let i be l(-9). What is y in 0*y + 3*y - 5*y + 4 - i*y**2 = 0?
-2, 1
Factor -3 + 9/4*w**2 + 3/4*w**3 + 0*w.
3*(w - 1)*(w + 2)**2/4
Let v = -58/91 - -12/13. Let d(o) = -o**3 + 3*o**2 + 3*o + 4. Let s be d(4). Factor s + 2/7*y - 4/7*y**2 + v*y**3.
2*y*(y - 1)**2/7
Factor -107*d + 107*d + 14*d**3 + 2*d**4 - 35*d**4 - 5*d**5.
-d**3*(d + 7)*(5*d - 2)
Let k(o) = 10*o**2 - 19*o + 5. Let d(j) = -5 - 3*j**2 + 6*j + 4 - 1. Suppose 0 = -2*x + 4*x, -3*b + 3*x = 42. Let c(m) = b*d(m) - 4*k(m). Factor c(w).
2*(w - 2)**2
Let x(b) be the third derivative of b**11/831600 + b**10/378000 - b**5/60 + 4*b**2. Let v(n) be the third derivative of x(n). Suppose v(m) = 0. What is m?
-1, 0
Let h(b) = -b**3 + b**2 + b - 1. Let v(k) = 6*k**3 + 4*k**2 + 6*k + 8. Let w(f) = 4*h(f) + v(f). Factor w(g).
2*(g + 1)**2*(g + 2)
Suppose -28/9*c - 4*c**2 + 8/9 = 0. What is c?
-1, 2/9
Let b = 1230 + -13528/11. Factor 0 + 2/11*d**2 - b*d + 2/11*d**3 - 2/11*d**4.
-2*d*(d - 1)**2*(d + 1)/11
Let g(x) be the first derivative of x**3/6 + 16. Solve g(w) = 0 for w.
0
Let l = 181/4 - 45. What is x in 0*x + 3/4*x**3 + 0 + 1/2*x**2 + l*x**4 = 0?
-2, -1, 0
Let i(l) be the third derivative of l**6/120 - l**5/30 - l**4/6 + 4*l**3/3 - l**2. Factor i(w).
(w - 2)**2*(w + 2)
Suppose d - 16*d**4 + 7*d - 4*d**5 - 12*d**3 + 16*d**2 + 8*d = 0. What is d?
-2, -1, 0, 1
Let a be (-2 - -4)/(10/4). Let s(z) be the second derivative of -z + 0 - 1/6*z**4 - 4/5*z**2 - a*z**3. Solve s(j) = 0.
-2, -2/5
Let n(g) be the second derivative of 1/30*g**4 + 0 - 2/15*g**3 + 0*g**2 - 6*g. What is l in n(l) = 0?
0, 2
Let h = 20 - 12. Let v = h + -8. Determine c, given that -2/3*c**3 + v*c + 2*c**2 - 8/3 = 0.
-1, 2
Let q be 3/(4 + -1)*0. Suppose q = -3*s - 3*w - 9, -s + 0*w = -w - 7. Factor 1/5*y + 0 - 4/5*y**s.
-y*(4*y - 1)/5
Solve 30/13*r + 0*r**4 + 20/13*r**3 + 40/13*r**2 - 2/13*r**5 + 8/13 = 0.
-1, 4
Let i be (-4)/(-4 - -2) + -2. Let b(l) be the first derivative of i*l + l**2 + 2/5*l**5 + 3/2*l**4 + 2*l**3 - 1. Factor b(u).
2*u*(u + 1)**3
Let s(a) be the second derivative of a**4/12 + a**3 - 2*a**2 - a. Let k be s(-7). Factor -2 - 5*w - 2*w - 2*w**4 - 12*w**2 - w - 8*w**k.
-2*(w + 1)**4
Let c(p) = -p**2 + 10*p - 14. Let k be c(8). Let -4/9*t**k + 0 - 2/9*t**4 + 0*t - 2/3*t**3 = 0. What is t?
-2, -1, 0
Let u(k) = k**3 + 15*k**2 + 15*k + 14. Let i be u(-14). Let g be 3 - (-2 - (-3 + i)). Find s such that 0*s + 0 - g*s**5 + 9/2*s**4 + 1/2*s**2 - 3*s**3 = 0.
0, 1/4, 1
Solve 0 + 4/5*b**2 - 2/5*b - 2/5*b**3 = 0 for b.
0, 1
Let b(m) be the first derivative of -5*m**6/3 - 32*m**5/5 - 13*m**4/2 - 4*m**3/3 + 4. Determine j so that b(j) = 0.
-2, -1, -1/5, 0
Let p(h) be the first derivative of -2*h**3/27 + 2*h**2/3 - 2*h + 18. Factor p(n).
-2*(n - 3)**2/9
Let w(j) be the third derivative of j**5/60 - j**4/6 + 13*j**2. Suppose w(z) = 0. What is z?
0, 4
Let g = -46 - -48. Let u(n) be the third derivative of -g*n**2 - 1/3*n**3 + 1/4*n**4 - 1/24*n**5 + 0 + 0*n. Factor u(f).
-(f - 2)*(5*f - 2)/2
Factor -10/3*w**4 + 4/3*w**3 + 0*w**2 + 0 + 0*w.
-2*w**3*(5*w - 2)/3
Suppose p - 4 = 5*p. Let a(i) = i**2 + i + 1. Let f(x) = 15*x**2 + 12*x + 9. Let d(k) = p*f(k) + 12*a(k). Suppose d(s) = 0. Calculate s.
-1, 1
Let f(u) be the third derivative of -1/48*u**4 - 1/840*u**7 + 0*u**3 + 0 + 1/240*u**5 + 6*u**2 + 1/240*u**6 + 0*u. Factor f(x).
-x*(x - 2)*(x - 1)*(x + 1)/4
Let h(c) = 4*c**3 + c**2 - c + 1. Let a be h(1). Suppose -12 = -r + 3*x, 0*r + 18 = r - a*x. Factor i**2 + 1/2*i**5 + 0 + 0*i**r - i**4 - 1/2*i.
i*(i - 1)**3*(i + 1)/2
Suppose 29*h - 8 = 25*h. Factor -2/3 - 1/3*b**h - b.
-(b + 1)*(b + 2)/3
Let v(b) be the first derivative of 14*b**6/3 - 216*b**5/5 + 110*b**4 + 48*b**3 - 378*b**2 - 216*b - 2. Factor v(r).
4*(r - 3)**3*(r + 1)*(7*r + 2)
Let c be 2/6 + 14/3. Factor c*p + 0*p - 2*p**2 - 2 + 0 - p.
-2*(p - 1)**2
Suppose -12 = -6*v + 2*v. Factor 3/2*r**3 + 0*r + 0 - v*r**2.
3*r**2*(r - 2)/2
Let g(l) = -l - 2. Let y be g(-6). Let p(k) be the first derivative of -1/10*k**2 - 1/20*k**y - 2/15*k**3 + 0*k + 2. Factor p(z).
-z*(z + 1)**2/5
Let d(b) = -5*b**3 - 3*b**2 - 9*b - 4. Let q(f) = 3*f**3 + 2*f**2 + 5*f + 2. Let u(v) = -4*d(v) - 7*q(v). Factor u(x).
-(x - 1)*(x + 1)*(x + 2)
Let u(t) = 5*t**3 + t + 3. Let j be -2 - (6 - 1*-2). Let c(w) = 16*w**3 + 4*w + 10. Let o(l) = j*u(l) + 3*c(l). Factor o(d).
-2*d*(d - 1)*(d + 1)
Let b(p) be the third derivative of p**5/48 + 35*p**4/96 + 5*p**3/4 - 27*p**2. Solve b(a) = 0.
-6, -1
Let k be -3 + (150/24 - 3). Factor 1/4*f**4 + k*f**3 + 0*f + 0*f**2 + 0.
f**3*(f + 1)/4
Let w(g) be the first derivative of g**4/4 + 2*g**3 + 9*g**2/2 + 4*g - 40. Factor w(b).
(b + 1)**2*(b + 4)
Suppose 3*o**2 + 0*o + 2*o - o**2 = 0. What is o?
-1, 0
Let b(y) = 4*y**4 - 4*y**2 + 3*y + 3. Let u(i) = 7*i**4 - 7*i**2 + 5*i + 5. Let x(d) = 5*b(d) - 3*u(d). Solve x(k) = 0.
-1, 0, 1
Let a be 3/(6/5) + 4/(-2). Let c(o) be the first derivative of 1/12*o**4 - a*o**2 + 2/3*o + 0*o**3 + 1. Factor c(z).
(z - 1)**2*(z + 2)/3
Let o(k) = -k**2 + 5*k - 4. Let a be o(4). Factor 1/4*q**2 + a - 1/4*q.
q*(q - 1)/4
Let t(z) be the second derivative of -z**4/6 + z**3/3 - z**2/4 - 7*z. Factor t(w).
-(2*w - 1)**2/2
Let q = 19/7 + -18/7. Let c(l) be the first derivative of 2/21*l**3 - 2/35*l**5 - 1 - 1/14*l**4 + q*l**2 + 0*l. Factor c(p).
-2*p*(p - 1)*(p + 1)**2/7
Let w(v) be the first derivative of 5*v**3/3 + 15*v**2/2 - 20*v + 11. Factor w(f).
5*(f - 1)*(f + 4)
Let s be 1/1 + ((-88)/20 - -4). Let d(x) be the first derivative of 6/5*x - 3/20*x**4 + s*x**3 + 3/2*x**2 - 3 - 3/25*x**5. What is p in d(p) = 0?
-1, 2
Let v(m) be the third derivative of 0*m**6 - 5*m**2 + 1/1155*m**7 + 0 + 1/33*m**3 + 0*m + 0*m**4 - 1/165*m**5. Factor v(i).
2*(i - 1)**2*(i + 1)**2/11
Factor 9*s**2 + 2*s**2 - 21*s**2 + 0*s + 5*s**5 + 10*s**4 - 5*s.
5*s*(s - 1)*(s + 1)**3
Let y(z) be the first derivative of 0*z**2 - 1/3*z**3 - 1/4*z**4 + z - 2. Let c(h) = -2*h**3 - 2*h**2 + 4. Let g(l) = c(l) - 4*y(l). Factor g(m).
2*m**2*(m + 1)
Let d(i) be the third derivative of i**5/105 - 2*i**4/21 + 8*i**3/21 + 3*i**2. Determine f so that d(f) = 0.
2
Fact