j**3 - 13*j**2 - 3*j. Let i(h) = 9*h**3 + 12*h**2 + 3*h. Let z(x) = u*i(x) + 6*p(x). Factor z(k).
3*k*(k + 1)**2
Let o be ((-5)/4)/(2/16). Let s be o/15 - (-14)/12. Factor 1/4*w**2 - s - 1/4*w.
(w - 2)*(w + 1)/4
Let v(i) be the first derivative of 2*i**6/3 - 4*i**5/5 - 3*i**4 + 4*i**3/3 + 4*i**2 + 24. Factor v(h).
4*h*(h - 2)*(h - 1)*(h + 1)**2
Suppose -3*f + c + 0*c = -6, 4 = 2*f + 5*c. Suppose 3*b - f = 10. Factor -12*q**2 + 6*q - 4*q + b*q**2.
-2*q*(4*q - 1)
Factor -27/7*z**2 + 3/7*z**3 - 48/7 + 72/7*z.
3*(z - 4)**2*(z - 1)/7
Let i(h) be the first derivative of -2/9*h - 1/9*h**2 + 1/18*h**4 + 2/27*h**3 + 3. Factor i(s).
2*(s - 1)*(s + 1)**2/9
Let k be (-2)/95*(-260)/12. Let y = 4/19 + k. Factor -2/3 - 5/3*n**3 + 5/3*n + y*n**2.
-(n - 1)*(n + 1)*(5*n - 2)/3
Let n = -7499/6 + 1250. Factor 2/3 + n*i**2 + 2/3*i.
(i + 2)**2/6
Let l(q) be the first derivative of q**4/18 + 2*q**3/9 + q**2/3 - 2*q + 3. Let h(r) be the first derivative of l(r). Determine t, given that h(t) = 0.
-1
Suppose 4*b - 7 = -0*s - 3*s, 5*b - 4*s = 32. Factor -o**4 + 5*o**3 + b*o**4 + o**3.
3*o**3*(o + 2)
Let y(u) = -2*u**4 - 10*u**3 + 10*u - 4. Suppose 0 = 2*h - 5 - 9. Let m(s) = 2*s**4 + 11*s**3 - 11*s + 5. Let r(f) = h*y(f) + 6*m(f). Solve r(c) = 0.
-1, 1
Suppose 5*q - 3*k - 76 = 0, -2*q + 3*q - 32 = -5*k. Suppose 0 = -4*g + 3 + q. Factor -y**2 + 2*y**4 + 2*y**2 - g*y**2 + 2 - 2*y - 2*y**5 + 4*y**3.
-2*(y - 1)**3*(y + 1)**2
Let r(c) be the first derivative of -c**3 - 3*c**2/2 + 6*c - 1. Factor r(i).
-3*(i - 1)*(i + 2)
Let y be 102/(-30) - (-2)/5. Let x be -1 + -1 - 7/y. Let a + 1/3 + x*a**3 + a**2 = 0. What is a?
-1
Let o(z) be the third derivative of -2*z**7/35 + z**6/15 + 4*z**5/15 - z**4/3 - 2*z**3/3 + z**2. Find f, given that o(f) = 0.
-1, -1/3, 1
Let n = 9 + -9. Determine a so that -a**3 + n*a**3 + 0*a**3 + 0*a**3 = 0.
0
Let a(b) = 2*b**2 + 7*b + 9. Let n(j) = -7*j**2 - 26*j - 35. Let w(s) = 22*a(s) + 6*n(s). Find t such that w(t) = 0.
-2, 3
Let 0*n + 2/9*n**5 + 14/9*n**2 - 2/9*n**3 - 8/9 - 2/3*n**4 = 0. What is n?
-1, 1, 2
Let i be 0/1*(-11)/33. Suppose i = -j + 4*j. Factor 0*l**4 - 3/4*l**3 + 0 + 0*l + j*l**2 + 3/4*l**5.
3*l**3*(l - 1)*(l + 1)/4
Let t(z) be the second derivative of -z**7/5040 + z**5/720 + z**3 + 5*z. Let x(p) be the second derivative of t(p). Factor x(i).
-i*(i - 1)*(i + 1)/6
Let q = -41 + 40. Let u be 1 - q*26/10. Determine b, given that 28/5*b**2 - 6*b**4 - u*b**5 + 2/5 + 4/5*b**3 + 14/5*b = 0.
-1, -1/3, 1
Let a = 11 - 9. Factor -3*q**2 - 3*q**a + 4*q**2 + 9*q**3 - 7*q**3.
2*q**2*(q - 1)
Factor 0 - 2*u**4 - 16/5*u**3 - 2/5*u**2 + 4/5*u.
-2*u*(u + 1)**2*(5*u - 2)/5
Let g(o) = -3*o - 24. Let t be g(-8). Let t + 2/5*b - 24/5*b**4 - 22/5*b**3 + 4/5*b**2 = 0. What is b?
-1, -1/4, 0, 1/3
Let z(f) be the third derivative of -f**5/20 + 5*f**4/64 + 3*f**3/16 + 18*f**2 + 1. Determine y, given that z(y) = 0.
-3/8, 1
Let v(j) be the second derivative of 0 - 2/21*j**6 - 1/49*j**7 + 4*j + 2/7*j**2 + 5/21*j**3 + 0*j**4 - 1/7*j**5. Factor v(o).
-2*(o + 1)**4*(3*o - 2)/7
Let x = 741 - 738. Suppose 0*i**2 + 0*i - 2/5*i**5 - 2/5*i**4 + 0*i**x + 0 = 0. What is i?
-1, 0
Let c(a) be the second derivative of 2*a**4/21 + 5*a**3/21 + a**2/7 + 2*a. Factor c(x).
2*(x + 1)*(4*x + 1)/7
Let z(j) be the first derivative of -j**7/56 - 2*j + 2. Let c(k) be the first derivative of z(k). Solve c(v) = 0 for v.
0
Suppose 0 = -c - 3*l - 1, 0 = -4*c + 2*l + 10 - 0. Factor -z + 7*z + c + 3*z**2 + 1.
3*(z + 1)**2
Suppose -3*q + 21 = -18. Suppose 5*o = q + 17. Factor 1/2 - 15/4*c + o*c**2 + 4*c**3.
(c + 2)*(4*c - 1)**2/4
Factor 0 + 16/7*x**2 - 12/7*x - 4/7*x**3.
-4*x*(x - 3)*(x - 1)/7
Let s be ((-26)/(-8) - 3) + (-10)/(-24). What is f in s*f**3 - 2/3*f**2 + 0*f - 2/3*f**5 + 0 + 2/3*f**4 = 0?
-1, 0, 1
Let y(g) be the first derivative of -3*g**5/5 + 3*g**4 - 5*g**3 + 3*g**2 + 5. Determine d so that y(d) = 0.
0, 1, 2
Suppose -24 = -18*y + 30. Factor 0*d + 3*d**2 + 0 + 3/2*d**y.
3*d**2*(d + 2)/2
Let r = -47 + 50. Let 0 + 0*n**r - 2/7*n**4 + 0*n + 2/7*n**2 = 0. What is n?
-1, 0, 1
Let 63/4*k + 15/4 + 3*k**2 = 0. Calculate k.
-5, -1/4
Let a(c) = -8*c + 2 - 3*c**2 - 3*c**2 + 4 + 2*c**3. Let i(q) = 6*q**3 - 17*q**2 - 23*q + 17. Let w(r) = -17*a(r) + 6*i(r). Let w(u) = 0. What is u?
-1, 0, 1
Let w = 2 - -2. Let g(a) be the second derivative of 1/12*a**3 + 0 + a - 1/8*a**2 - 1/48*a**w. Let g(r) = 0. What is r?
1
Let k(c) be the first derivative of 0*c**3 + 1/3*c**6 + 4/5*c**5 + 1/2*c**4 - 2 + 0*c + 0*c**2. Determine o so that k(o) = 0.
-1, 0
Let o(g) be the first derivative of 4*g**6/3 + 44*g**5/5 + 23*g**4 + 92*g**3/3 + 22*g**2 + 8*g - 15. Suppose o(a) = 0. Calculate a.
-2, -1, -1/2
Let i(g) be the third derivative of -5*g**8/36 + g**7/126 + 23*g**6/72 - g**5/6 - 17*g**2. Solve i(h) = 0 for h.
-1, 0, 2/7, 3/4
Determine z, given that -26*z + 5*z - 2 - 15*z**2 - 1 - 3 = 0.
-1, -2/5
Let b be (2/44)/((-29)/(-348)). Let -4/11 - 2/11*s**3 - 2/11*s**4 + b*s**2 + 2/11*s = 0. What is s?
-2, -1, 1
Let t(p) be the third derivative of p**5/240 - p**4/48 + p**3/24 + 3*p**2. Factor t(u).
(u - 1)**2/4
Suppose -f - 4 = 2. Let z(q) = -3*q**4 + 6*q**3 - 3*q**2 - 6. Let w(h) = 6*h**4 - 12*h**3 + 5*h**2 + h + 11. Let j(s) = f*w(s) - 11*z(s). Factor j(v).
-3*v*(v - 2)*(v - 1)*(v + 1)
Let c be 2/(-7) + 4/14. Let u(s) = s**3 + s. Let b be u(1). Factor 2/9*k**b + 0 - 2/9*k**3 - 2/3*k**5 - 10/9*k**4 + c*k.
-2*k**2*(k + 1)**2*(3*k - 1)/9
Suppose -2/3*l**4 - 2/3 + 4/3*l**3 + 4/3*l**2 - 2/3*l**5 - 2/3*l = 0. Calculate l.
-1, 1
Suppose 32*q - 4 = 30*q. Factor -66/5*h**3 - 81/5 - 13/5*h**4 - 1/5*h**5 - 189/5*h - 162/5*h**q.
-(h + 1)*(h + 3)**4/5
Let l be (-4 + 2)*(-3 + 1). Suppose -9*n**l - 5/2*n**5 + 1 - 11*n**3 - 4*n**2 + 3/2*n = 0. Calculate n.
-1, 2/5
Let i(o) = 8*o**4 + 12*o**3 - 34*o**2 + 20*o + 4. Let h(n) = -n**4 + n**2 - 1. Let z(f) = -10*h(f) - i(f). Let z(s) = 0. Calculate s.
1, 3
Let o(v) be the third derivative of v**8/26880 + v**7/10080 - v**6/2880 - v**5/480 - v**4/3 - 8*v**2. Let u(m) be the second derivative of o(m). Factor u(b).
(b - 1)*(b + 1)**2/4
Let b(c) = c**2 - 5*c + 2. Let f be b(5). Factor 2 - x**2 + x + 0*x - f*x.
-(x - 1)*(x + 2)
Let s(v) = -64*v**2 - 160*v - 97. Let a(p) = 1. Let k(l) = -3*a(l) + s(l). Factor k(h).
-4*(4*h + 5)**2
Let a(i) be the first derivative of 3*i**6/2 - 6*i**5 + 9*i**4/4 + 4. Factor a(v).
3*v**3*(v - 3)*(3*v - 1)
Let z(d) be the third derivative of 4*d**7/945 + d**6/180 - d**5/270 + 2*d**2. Solve z(o) = 0.
-1, 0, 1/4
Let r(m) = -15*m**3 - 9*m**2 - 2*m. Let w(i) = -7*i**3 - 4*i**2 - i. Let s(a) = 6*r(a) - 13*w(a). Factor s(l).
l*(l - 1)**2
Let k(y) = -20*y**3 - 25*y**2 + 60*y + 15. Let p(n) = 5*n**3 + 6*n**2 - 15*n - 4. Let z(j) = -4*k(j) - 15*p(j). Factor z(g).
5*g*(g - 1)*(g + 3)
Let b(f) be the first derivative of 6 - 1/2*f**2 + 1/2*f - 1/2*f**3. Factor b(c).
-(c + 1)*(3*c - 1)/2
Let v(q) be the third derivative of -q**8/672 - q**7/60 - q**6/24 + q**5/60 + 11*q**4/48 + 5*q**3/12 - 44*q**2. Factor v(m).
-(m - 1)*(m + 1)**3*(m + 5)/2
Let j(b) be the second derivative of -1/45*b**6 + 0*b**4 - 9*b + 1/60*b**5 + 0*b**2 - 1/42*b**7 + 0*b**3 + 0. Factor j(h).
-h**3*(h + 1)*(3*h - 1)/3
Let g = -7 - -11. Factor -w**2 + w**3 - 2*w**3 + w + 5*w**4 - g*w**4.
w*(w - 1)**2*(w + 1)
Let w be -6 + -1 - 78/(-7). Let 19/7*f - 36/7*f**5 - 55/7*f**2 - 2/7 + 69/7*f**4 + w*f**3 = 0. What is f?
-1, 1/4, 1/3, 2
Let m(q) be the third derivative of -q**5/6 + q**4 - 4*q**3/3 - q**2 - 2. Factor m(j).
-2*(j - 2)*(5*j - 2)
Let m be 1/1*2 + 0. Let -4 + m*f**2 + f - f + 2*f = 0. Calculate f.
-2, 1
Let x(f) = f**2 - 15*f - 30. Let u be x(17). Let 1/4*s + 0*s**3 - 1/2*s**2 + 1/2*s**u - 1/4*s**5 + 0 = 0. What is s?
-1, 0, 1
Suppose 18 = 6*a - 0. Let b(g) be the first derivative of -1/4*g**4 + 1/2*g**2 + a + 1/3*g**3 - g. Suppose b(f) = 0. Calculate f.
-1, 1
Let l(b) be the first derivative of 1/4*b**6 + 0*b - 3/8*b**4 - 5 + 0*b**3 + 0*b**5 + 0*b**2. Factor l(v).
3*v**3*(v - 1)*(v + 1)/2
Let g(k) be the first derivative of 2 + 1/4*k**3 - 3/10*k**5 + 0*k + 0*k**2 - 3/16*k**4. Factor g(f).
-3*f**2*(f + 1)*(2*f - 1)/4
Let c = -85 - -767/9. Factor -c - 2/9*m**2 + 4/9*m.
-2*(m - 1)**2/9
Let k = 1229/4030 - 2/403. Let i = 11/20 - k. Factor 1/2*b - 1/4*b**2 - i.
-(b - 1)**2/4
Suppose -6*o + 22 + 8 = 0. Let l(r)