 j(1). Let d = -7 + 10. Factor 2*v - v**3 + 0*v**d - v - 3*v**2 + 2*v**2 + v**s.
v*(v - 1)**2*(v + 1)
Let w(z) = -2*z**4 + z**3 - z**2 - 4*z + 3. Suppose -9*r + 11*r + 6 = 0. Let f(u) = -3*u**4 - u**2 - 4*u + 4. Let c(p) = r*f(p) + 4*w(p). Factor c(y).
y*(y - 1)*(y + 1)*(y + 4)
Let t(w) be the third derivative of -1/12*w**5 + 0*w**4 + 0*w**3 + 0 + 1/8*w**6 + 12*w**2 + 0*w. Find u such that t(u) = 0.
0, 1/3
Suppose -2*o - 2*b + 10 = 0, 4*b = -0*o - 5*o + 26. Factor 2 + 3*u - 8*u - u + 13*u**3 - 15*u**3 + o*u**2.
-2*(u - 1)**3
Let a = 132 + -115. Suppose -4*y + a + 3 = 0. Find z, given that -1/4*z**y - 7/4*z**3 - 5/4*z**4 + 1 + 1/4*z**2 + 2*z = 0.
-2, -1, 1
Let d(l) = -4239*l**2 + 736*l - 39. Let g(f) be the first derivative of -2119*f**3/3 + 184*f**2 - 19*f + 3. Let k(t) = 3*d(t) - 7*g(t). Factor k(c).
4*(23*c - 2)**2
Let o be (2 + 40)*4/14. Let r be 3 + -1 - (-8)/2. Determine l so that -3/2 + 6*l**5 - 3/2*l**4 - o*l**3 + 3*l**2 + r*l = 0.
-1, 1/4, 1
Let s be (-102)/36 - ((-24)/4)/2. Let j(n) be the first derivative of 3 - 4*n**2 - 4/3*n**3 - s*n**4 - 16/3*n. Factor j(k).
-2*(k + 2)**3/3
Let t(o) be the third derivative of 0*o**3 + 0 + 1/100*o**5 + 1/20*o**4 + 0*o - 1/350*o**7 - 27*o**2 - 1/100*o**6. Solve t(n) = 0 for n.
-2, -1, 0, 1
Let p(z) be the third derivative of z**5/30 + 38*z**4/3 + 5776*z**3/3 + 565*z**2. Factor p(h).
2*(h + 76)**2
Solve 0 + 3*f**4 - 3/5*f**3 + 0*f**2 + 0*f = 0.
0, 1/5
Find x such that -6*x**3 - 28*x**2 + 40/3*x + 400/3 = 0.
-10/3, 2
Factor 3*c**2 + 138/7*c + 9 - 6/7*c**3.
-3*(c - 7)*(c + 3)*(2*c + 1)/7
Let k(m) be the third derivative of m**5/5 - m**4/3 - 2*m**3/3 + 63*m**2. Factor k(r).
4*(r - 1)*(3*r + 1)
Let s(u) = 10*u**2 + 5*u + 5. Let g(o) = o**2 + 1. Let k(t) = -4*t + 8. Let x be k(-9). Let m(v) = x*g(v) - 4*s(v). Factor m(p).
4*(p - 3)*(p - 2)
Factor 3 + 102*r - 12*r**3 - 12 - 4 - 33*r**2 - 33 - 11.
-3*(r - 1)**2*(4*r + 19)
Suppose 0 = 13*w + 55*w - 816. Let i(f) be the second derivative of 0*f**5 - w*f + 0*f**3 + 0*f**4 - 1/45*f**6 + 0*f**2 + 0. Let i(j) = 0. Calculate j.
0
Suppose -5*t + 5*z + 25 = 0, -162*z + 165*z + 6 = 0. Suppose 2*c - 6*c - 3 = 3*n, -5*n - 5 = 5*c. Factor -3/2*q**2 + c - t*q.
-3*q*(q + 2)/2
Factor 1/5*p**2 + 1/5*p - 2/5.
(p - 1)*(p + 2)/5
Let b(y) be the first derivative of y**3/12 + 25*y**2/8 - 13*y/2 - 178. Factor b(t).
(t - 1)*(t + 26)/4
Let i be (-52)/4*((-2)/2 + -1). Let u be (-2 - -1)*2 - (-56)/i. Factor -u*w**2 + 0 - 2/13*w**3 + 0*w.
-2*w**2*(w + 1)/13
Suppose -9*y = -4*y. Suppose -4*r = -g - 1 + 6, 0 = 4*r - 3*g + 15. Determine w so that y - 2/9*w + 4/9*w**4 + 2/9*w**5 - 4/9*w**2 + r*w**3 = 0.
-1, 0, 1
Suppose -4*o - 52 = -3*q, 3*q - 5*q - o + 20 = 0. Let l be 6*3/q - (-108)/(-104). Determine r so that -l - 8/13*r - 2/13*r**2 = 0.
-3, -1
Suppose 0 = 3*m + d - 1, -5*m + d - 1 = -m. Let -1/2*a**3 + 0 + 1/4*a**4 + 1/4*a**2 + m*a = 0. What is a?
0, 1
Suppose -90*r = -92*r. Let u(b) be the first derivative of 2/3*b**3 + 0*b + b**4 + 2/5*b**5 + 6 + r*b**2. Factor u(j).
2*j**2*(j + 1)**2
Suppose 1 + 1 - 26*n - 3 + 6*n**2 + 9 = 0. Calculate n.
1/3, 4
Let n(r) be the first derivative of r**6/120 + 7*r**3/3 - 1. Let s(m) be the third derivative of n(m). Factor s(p).
3*p**2
Let l(w) be the second derivative of -w**7/252 + w**5/72 - 7*w**2/2 - 13*w. Let a(n) be the first derivative of l(n). Let a(s) = 0. What is s?
-1, 0, 1
Let o(g) be the third derivative of g**7/1050 - g**6/300 - 2*g**5/75 + 3*g**4/20 - 3*g**3/10 + 83*g**2 + 2. Factor o(z).
(z - 3)*(z - 1)**2*(z + 3)/5
Factor -105/4 - 9*q - 3/4*q**2.
-3*(q + 5)*(q + 7)/4
Let d be (2 + 84/(-70))/(2 + (-1)/1). Factor -d*h + 0 - 4/5*h**4 - 12/5*h**3 - 12/5*h**2.
-4*h*(h + 1)**3/5
Let c be -1 - ((-1)/(-22))/(16/(-992)). Let j = -69/44 + c. Factor -9*f**2 - j + 3*f.
-(6*f - 1)**2/4
Let t(k) = k**3. Let x(w) = 47*w**3 + 240*w**2 + 168*w + 32. Let o = -28 + 31. Let b(m) = o*t(m) + x(m). Find u such that b(u) = 0.
-4, -2/5
Let c(k) be the second derivative of -k**6/50 - 3*k**5/25 - k**4/10 + 2*k**3/5 + 9*k**2/10 + 55*k - 1. Solve c(g) = 0 for g.
-3, -1, 1
Let l be 4*3/126 + 696/1218. Solve 10/3*x**3 - l*x**4 - 8/3*x - 4*x**2 + 16/3 = 0.
-1, 2
Let n(q) be the third derivative of 2*q**8/483 - 16*q**7/2415 + 2*q**5/345 - q**4/276 - 105*q**2. Factor n(x).
2*x*(2*x - 1)**3*(2*x + 1)/23
Let c(i) be the third derivative of -i**8/840 + 13*i**7/350 - 179*i**6/600 - 2*i**5/5 + 5*i**4/6 + i**2. Let c(m) = 0. Calculate m.
-1, 0, 1/2, 10
Let o be 0/1*-1*8/(-16). Let u(p) be the third derivative of 0*p**4 + 0*p**5 - 1/112*p**8 + 3*p**2 + 0*p + 0*p**6 + o*p**3 + 0 + 1/70*p**7. Factor u(i).
-3*i**4*(i - 1)
Let o(j) be the second derivative of 2*j**7/21 + j**6/6 - 11*j**5/20 - 7*j**4/12 + 7*j**3/6 + j**2 - 53*j - 2. Determine a so that o(a) = 0.
-2, -1, -1/4, 1
Let w(s) be the third derivative of -s**7/105 + s**6/12 + s**5/30 - 5*s**4/12 + 344*s**2 - 2*s. Factor w(m).
-2*m*(m - 5)*(m - 1)*(m + 1)
Let j(q) be the first derivative of 3*q**5/5 + 3*q**4 + 5*q**3 + 3*q**2 + 86. Find d such that j(d) = 0.
-2, -1, 0
Let p(x) be the first derivative of 2/17*x - 2/17*x**2 - 40 + 2/51*x**3. Solve p(l) = 0 for l.
1
Let w = 5433 - 3911759/720. Let f(v) be the third derivative of -1/48*v**4 + 1/36*v**3 - w*v**6 - 4*v**2 + 0*v + 0 + 1/120*v**5. Let f(d) = 0. What is d?
1
Let x(f) be the third derivative of f**7/420 - f**6/24 - 3*f**5/10 - 19*f**4/24 - 13*f**3/12 - 92*f**2. Suppose x(u) = 0. Calculate u.
-1, 13
Let b(a) be the second derivative of -a**8/10080 + a**7/3780 - a**4/3 - 2*a. Let x(h) be the third derivative of b(h). Solve x(t) = 0 for t.
0, 1
Suppose 0 = -13*b + 3*b + 60. Factor -20*t**2 + 8*t**2 + 10*t + 11*t + b.
-3*(t - 2)*(4*t + 1)
Factor -185*y**3 - 22*y + 2*y + 4*y**2 + 12 + 189*y**3.
4*(y - 1)**2*(y + 3)
Let t(w) = 5*w**3 - 45*w**2 + 98*w - 2. Let b(k) = -20*k**3 + 180*k**2 - 391*k + 9. Let c(f) = 2*b(f) + 9*t(f). Factor c(y).
5*y*(y - 5)*(y - 4)
Suppose -4*w = -6*v + 9*v, -4*w + 4*v = 0. Let z(k) be the second derivative of 1/20*k**5 - 1/4*k**4 + 1/3*k**3 - 5*k + 0*k**2 + w. Factor z(r).
r*(r - 2)*(r - 1)
Suppose -20*u**2 + 61/2*u**3 - 9/2*u**4 + 0 - 6*u = 0. What is u?
-2/9, 0, 1, 6
Suppose 2*q + 37 - 41 = 0. Factor 4*o**4 + q + 8*o**3 - 8*o - 6 + 0*o.
4*(o - 1)*(o + 1)**3
Suppose -5*n + 17 = 3*l, -n + 5*l + 17 = 2*n. Suppose -3*y = -n*g + y, -3*y = 4*g - 21. Suppose -30 + 0*m**2 - 4*m**2 + 55*m - 8*m**2 - g*m**2 = 0. What is m?
2/3, 3
Let c(t) be the first derivative of t**7/42 - 5*t**6/24 + t**5/12 + 35*t**4/8 - 15*t**3 + 3*t**2/2 + 22. Let v(y) be the second derivative of c(y). Factor v(h).
5*(h - 3)**2*(h - 1)*(h + 2)
Suppose -3*n - 18 = -3*v, 141*n = 140*n - v + 6. Let 0 + 0*i**2 + 21/5*i**4 - 3*i**5 + n*i - 6/5*i**3 = 0. Calculate i.
0, 2/5, 1
Factor 7894 - 2*a**3 - 132*a**2 - 7894.
-2*a**2*(a + 66)
Let a(r) = -r - 1. Let u be 1/(-2) + 10/(-20). Let z be a(u). Suppose 3*t**2 - 5*t**2 - 2*t**3 + 2 + z*t + 2*t + 0*t = 0. What is t?
-1, 1
Suppose -32*r - 48 = -36*r. Suppose -12*v + 6 - 5 + 8 + 8*v**3 - 1 - r*v**2 = 0. What is v?
-1, 1/2, 2
Let v(p) be the first derivative of 5*p**6/42 - p**5/5 - 13*p**4/28 + 31*p**3/21 - 10*p**2/7 + 4*p/7 + 51. Factor v(c).
(c - 1)**3*(c + 2)*(5*c - 2)/7
Let 0*k + 1/3*k**3 - 1/3*k**2 + 0 = 0. What is k?
0, 1
Let l(m) be the second derivative of 0*m**3 + 0 - 1/4*m**2 + 1/24*m**4 - 12*m. Factor l(d).
(d - 1)*(d + 1)/2
Let b = 1365 + -2729/2. What is s in 0*s - b*s**2 + 1/2 = 0?
-1, 1
Let b = -41 - -50. Suppose 3 + b - n**2 + 10*n - 5*n**2 + 4*n**2 = 0. Calculate n.
-1, 6
Factor 8483*x**2 - 295 + 216*x - 2621 - 8487*x**2.
-4*(x - 27)**2
Let f = 2/1075 + 213/1075. Suppose 3*l + 2*d = -2, -4*l + 2*d - 1 = -3. Factor f*w**5 + l*w**4 + 0 - 2/5*w**3 + 0*w**2 + 1/5*w.
w*(w - 1)**2*(w + 1)**2/5
Let b = 164/19 + -24581/2850. Let g(j) be the third derivative of 0 + 6*j**2 + 0*j**4 - 1/300*j**6 + 0*j**3 + 0*j - b*j**5. Factor g(y).
-2*y**2*(y + 1)/5
Suppose 0 + 2/7*t**5 + 162/7*t**3 + 0*t**2 + 0*t + 36/7*t**4 = 0. Calculate t.
-9, 0
Let z be ((-2)/(-30))/(4/25)*1280/48. Factor 4/9*u**3 + z*u - 40/9*u**2 + 0.
4*u*(u - 5)**2/9
Let s = -3613 + 3617. Factor 35/2*z**3 + 5/2*z**5 + 0 - 15/2*z**2 - 25/2*z**s + 0*z.
5*z**2*(z - 3)*(z - 1)**2/2
Let l(h) be the first derivative of 13 - 3*h**2 - 1/4*h**3 - 12*h. Find o, given that l(o) = 0