**4 - 16/5*j**2 + 2*j**3.
-2*j*(j - 2)**2*(j - 1)/5
Let h(a) be the first derivative of a**6/120 + a**5/180 - 35*a**2/2 + 3. Let p(b) be the second derivative of h(b). Determine y so that p(y) = 0.
-1/3, 0
Let o(a) be the first derivative of 10 + 7/2*a**2 - 1/3*a**3 + 0*a. Let o(w) = 0. What is w?
0, 7
Factor 8/7*f**3 + 0 + 2/7*f**5 + 384/7*f**2 + 512/7*f - 24/7*f**4.
2*f*(f - 8)**2*(f + 2)**2/7
Let b(d) be the third derivative of 0*d + 0*d**4 + 0*d**3 - 1/480*d**6 + 0*d**5 - 1/840*d**7 + 0 + 13*d**2. Factor b(m).
-m**3*(m + 1)/4
Let a(t) = -t**3 + 5*t**2 - t. Let w be a(5). Let m be (0 + 2/w)/((-27)/15). Factor -2/9*h**5 + 2/9*h**2 + 0 + 2/9*h**3 - m*h**4 + 0*h.
-2*h**2*(h - 1)*(h + 1)**2/9
Suppose 3*k + 5*k = 0. Let b be (-45)/(-12) - (-2)/8. Solve k + 1/3*u**b - 1/3*u**2 + 1/3*u**3 - 1/3*u = 0.
-1, 0, 1
Let n(u) be the third derivative of 0*u**4 + 1/2100*u**7 + 1/400*u**6 - 11*u**2 + 0*u**3 + 0 + 0*u + 1/300*u**5. Factor n(h).
h**2*(h + 1)*(h + 2)/10
Let s = -180701/15 + 12047. Suppose s*n**2 + 0*n + 0 + 2/5*n**4 - 2/3*n**3 = 0. Calculate n.
0, 2/3, 1
Suppose 3*z + o - 36 = 4*o, -5*o = z - 30. Let s = -3 + z. Factor 84*v**3 - 171*v**4 - s*v**2 + 50*v**4 - 26*v**4.
-3*v**2*(7*v - 2)**2
Suppose 3*i + 3*f + 3 = 0, -3*i - 1 = -8*f + 9*f. Determine q, given that 2/3*q**3 + 2/3*q**4 - 2/3*q**2 + i - 2/3*q = 0.
-1, 0, 1
Let z(b) be the third derivative of -13*b**2 + 1/15*b**4 + 0*b - 1/75*b**5 + 0 - 2/15*b**3. Factor z(y).
-4*(y - 1)**2/5
Let u(y) be the third derivative of -5*y**9/1512 - y**8/1120 + y**7/840 + 5*y**3 - 26*y**2. Let w(q) be the first derivative of u(q). Factor w(k).
-k**3*(4*k - 1)*(5*k + 2)/2
Let w(i) = i**3 - i**2 + 1. Suppose -3*y = -2*y - 1. Let x(h) = h**4 - 2*h**3 + 3*h**2 - 3. Let p(o) = y*x(o) + 3*w(o). Solve p(k) = 0 for k.
-1, 0
Let r(z) = -z**2 - 1. Let w(n) = 11*n**2 + 5*n - 4. Let i(y) = -6*r(y) - w(y). Determine b, given that i(b) = 0.
-2, 1
Let j be ((0 - -14)/(-2))/1 + 9. Factor 4/15 + 2/15*k - 2/15*k**j.
-2*(k - 2)*(k + 1)/15
Suppose -4*u - 6 - 34 = 0. Let a be 4/u*180/(-42). Factor 18/7 + 2/7*z**2 + a*z.
2*(z + 3)**2/7
Let c be (-20)/(-14) + ((-84)/(-392))/((-72)/32). Factor 1/9*j**2 + c*j - 13/9.
(j - 1)*(j + 13)/9
Let a be (-56)/(-10) - (-17)/(-17)*4. Let y(k) be the first derivative of 2 + 6/5*k**2 + 3/4*k**4 + a*k**3 + 3/25*k**5 + 0*k. Factor y(c).
3*c*(c + 1)*(c + 2)**2/5
Let j(y) be the third derivative of -y**5/210 + 61*y**4/42 - 121*y**3/21 + 47*y**2 - 3*y. Factor j(v).
-2*(v - 121)*(v - 1)/7
Let v(y) be the third derivative of -y**8/1344 - y**7/280 + 7*y**6/480 + 7*y**5/240 - 3*y**4/16 + y**3/3 - 38*y**2. Find z such that v(z) = 0.
-4, -2, 1
Let d(i) be the third derivative of -7/240*i**6 + 1/105*i**7 + 12*i**2 - 7/60*i**5 + 0*i - 1/16*i**4 + 0*i**3 + 0. Solve d(q) = 0.
-1, -1/4, 0, 3
Let c(k) be the third derivative of k**6/30 + 2*k**5/5 + 2*k**4 + 16*k**3/3 - 172*k**2. Factor c(g).
4*(g + 2)**3
Let b(f) = -13*f**3 - 8*f**2 - f + 6. Let v(c) = 2*c**3 + c**2 - 1. Let g(k) = -b(k) - 6*v(k). Determine s, given that g(s) = 0.
-1, 0
Let d(w) be the first derivative of w**4/4 + 9*w**3/2 + 12*w**2 - 15*w - 21. Let h(s) be the first derivative of d(s). Solve h(b) = 0.
-8, -1
Let x(h) = -h**3 + h**2 + 4. Let c be x(3). Let l = 16 + c. Factor 1/3*p**l + 1/3*p + 0.
p*(p + 1)/3
Let q(h) be the first derivative of 3/10*h**2 + 3*h + 11 + 0*h**3 - 1/20*h**4. Let i(b) be the first derivative of q(b). Factor i(x).
-3*(x - 1)*(x + 1)/5
Factor c**3 + 4*c**3 - 45*c**2 - 10*c - 32*c + 132*c.
5*c*(c - 6)*(c - 3)
Suppose -36*b**4 - 306*b**5 + 96*b**3 - 77*b**2 + 13*b**2 + 310*b**5 = 0. Calculate b.
0, 1, 4
Let r be 2 + 1 + (-2 - 1). Suppose r*d - 2 = -d. Find q, given that -q**2 - 4*q**3 + 7*q**d - 16*q**4 - 6*q**2 - 7*q**5 = 0.
-2, -2/7, 0
Let y(d) be the second derivative of d**4 - 7*d + 7/10*d**5 - 32*d**2 + 1/15*d**6 - 32/3*d**3 + 1. Suppose y(u) = 0. Calculate u.
-4, -1, 2
Let j(h) = 5*h**2 - 7*h - 4. Let m(y) = -16 - 21*y + 8*y**2 + 5 + 7*y**2. Let l(p) = 17*j(p) - 6*m(p). Let l(f) = 0. What is f?
2/5, 1
Solve 26/9*p**4 + 0 + 10/3*p**5 + 0*p + 8/9*p**2 - 64/9*p**3 = 0 for p.
-2, 0, 2/15, 1
Let u(w) = 2*w**3 + 5*w**2 + 5*w - 3. Let n(v) = 2*v + 22. Let s be n(-9). Let h(g) = -2*g**3 - 4*g**2 - 4*g + 4. Let t(o) = s*u(o) + 3*h(o). Factor t(i).
2*i*(i + 2)**2
Let w(o) = o**3 - o**2 - o + 4. Let t(p) = -4*p**3 + 9*p**2 + 3*p - 12. Let r(q) = -t(q) - 3*w(q). Suppose r(i) = 0. Calculate i.
0, 6
Suppose 8/5*b**3 + 0 + 4/5*b + 2*b**2 + 2/5*b**4 = 0. What is b?
-2, -1, 0
Let r = -6 - -2. Let t be (-8)/(-6) + -2*r/12. Factor 0*j + 0 - 1/2*j**t.
-j**2/2
Let s(b) be the second derivative of 0 - 29*b + 0*b**2 - 1/30*b**6 - 1/105*b**7 + 0*b**4 - 1/50*b**5 + 0*b**3. Let s(r) = 0. What is r?
-2, -1/2, 0
Suppose -l - 4*o - 3 = 3, 18 = 5*l - 4*o. Let j = 46 - 41. Factor 4*p**l + 19*p**j - 4*p**4 + 4*p**3 + 0*p**4 - 23*p**5.
-4*p**2*(p - 1)*(p + 1)**2
Let q(f) = 3*f**3 - 126*f**2 - 299*f. Let a(m) = 4*m**3 - 188*m**2 - 448*m. Let z(p) = 5*a(p) - 8*q(p). Factor z(u).
-4*u*(u - 19)*(u + 2)
Factor 2*f**3 - 202*f + 3*f**3 - 10*f**2 + 21*f - 134*f.
5*f*(f - 9)*(f + 7)
Suppose 0 = -9*f + 18. Factor 21*s**2 - 25*s**f + 26*s + 34*s**2 + 8 + 2*s**4 + 14*s**3.
2*(s + 1)**3*(s + 4)
Let r(v) be the first derivative of v**5/30 - v**4/6 - v**3/3 + v**2/3 + 5*v/6 - 77. Suppose r(j) = 0. Calculate j.
-1, 1, 5
Suppose 3*w - 16 = x, 0 = -2*x - 175*w + 180*w - 26. Suppose -68/5*n - 6/5*n**x - 22/5 = 0. What is n?
-11, -1/3
Let i = -358/3 + 719/6. Factor i*g**2 - 2 + 3/2*g.
(g - 1)*(g + 4)/2
Let h(b) be the first derivative of -2*b**3/27 - 4*b**2/9 - 8*b/9 - 291. Let h(k) = 0. Calculate k.
-2
Suppose -13/4*f**4 - f**5 + 0*f - 1/2*f**2 - 11/4*f**3 + 0 = 0. What is f?
-2, -1, -1/4, 0
Let q(d) = -2*d**2 + 11*d - 3. Let t(x) = 6*x**2 - 32*x + 8. Let u be (-2)/(-6) - (-136)/51. Let r(p) = u*t(p) + 8*q(p). Determine n so that r(n) = 0.
0, 4
Factor -3/8*c**2 - 3/8*c**3 + 9/4*c + 0.
-3*c*(c - 2)*(c + 3)/8
What is s in s - 4/5*s**3 - 22/5*s**2 - 1/5*s**5 + 8/5*s**4 + 14/5 = 0?
-1, 1, 2, 7
Suppose 119471 + 116*o + 2*o**2 - 119471 = 0. What is o?
-58, 0
Let x be (-50)/(-84) + (-6)/(-70)*-5. Let m(h) be the second derivative of -x*h**4 + 2*h**3 - 9*h**2 + 0 + 2*h. Factor m(g).
-2*(g - 3)**2
Let c(r) be the second derivative of 0 - 3/28*r**4 + 13*r + 1/140*r**5 + 11/42*r**3 + 1/210*r**6 - 2/7*r**2. Factor c(u).
(u - 1)**3*(u + 4)/7
Let 3 + 8/3*v - 1/3*v**2 = 0. What is v?
-1, 9
Let n(f) be the first derivative of -4/3*f**3 + 4/5*f**5 + 0*f**2 + 0*f + 14 + 2/3*f**6 - f**4. Suppose n(i) = 0. What is i?
-1, 0, 1
Let b(p) be the second derivative of -15*p**7/14 - 46*p**6/3 - 335*p**5/4 - 650*p**4/3 - 790*p**3/3 - 120*p**2 - 32*p + 5. Let b(o) = 0. What is o?
-4, -3, -2, -1, -2/9
Let v(m) be the third derivative of -m**10/50400 - m**9/6720 + m**8/1680 - 17*m**5/20 - 8*m**2. Let g(f) be the third derivative of v(f). Factor g(t).
-3*t**2*(t - 1)*(t + 4)
Let z = 1463/5 + -292. Let v(u) be the first derivative of 0*u - u**2 - u**3 - 6 + 1/4*u**4 + z*u**5 + 1/6*u**6. Factor v(i).
i*(i - 1)*(i + 1)**2*(i + 2)
Let h(a) be the second derivative of 3*a**5/4 + 95*a**4/6 - 65*a**3/6 - 7*a - 16. Factor h(u).
5*u*(u + 13)*(3*u - 1)
Suppose -9*k**2 - 12*k**4 - k**2 + 7*k**4 - 15*k**3 = 0. Calculate k.
-2, -1, 0
Find j, given that 42*j**3 + 72*j**4 + 114*j**4 - 240*j**2 + 416*j - 188*j**4 = 0.
0, 4, 13
Let c(r) be the second derivative of r**5/72 - r**4/12 + r**3/9 - 9*r**2/2 - 11*r. Let x(v) be the first derivative of c(v). Solve x(w) = 0 for w.
2/5, 2
Let r(b) be the first derivative of b**6/10 - b**4/4 + 15*b + 2. Let h(z) be the first derivative of r(z). Factor h(n).
3*n**2*(n - 1)*(n + 1)
Let s(c) be the first derivative of 0*c**2 - 12 + 1/24*c**4 - 1/9*c**3 + 0*c. Factor s(y).
y**2*(y - 2)/6
Let z be 28/7 + 477/(-195). Let c = z + 3/65. Let 14/5*a - 6/5*a**2 - c = 0. Calculate a.
1, 4/3
Factor -31*v**2 - 12 - 15*v - 6 + 34*v**2.
3*(v - 6)*(v + 1)
Let n(t) be the second derivative of t**5/60 + 5*t**4/36 + t**3/6 - 3*t**2/2 - 536*t. Factor n(s).
(s - 1)*(s + 3)**2/3
Factor 198/13*j - 194/13*j**2 - 4/13.
-2*(j - 1)*(97*j - 2)/13
Suppose -2*u + 2*w + 2*w + 22 = 0, 0 = -u - 3*w - 9. Suppose -3*h = -0*h - 138. Factor 49*y**2 + 6*y**3 - u*y - h*y**2 - 3*y**4 - 3*y.
-3*y*(y - 2)*(y - 1)*