3 - 31*r**4 = 0. Calculate r.
-2, -1, -2/7, 0, 2
Let d(y) be the third derivative of 5*y**8/336 + 5*y**7/42 + 3*y**6/8 + 7*y**5/12 + 5*y**4/12 - 6*y**2. Factor d(a).
5*a*(a + 1)**3*(a + 2)
Let d(j) be the first derivative of j**4/42 - j**3/21 + j - 5. Let x(h) be the first derivative of d(h). Factor x(c).
2*c*(c - 1)/7
Let p(z) be the third derivative of 0 + 1/28*z**6 + 1/784*z**8 + 11*z**2 - 1/98*z**7 - 1/14*z**5 - 1/14*z**3 + 0*z + 5/56*z**4. Determine w so that p(w) = 0.
1
Let f(c) = -c**2 - 15*c - 18. Let g be f(-13). Determine w so that -18 + 17 - 7 - 2*w**2 + 0*w - g*w = 0.
-2
Let z be 23 - (-5)/(350/(-1554)). Factor 4/5*y**2 + 4/5*y - z - 4/5*y**3.
-4*(y - 1)**2*(y + 1)/5
Solve q + 1/2*q**2 - 1/2*q**4 + 0 - q**3 = 0 for q.
-2, -1, 0, 1
Let g(j) be the third derivative of j**5/45 + 11*j**4/18 + 16*j**3/3 - 3*j**2 + 3*j. Factor g(t).
4*(t + 3)*(t + 8)/3
Suppose 0*m - 12/7*m**4 - 2/7*m**5 + 0 + 0*m**2 - 18/7*m**3 = 0. Calculate m.
-3, 0
Let u(l) be the first derivative of -l**6/540 + 2*l**5/135 - l**4/27 - 4*l**2 + 6. Let k(p) be the second derivative of u(p). Suppose k(y) = 0. Calculate y.
0, 2
Let m(k) be the second derivative of -k**4/48 + 4*k**3 - 288*k**2 - 2*k - 49. Factor m(f).
-(f - 48)**2/4
Let m(u) be the second derivative of -u**6/30 + 9*u**5/50 - 19*u**4/60 + u**3/5 - 18*u. Let m(t) = 0. What is t?
0, 3/5, 1, 2
Let k(q) = -6*q**2 + 3*q - 5. Suppose -2*j - 30 = -j - 5*s, 4*j + s + 36 = 0. Let f(n) = -n**2 + n - 1. Let c(o) = j*f(o) + 2*k(o). Factor c(z).
-2*z*(z + 2)
Let u(d) be the first derivative of 2*d**3/3 - 2*d**2 - 6*d - 191. Factor u(k).
2*(k - 3)*(k + 1)
Let r(z) be the second derivative of -1/16*z**2 - 5/48*z**3 - 1/16*z**5 - 3*z + 0 - 1/336*z**7 - 1/48*z**6 - 5/48*z**4. Factor r(p).
-(p + 1)**5/8
Suppose -20*j + 31*j - 22 = 0. Solve 4 - 4*x + x - j*x**2 + x = 0.
-2, 1
Let v(s) = 2*s**3 + 2*s**2 + s - 1. Let k(x) = 289*x**4 + 791*x**3 + 370*x**2 - 128*x + 12. Let m(z) = -k(z) - 4*v(z). Factor m(d).
-(d + 1)*(d + 2)*(17*d - 2)**2
Let -1/4*m**3 - 3/4*m + m**2 + 0 = 0. Calculate m.
0, 1, 3
Let -393354/11*z**3 + 48/11 - 2936/11*z - 137842/11*z**4 + 5412*z**2 = 0. Calculate z.
-3, 2/41
Let b(s) = -s**5 + s**3 + s. Let f(w) = 4*w**5 + w**4 - 16*w**3 - w**2 + 45*w - 36. Let u(h) = -3*b(h) - f(h). Factor u(i).
-(i - 2)**2*(i - 1)*(i + 3)**2
Let p(y) be the second derivative of y**5/100 + 2*y**4/15 + 8*y**3/15 + 80*y. Determine t, given that p(t) = 0.
-4, 0
Let t be 6/(4/4)*(12 - 184/16). Factor 2/5*i**t + 2/15*i**5 + 2/15*i**2 + 0 + 2/5*i**4 + 0*i.
2*i**2*(i + 1)**3/15
Let m be (-2)/(-1) + 6/2. Suppose 6*p = 31 - 7. Factor -m*c**2 + 2*c**3 - p*c**2 + 8*c + c**2.
2*c*(c - 2)**2
Suppose -36*p + 22*p = 140. Let r be (45/p - -5)/1. Factor 1/4*k**3 - 1/2*k**2 - 1/4*k + r.
(k - 2)*(k - 1)*(k + 1)/4
Let m be (-4 + 1)*1 - -22. Let x = m - 15. Determine n, given that 24 + 5*n**3 + 18*n**2 + x*n**3 + 36*n - 6*n**3 = 0.
-2
Let k(l) = l**3 + 2*l**2 + 3*l + 6. Suppose 5*m = 3*r + 45, -m + r = -2*m + 1. Let o(y) = -2*y + 3*y - 2*y - 1. Let s(j) = m*o(j) + k(j). Factor s(h).
h*(h - 1)*(h + 3)
Suppose -3*y = -9*y + 18. Factor 18 - 6 + 100*s + 311*s**2 + 196*s**y - 52*s**2.
(4*s + 3)*(7*s + 2)**2
Let t(s) be the first derivative of 3/7*s + 3/35*s**5 - 12 - 3/7*s**4 - 6/7*s**2 + 6/7*s**3. Factor t(m).
3*(m - 1)**4/7
Let q(g) be the first derivative of 99*g**2/2 - 5*g - 3. Let p be q(2). Factor 17 + 51 - 192*r - p - 48*r**2 - 131 - 4*r**3.
-4*(r + 4)**3
Factor -1244/11*a**2 - 2/11*a**4 + 2808/11*a - 1458/11 - 104/11*a**3.
-2*(a - 1)**2*(a + 27)**2/11
Let b(w) be the first derivative of -1/45*w**6 + 3 - 4/75*w**5 + 0*w**4 + 0*w + 4/45*w**3 + 1/15*w**2. Factor b(n).
-2*n*(n - 1)*(n + 1)**3/15
Solve 38*v + 1/2*v**3 - 15*v**2 - 28 + 1/2*v**4 = 0.
-7, 2
Let k be (-990)/2541*((-336)/(-18))/(-8). Factor 1/11*v + 0 + 25/11*v**3 + k*v**2.
v*(5*v + 1)**2/11
Let i(y) be the second derivative of 1/15*y**5 - 1/90*y**6 - 1/6*y**2 - 12*y + 2/9*y**3 - 1/6*y**4 + 0. Factor i(c).
-(c - 1)**4/3
Suppose 0*q - 18*q = -11 + 11. What is z in 1/4*z**2 + 0 + 1/4*z**3 + q*z = 0?
-1, 0
Let y(f) be the second derivative of f**4/3 - 10*f**3 - 32*f**2 + 524*f. Find v, given that y(v) = 0.
-1, 16
Let v(c) be the third derivative of c**6/160 - c**5/16 - 13*c**4/32 - 7*c**3/8 - 73*c**2 + c. Factor v(i).
3*(i - 7)*(i + 1)**2/4
Solve -9/5*s**2 - 27/5*s**3 + 12/5 + 24/5*s = 0.
-2/3, 1
Let t be (-16)/(4/(-1)) - -16. Find c such that 12*c + 68*c + 0 + 45*c**2 + 0*c - t = 0.
-2, 2/9
Factor -4/5 + 4/5*n**2 - 2/5*n**3 + 2/5*n.
-2*(n - 2)*(n - 1)*(n + 1)/5
Let p(y) = -2*y**2 - 35*y + 15. Let f(v) = 2*v**2 + 35*v - 16. Let l(x) = 3*f(x) + 2*p(x). Factor l(m).
(m + 18)*(2*m - 1)
Let y = -1209450/7 - -173067. Let z = y + -288. Factor 0 - z*a - 9/7*a**2 - 9/7*a**3 - 3/7*a**4.
-3*a*(a + 1)**3/7
Let f(x) be the second derivative of x**5/160 + x**4/16 + x**3/6 + 18*x - 3. Suppose f(g) = 0. What is g?
-4, -2, 0
Suppose -29*s = -28*s - 2. Factor 64/11*j - 194/11*j**s + 278/11*j**3 - 8/11 - 190/11*j**4 + 50/11*j**5.
2*(j - 1)**3*(5*j - 2)**2/11
Let u be (9 - 15)/(36/(-24)). Factor 3/2*h + 3/2*h**u - 3/2*h**3 + 0 - 3/2*h**2.
3*h*(h - 1)**2*(h + 1)/2
Let n(z) = z**3 - 6*z + 9. Let g be n(-3). Let c(q) be the first derivative of 4/15*q**3 + 4 + 1/10*q**4 + 1/5*q**2 + g*q. Determine l so that c(l) = 0.
-1, 0
Determine l so that 32 - 50*l**2 - 48*l**2 - 7*l + 97*l**2 - 7*l = 0.
-16, 2
Suppose 3*y = 5*n - 20, 4*y + 82*n = 83*n + 13. Let -1/3*d**y - 25/3*d**2 - 19/3*d**3 - 4/3 - 16/3*d - 7/3*d**4 = 0. Calculate d.
-2, -1
Let n(o) = -42*o - 23. Let p be n(-7). Factor 8*r + 5*r**2 + 263 - 2*r**3 - 3*r**2 - p.
-2*(r - 2)*(r - 1)*(r + 2)
Suppose -2*m = 3*r - 24, -3*r - 3*m = -5*r + 16. Let j(k) be the first derivative of 4*k**3 + 0*k**2 - 7*k**4 + 0*k + 4*k**5 - r - 2/3*k**6. Factor j(y).
-4*y**2*(y - 3)*(y - 1)**2
Let t(l) be the first derivative of l**7/42 + l**6/24 + 3*l**2 - 8. Let a(b) be the second derivative of t(b). Factor a(k).
5*k**3*(k + 1)
Let u(x) = x**3 + 7*x**2 + 4*x. Let b(n) = 2*n**3 + 15*n**2 + 8*n. Let m(c) = -2*b(c) + 5*u(c). Factor m(p).
p*(p + 1)*(p + 4)
Factor 3/2*y**4 - 11/4*y**3 - 2 + 3*y + 1/2*y**2 - 1/4*y**5.
-(y - 2)**3*(y - 1)*(y + 1)/4
Let n(j) be the first derivative of j**6/144 - 8*j**3/3 + 12. Let d(g) be the third derivative of n(g). Suppose d(m) = 0. What is m?
0
Factor 233*c**3 - 4*c**5 - 80*c**4 - 5740*c**2 + 5272*c**2 + 4*c**4 - 581*c**3.
-4*c**2*(c + 3)**2*(c + 13)
Let q = 403/118 - 3391/1062. Determine y so that 4/9*y + 0 + q*y**2 = 0.
-2, 0
Let r be 3/(-9) + (-3)/(-9). Suppose r = 7*d - 4*d - 6. Factor -d*l + 2*l + 0*l - 2*l**2.
-2*l**2
Let r(j) be the first derivative of j**5/15 - 11*j**4/4 + 32*j**3/9 - 131. Find m such that r(m) = 0.
0, 1, 32
Let h = -1151 - -3454/3. Solve -h*g**2 - 1/3*g**3 + 1/6*g**5 + 1/6*g**4 + 1/6*g + 1/6 = 0 for g.
-1, 1
Let g(i) be the second derivative of i**6/90 + 2*i**5/15 + i**4/18 - 40*i**3/9 - 25*i**2/2 + 152*i. Factor g(u).
(u - 3)*(u + 1)*(u + 5)**2/3
Suppose -t - 2*t = 0. Let g be 33/((-1980)/(-200))*(-6)/(-5). Factor 0*o + t*o**2 + 0 - 1/7*o**5 + 2/7*o**g - 1/7*o**3.
-o**3*(o - 1)**2/7
Let -4/5*r**5 - 12988/5*r**3 - 92*r**4 + 13916/5*r**2 + 12992/5*r - 13456/5 = 0. What is r?
-58, -1, 1
Determine f, given that -212 - 12*f**2 + 212 - 12*f**3 - 3*f = 0.
-1/2, 0
Suppose 10 = 8*b - 46. Let u(x) be the second derivative of 0 - 9/32*x**4 + 0*x**2 - 1/8*x**3 - 21/160*x**5 + b*x. Determine z, given that u(z) = 0.
-1, -2/7, 0
Let x(v) be the second derivative of -64*v**4/3 - 160*v**3 - 450*v**2 + 94*v. Factor x(m).
-4*(8*m + 15)**2
Let b = -1 + -30. Let o = -31 - b. Factor 2/7*s + o + 2/7*s**2.
2*s*(s + 1)/7
Let t(j) be the first derivative of -8/7*j**3 + 4/7*j**2 + 13/14*j**4 + 1/21*j**6 + 7 - 12/35*j**5 + 0*j. Solve t(o) = 0 for o.
0, 1, 2
Let z(h) = -8*h**2 - 13*h + 15. Let c(y) = -1 - 10 - 8 + 4 + 14*y + 9*y**2. Let x(i) = 3*c(i) + 4*z(i). Factor x(a).
-5*(a - 1)*(a + 3)
Let v(l) be the second derivative of 0 - 7/20*l**5 - 13/12*l**4 + 1/30*l**6 + 1/42*l**7 - l**3 + 0*l**2 - 35*l. Factor v(j).
j*(j - 3)*(j + 1)**2*(j + 2)
Let l(r) be the second derivative of r**4/30 + 22*r**3/3 - 111*r**2/5 + 561*r. Suppose l(v) = 0. What is v?
-111, 1
Let a(s) be the first derivative of 0*s - 7 - 3/8*s**2 - 1/4*s**3. Factor a(p).
-3*p*(p + 1)/4
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