0 + 1/8*a**4 + a**2. Factor x(n).
-(n - 2)*(n - 1)
Let q(v) be the third derivative of -3*v**7/35 + 7*v**6/20 - 8*v**5/15 + v**4/3 + 2*v**2 - 2. Factor q(f).
-2*f*(f - 1)*(3*f - 2)**2
Let g = 732 + -730. Solve 0 - 1/4*m**4 + 0*m + 1/4*m**5 + 1/4*m**g - 1/4*m**3 = 0 for m.
-1, 0, 1
Factor 1/2*y**2 - 3/2 + y.
(y - 1)*(y + 3)/2
Let b(u) be the third derivative of 0 + 4/15*u**5 + 0*u**3 + 8*u**2 + 1/6*u**4 + 0*u. Factor b(q).
4*q*(4*q + 1)
Let u(c) be the first derivative of c**6/540 + c**5/45 + c**4/12 - 2*c**3/3 - 1. Let l(o) be the third derivative of u(o). Factor l(p).
2*(p + 1)*(p + 3)/3
Let f(g) = -g**3 + 7*g**2 - 2*g + 8. Let w be f(6). Let x be 2/5 - w/(-20). Factor -3/4*k**x + 0*k - 1/2*k**3 + 1/4.
-(k + 1)**2*(2*k - 1)/4
Let h(m) be the first derivative of 0*m**2 + 0*m**3 + 1/2*m**6 + 0*m**4 - 1 + 0*m**5 + 0*m. Let h(i) = 0. Calculate i.
0
Let g = -9/28 + 73/140. Find r such that 0 + 1/5*r**3 + 0*r**4 + 0*r - g*r**5 + 0*r**2 = 0.
-1, 0, 1
Let s(f) be the second derivative of f**5/120 + f**4/48 - f**2 + 6*f. Let r(b) be the first derivative of s(b). Find l such that r(l) = 0.
-1, 0
Let n(x) be the third derivative of -x**6/340 - x**5/102 - x**4/102 - 7*x**2. Factor n(q).
-2*q*(q + 1)*(3*q + 2)/17
Let r(j) be the second derivative of j**5/110 - 2*j**4/33 + j**3/11 + 25*j. Factor r(l).
2*l*(l - 3)*(l - 1)/11
Let j(t) be the first derivative of -3/2*t**2 - 1/8*t**4 - 1/30*t**5 + 0*t - 3 - 1/6*t**3. Let c(i) be the second derivative of j(i). Factor c(n).
-(n + 1)*(2*n + 1)
Suppose 2*q - 2 = -0*q. Let c(l) = -1. Let b(x) = x**2 - x + 2. Let u(j) = q*b(j) + 4*c(j). Factor u(r).
(r - 2)*(r + 1)
Let m(k) = 20*k**4 - 6*k**3 - 26*k**2 - 14*k - 14. Let p(z) = -7*z**4 + 2*z**3 + 9*z**2 + 5*z + 5. Let f(x) = 5*m(x) + 14*p(x). Factor f(g).
2*g**2*(g - 2)*(g + 1)
Let c(h) be the first derivative of -3/2*h**2 + 3/16*h**4 + 0*h**3 - 2 - 3/80*h**5 - 2*h. Let n(m) be the first derivative of c(m). Solve n(a) = 0 for a.
-1, 2
Let q be (-90)/54*(-6)/5. Let y**q + 2/5*y + 1/5*y**4 + 4/5*y**3 + 0 = 0. Calculate y.
-2, -1, 0
Let k(w) be the third derivative of w**5/20 - 2*w**3 + w**2. Suppose k(d) = 0. Calculate d.
-2, 2
Let m(i) be the first derivative of -i**3/15 - i**2/5 - i/5 - 6. Factor m(b).
-(b + 1)**2/5
Factor -4 + 4*a**4 - 8*a**3 + 17*a**5 + 8*a**4 - 8*a**2 + 20*a**5 - 41*a**5 + 12*a.
-4*(a - 1)**4*(a + 1)
Let v(p) be the first derivative of p**5/10 - p**4/8 - p**3/2 + p**2/4 + p - 3. Determine c so that v(c) = 0.
-1, 1, 2
Let u(y) be the first derivative of y**5/60 + y**4/12 + y**3/9 - y - 3. Let r(j) be the first derivative of u(j). Let r(n) = 0. Calculate n.
-2, -1, 0
Factor -5*p**3 + 11*p - 57*p**2 + 10 + 72*p**2 + 14*p - 5*p**4.
-5*(p - 2)*(p + 1)**3
Let p(f) = -f**2 - 6*f + 1. Let d(r) be the second derivative of r**3/6 - r**2/2 - r. Let t(i) = -6*d(i) - 2*p(i). Suppose t(h) = 0. Calculate h.
-2, -1
Let l(a) be the second derivative of a**6/480 + a**5/240 - a**2 - 3*a. Let j(c) be the first derivative of l(c). Factor j(d).
d**2*(d + 1)/4
Factor 6*l**3 + 16 - 6*l**2 - 8 - 4*l**3.
2*(l - 2)**2*(l + 1)
Let p(o) be the second derivative of -o**4/12 + o**3/3 - o**2/2 + 9*o. Factor p(s).
-(s - 1)**2
Let -4/3 + 77/3*l**4 - 32/3*l - 17/3*l**3 + 49/3*l**5 - 73/3*l**2 = 0. What is l?
-1, -2/7, 1
Factor 4/7*u**3 - 2/7*u**4 + 0 + 6/7*u**2 + 0*u.
-2*u**2*(u - 3)*(u + 1)/7
Suppose -p + 2*p = 3. Factor -6*q**3 + 6*q - 2*q**4 + 3 - p + 4 + 0*q - 2*q**2.
-2*(q - 1)*(q + 1)**2*(q + 2)
Let o = 813/2045 + 1/409. Factor 0*g + o - 4/5*g**3 - 6/5*g**2.
-2*(g + 1)**2*(2*g - 1)/5
Let m(c) be the first derivative of c**4/6 + 8*c**3/9 + 5*c**2/3 + 4*c/3 - 7. Factor m(a).
2*(a + 1)**2*(a + 2)/3
Suppose -25/7*y**3 - 20/7*y**2 + 0 - 4/7*y = 0. What is y?
-2/5, 0
Let d(w) be the third derivative of -w**6/300 - w**5/150 + w**4/30 - 17*w**2. Factor d(a).
-2*a*(a - 1)*(a + 2)/5
Let w be -4 + 8 + (-2 + 0 - 2). Factor 3/2*v**2 + w + 1/2*v.
v*(3*v + 1)/2
Let i(o) be the first derivative of -2*o**5/9 + 17*o**4/18 - 14*o**3/9 + 11*o**2/9 - 4*o/9 - 14. Determine w so that i(w) = 0.
2/5, 1
Let j(f) be the first derivative of 1/200*f**6 + 0*f + 1/10*f**4 + 1/25*f**5 - f**2 + 0*f**3 + 1. Let c(w) be the second derivative of j(w). Factor c(l).
3*l*(l + 2)**2/5
Let d(s) be the second derivative of 0 + 2*s**2 - 1/3*s**3 - 1/6*s**4 + 3*s. Let d(j) = 0. What is j?
-2, 1
Let q(r) = r**4 - 4*r**3 - r**2 + 2*r + 2. Let y(k) = -3*k**4 + 9*k**3 + 2*k**2 - 5*k - 5. Let b(c) = -15*q(c) - 6*y(c). Factor b(m).
3*m**2*(m + 1)**2
Let x(j) = j**3 + 4*j**2 - 2*j - 4. Let v be x(-4). Suppose v*c - c = 6. Suppose 0*t + 1/4 - 1/4*t**c = 0. Calculate t.
-1, 1
Let b(y) be the first derivative of -y**2/2 - 3*y - 1. Let p be b(-5). Factor 2*i**2 + p*i - 3*i**2 - i.
-i*(i - 1)
Factor 96*o - 196*o**3 + 840*o**2 - 400*o + 207*o**4 + 32 - 885*o**4 - 694*o**4.
-4*(o + 1)*(7*o - 2)**3
Let k = 9 - 6. Factor 4*t**k - t**5 - 4*t**3 + 3*t**3 - 2*t**5.
-3*t**3*(t - 1)*(t + 1)
Let x = 744 + -744. Factor 0 - 1/6*s + x*s**2 + 2/3*s**3.
s*(2*s - 1)*(2*s + 1)/6
Let n(h) = -h - 5. Let x be n(-7). Let t be ((-3)/x)/(6 + -9). Factor 0 + 2*a**4 + 2*a**2 + t*a**5 + 3*a**3 + 1/2*a.
a*(a + 1)**4/2
Suppose -5*o + 15 = 5. Solve -u - 2*u**2 - o*u + u = 0 for u.
-1, 0
Let r = 20 - 36. Let t be 4/r - (-2)/4. Find c such that 0*c**2 + 0 - t*c**3 + 1/4*c**5 + 0*c**4 + 0*c = 0.
-1, 0, 1
Let l(z) be the first derivative of z**8/56 + z**7/21 + z**6/30 - z**2 + 1. Let a(u) be the second derivative of l(u). Let a(r) = 0. What is r?
-1, -2/3, 0
Let i = 191/3 - 63. Let c = -8 - -26/3. Solve c*t**2 - i*t + 2/3*t**3 - 2/3 = 0 for t.
-1, 1
Factor 8/7 + 8/7*t + 2/7*t**2.
2*(t + 2)**2/7
Let g(c) be the third derivative of c**6/480 + c**5/80 + c**4/32 + c**3/24 - 5*c**2. Let g(o) = 0. Calculate o.
-1
Factor -24/7 + 40/7*z - 6/7*z**2.
-2*(z - 6)*(3*z - 2)/7
Let d(c) be the first derivative of c**7/21 + 2*c**6/15 - c**4/3 - c**3/3 - 5*c - 4. Let t(x) be the first derivative of d(x). Let t(s) = 0. What is s?
-1, 0, 1
Suppose 5*j - 9*j = -212. Suppose 0 = 4*c + 45 - j. Solve -1/5*y**4 - 4/5*y + 3/5*y**c - 4/5 + 2/5*y**3 = 0.
-1, 2
Let k(r) be the first derivative of -r**6/180 + 2*r**3/3 + 2. Let n(b) be the third derivative of k(b). Determine u so that n(u) = 0.
0
Let i be -2*(6/(-20) - 0). Let b be (-246)/240*-2 - (-1)/(-4). Determine d, given that -2*d**2 - 2/5 - b*d - i*d**3 = 0.
-2, -1, -1/3
Let b(m) = -3*m + 66. Let i be b(21). Factor 5/4*l**5 + 3*l**4 - 1/2 + l**i - 9/4*l - 5/2*l**2.
(l - 1)*(l + 1)**3*(5*l + 2)/4
Let h be 4/(-1) - (7 - 11). Factor 0 + 1/3*f**2 + h*f.
f**2/3
Let q(u) be the second derivative of 3/20*u**5 - 7*u + 0 + 3/2*u**3 - 3/4*u**4 - 3/2*u**2. Factor q(f).
3*(f - 1)**3
Let i = 961/5 - 192. Factor 16/5*m**2 + i + 8/5*m.
(4*m + 1)**2/5
Determine t, given that 63*t + 5*t**3 - 20 + 10*t - 13*t - 55*t**2 + 15*t**4 - 5*t**5 = 0.
-2, 1, 2
Suppose o = -2*o + 24. Suppose i - o = 8. Let -4 + 24*t - 6 + 1 - i*t**2 = 0. What is t?
3/4
Determine p, given that -8/13*p**3 - 14/13*p**2 + 8/13 + 8/13*p + 6/13*p**4 = 0.
-1, -2/3, 1, 2
Let f(x) = 0*x + 0*x + x**3 + 4*x - 3*x. Let b(m) = -4*m**3 + m**2 - 7*m. Let n(h) = b(h) + 5*f(h). Solve n(k) = 0.
-2, 0, 1
Suppose 5*s + 5*w = 6 + 4, -3*s - 4*w + 7 = 0. Let u(v) = 8*v + 1. Let i be u(s). Factor 2*f + f**2 - 4*f**2 - 4*f**2 - i*f**3.
-f*(f + 1)*(9*f - 2)
Let p be -2*1*1/((-4)/6). Let y(k) be the third derivative of 0*k + 1/8*k**4 + 1/60*k**5 + 1/3*k**3 + 0 + p*k**2. Determine s, given that y(s) = 0.
-2, -1
Let v(l) = l**2 - 4*l + 11. Suppose d + 2 = 7. Let y(x) = 2*x**2 - 7*x + 23. Let j(b) = d*v(b) - 2*y(b). Suppose j(w) = 0. What is w?
3
Suppose -4 = -5*d + 6. Factor 0 - 3*u**d + 3*u - 6*u + 0.
-3*u*(u + 1)
Let p = -4 - -8. Let h(m) be the first derivative of -2 - 1/8*m**2 - 1/12*m**3 + 1/4*m + 1/16*m**p. Factor h(v).
(v - 1)**2*(v + 1)/4
Let o(d) be the third derivative of -d**9/37800 + d**8/8400 - d**6/900 + d**5/300 - d**4/24 + 3*d**2. Let s(f) be the second derivative of o(f). Factor s(u).
-2*(u - 1)**3*(u + 1)/5
Suppose -3*k = -2*k - 2*v + 2, 4*v = 4*k - 4. Determine l so that -4*l**3 + 7*l + 7*l + k - 2*l + 4 = 0.
-1, 2
Let y(b) be the second derivative of b**10/15120 - b**9/1890 + b**8/672 - b**7/630 + b**4/4 - 2*b. Let k(t) be the third derivative of y(t). Factor k(u).
2*u**2*(u - 2)*(u -