tive of -t**8/2016 + t**6/360 - t**4/144 - 14*t**2. Factor b(r).
-r*(r - 1)**2*(r + 1)**2/6
Suppose -i = 2*i - 6. Factor 16*g - 10*g + g**i + 2*g**2.
3*g*(g + 2)
Let r(u) = -u**2 - 3*u - 8. Let z(g) = g**2 + 2*g + 7. Let d(p) = -5*r(p) - 6*z(p). Factor d(v).
-(v - 2)*(v - 1)
Let l = 3007/227760 - 2/2847. Let d(q) be the second derivative of 0 + 0*q**2 - q + 1/24*q**3 + l*q**5 + 1/24*q**4. Factor d(x).
x*(x + 1)**2/4
Let o be ((-444)/(-1813))/(2/14). Solve -3/7*d**5 + 6/7 - 6/7*d**2 + o*d**3 - 9/7*d + 0*d**4 = 0 for d.
-2, -1, 1
Let y be 11/4 + 3/12. What is w in 0 - 2/7*w**4 - 4/7*w + 2/7*w**2 + 4/7*w**y = 0?
-1, 0, 1, 2
Let v(n) = -n**2 - 9*n. Let t be v(-9). Let z(b) be the second derivative of 0 - 1/3*b**3 - 2/5*b**5 + b + 5/6*b**4 + t*b**2. Factor z(o).
-2*o*(o - 1)*(4*o - 1)
Let s = -14 - -10. Let v be (6/s)/(9/(-12)). Let 1/5*i**v + 2/5*i + 1/5 = 0. Calculate i.
-1
Let p(z) = -z**2 + 3*z + 2. Let m be p(3). Let f = 2 + 1. Factor -f*g - g**m + 2 + 2*g + 0.
-(g - 1)*(g + 2)
Let f be 2/(-8) + 40/40. Let 0 - 3/4*k**4 - f*k**3 + 0*k + 3/2*k**2 = 0. Calculate k.
-2, 0, 1
Factor -2/3 + 2/3*a**2 - 1/3*a + 1/3*a**3.
(a - 1)*(a + 1)*(a + 2)/3
Let t(l) = l + 13. Let u be t(-9). Factor -n - 3 + u*n**2 - 3*n**2 + 3.
n*(n - 1)
Let j(u) be the first derivative of -u**6/30 - u**5/20 + 4*u - 1. Let a(z) be the first derivative of j(z). Factor a(n).
-n**3*(n + 1)
Let k(m) be the third derivative of -m**7/105 - m**6/15 - m**5/5 - m**4/3 - m**3/3 - 11*m**2. Factor k(j).
-2*(j + 1)**4
Let t = -3 - 3. Let q = t + 6. Solve 1/2*o**5 - 1/2*o**4 + q + 0*o - 1/2*o**3 + 1/2*o**2 = 0.
-1, 0, 1
Let j(b) be the third derivative of b**11/66528 + b**10/12600 + b**9/6720 + b**8/10080 + b**5/30 + b**2. Let d(a) be the third derivative of j(a). Factor d(f).
f**2*(f + 1)**2*(5*f + 2)
Let x(v) = -v**4 + 4*v**3 - 2*v**2 - 2*v + 1. Let z(s) = s**4 - s**3 + s**2 - 1. Let a = 11 + -10. Let j(t) = a*x(t) + 2*z(t). What is u in j(u) = 0?
-1, 1
Let y(k) be the second derivative of 3/4*k**4 + k**3 + 1/2*k**2 + 2*k + 0. Let y(u) = 0. What is u?
-1/3
Let u(w) be the third derivative of -w**5/30 + w**3/3 + 4*w**2. Solve u(b) = 0 for b.
-1, 1
Factor -17/7*r**2 - 5/7*r**3 - 4/7 - 16/7*r.
-(r + 1)*(r + 2)*(5*r + 2)/7
Let w(a) = 4*a. Let m be w(1). Let r be (4/10)/(2/20). Factor 0 + 1 - r*k**2 + 0*k**4 + 2*k**m + 1.
2*(k - 1)**2*(k + 1)**2
Let r be 4/(-18) - (-54)/243. Factor 4/13*z**3 + 0*z**2 - 2/13*z**5 + 0 + r*z**4 - 2/13*z.
-2*z*(z - 1)**2*(z + 1)**2/13
Suppose -2*d = -3 - 3. Let p(x) be the second derivative of 0*x**2 + 0 - 1/40*x**5 - 1/60*x**6 + 1/24*x**4 + 2*x + 1/12*x**d. Find c, given that p(c) = 0.
-1, 0, 1
Let v(l) be the second derivative of l**4/16 - l**3/8 - 3*l**2/4 + 15*l. Factor v(r).
3*(r - 2)*(r + 1)/4
Suppose -19*c - 1 + 9 - 5 - 7 - 24*c**2 - 9*c**3 = 0. What is c?
-4/3, -1, -1/3
Let r(x) be the third derivative of x**5/420 - x**4/56 + x**3/21 - 28*x**2. Determine d so that r(d) = 0.
1, 2
Solve 5*f**3 + 8*f**2 + 10*f**2 - 20*f - 12*f**2 + 9*f**2 = 0.
-4, 0, 1
Suppose 0 = -q + 2*q. Suppose 3*g - g - 10 = q. Find u, given that 29/2*u**2 - 8*u - 2 - 25/2*u**4 + 58*u**3 - 50*u**g = 0.
-1, -2/5, -1/4, 2/5, 1
Let s(j) be the second derivative of 0 + 0*j**6 + j + 0*j**4 - 1/60*j**5 + 0*j**2 + 1/252*j**7 + 1/36*j**3. Factor s(i).
i*(i - 1)**2*(i + 1)**2/6
Suppose 9 = -5*r + 29. Let -1/4*b**4 - 2*b**3 - 6*b**2 - r - 8*b = 0. What is b?
-2
Let y be (26/(-455))/((-24)/14). Let w(u) be the third derivative of 0 + y*u**5 + 0*u - 1/12*u**4 - u**2 + 0*u**3. Find h such that w(h) = 0.
0, 1
Let -8*a - 16*a**2 - 22 + 15*a**2 + 6 = 0. What is a?
-4
Let c(p) = -32*p**5 - 23*p**4 - 17*p**3. Let i(n) = 11*n**5 + 8*n**4 + 6*n**3. Let y(k) = 6*c(k) + 17*i(k). Suppose y(z) = 0. What is z?
-2/5, 0
Let p(d) be the third derivative of 1/30*d**6 + 0*d - 5*d**2 + 0 - 1/35*d**7 + 0*d**3 + 0*d**4 + 1/30*d**5. Determine v so that p(v) = 0.
-1/3, 0, 1
Suppose 0 = t - 9 + 5. Let 6/5*u**2 - 14/5*u**3 + 2*u**5 + 4/5*u - 6/5*u**t + 0 = 0. Calculate u.
-1, -2/5, 0, 1
Let s(v) be the second derivative of -1/10*v**5 - 1/30*v**6 + 2/3*v**3 + 3*v + 1/4*v**4 + 0 - 2*v**2. Find j, given that s(j) = 0.
-2, 1
Let i(m) be the second derivative of -m**4/36 - m**3/18 + 2*m. Factor i(t).
-t*(t + 1)/3
Suppose -c + 3*u + 17 = 8*u, 2*c - 1 = u. Factor -g**3 + g**2 - 2*g**3 - g**4 + 2*g**3 + c*g**5 - g**5.
g**2*(g - 1)**2*(g + 1)
Let w(c) be the second derivative of 1/2*c**4 - 1/10*c**5 + c**2 - c + 0 - c**3. Determine g, given that w(g) = 0.
1
Let u(a) be the first derivative of 0*a - 1/3*a**3 + 0*a**2 - 5. Let u(f) = 0. Calculate f.
0
Let t = 682/5 - 136. What is g in -t*g**2 + 2/5*g + 2/5 - 2/5*g**3 = 0?
-1, 1
Let d(w) be the third derivative of -w**7/840 - w**6/480 + w**5/240 + w**4/96 + 16*w**2. Find h, given that d(h) = 0.
-1, 0, 1
Let m(i) = -2*i**2 + 7*i + 9. Let y(s) = 2*s**2 - 8*s - 10. Suppose o = -2 + 6. Let u(q) = o*m(q) + 3*y(q). Determine h, given that u(h) = 0.
-1, 3
What is r in -10*r**3 - 15*r**4 - 7*r**5 + 6*r**5 - 4*r**5 = 0?
-2, -1, 0
Suppose -11 = -5*v - 1. Let u = 0 + v. Suppose 0*t**2 + 1 - 3*t**2 + u*t**2 = 0. What is t?
-1, 1
Let u(z) be the third derivative of -2/9*z**3 + 2*z**2 + 0 + 0*z + 1/360*z**6 - 1/36*z**5 + 1/9*z**4. Factor u(r).
(r - 2)**2*(r - 1)/3
Let p(x) be the first derivative of -x**4/6 - 4*x**3/9 + x**2/3 + 4*x/3 - 18. Let p(f) = 0. What is f?
-2, -1, 1
Let s(o) = o**4 - o**3 + 3*o**2 - 3*o + 4. Let j(k) = 5*k**4 - 5*k**3 + 12*k**2 - 11*k + 17. Let f(n) = 4*j(n) - 18*s(n). Factor f(v).
2*(v - 1)**3*(v + 2)
Suppose 3*c - 2*k + 40 = 3*k, 4*k = -c - 19. Let x be 7/(-21) + (-8)/c. Factor 1/5*a**4 + 1/5*a - 2/5*a**2 - 2/5*a**3 + x + 1/5*a**5.
(a - 1)**2*(a + 1)**3/5
Let b(f) = -f + 7. Let s be b(4). Factor 2*r + 2*r**2 + 0*r**4 - 4*r**3 + 5*r**3 - s*r**3 - 2*r**4.
-2*r*(r - 1)*(r + 1)**2
Suppose 3*h = -0*h + 30. Suppose -5*l + 0*l = -h. Factor x**2 + 0*x + 4 - 8*x**2 - 3*x**l + 6*x.
-2*(x - 1)*(5*x + 2)
Suppose 20*w = 17*w - 6. Let c be -1 - w - 3/6. Let -5/4*i**3 + 0*i + c*i**2 + 0 = 0. What is i?
0, 2/5
Determine u so that 0 + 2*u**2 - 2/5*u**3 + 0*u = 0.
0, 5
Let z(n) = -2*n**3 - n. Let a be z(-1). Let s = 39 - 37. Factor -1/4*y**s + y - y**a + 1/4.
-(y - 1)*(y + 1)*(4*y + 1)/4
Let z = 29 + -40. Let b(j) = -j**3 - j**2 - 2*j. Let n(g) = 6*g**3 + 6*g**2 + 11*g. Let d(r) = z*b(r) - 2*n(r). Determine f, given that d(f) = 0.
-1, 0
Let t(o) be the third derivative of o**8/3024 + o**7/945 - o**6/1080 - o**5/270 - 15*o**2. Determine b, given that t(b) = 0.
-2, -1, 0, 1
Factor 8/5*m**2 + 2/5*m**4 - 8/5*m**3 + 0 + 0*m.
2*m**2*(m - 2)**2/5
Solve -m**5 - 5*m**2 - m + 4*m**4 + 0*m**2 + 3*m**2 - 6*m**3 + 6*m**2 = 0.
0, 1
Let x = -36/17 - -35/17. Let b = 301/85 - x. Let 54/5*q**2 + 8/5 + 8*q + b*q**3 = 0. Calculate q.
-2, -2/3, -1/3
Let h(b) be the second derivative of 32*b**6/105 - 8*b**5/35 - 5*b**4/7 + 6*b**3/7 + 16*b. Find m such that h(m) = 0.
-1, 0, 3/4
Let 16*b**2 + 4*b - 13*b**2 + 2*b = 0. Calculate b.
-2, 0
Let k(o) = -12*o**5 + 38*o**4 - 32*o**3 + 2*o. Let t = 4 - 5. Let x(h) = h**5 - h**3 - h**2 - h. Let j(i) = t*k(i) + 2*x(i). Factor j(q).
2*q*(q - 1)**3*(7*q + 2)
Let g = -373/36 - -100/9. What is m in 3/8*m**4 + 0*m**2 - g*m + 3/4*m**3 - 3/8 = 0?
-1, 1
Let x(k) be the second derivative of k**4/4 + k**3/2 - 30*k. Factor x(b).
3*b*(b + 1)
Solve 378*a + 35 - 758*a + 5*a**3 - 35*a**2 + 375*a = 0.
-1, 1, 7
Let v(b) be the first derivative of -b**3 + 0*b**2 + 1/1080*b**6 + 0*b - 1/360*b**5 - 1 + 0*b**4. Let d(r) be the third derivative of v(r). Factor d(w).
w*(w - 1)/3
Let v = 386 + -383. Factor 0*u - 1/7*u**4 + 0 + 0*u**2 + 1/7*u**v.
-u**3*(u - 1)/7
Let q(i) = 3*i**3 + 7*i**2 + 4*i + 6. Let f be (-5)/25 - 29/5. Let c(y) = -4*y**3 - 7*y**2 - 5*y - 7. Let u(o) = f*c(o) - 7*q(o). Find v, given that u(v) = 0.
0, 1/3, 2
Let c(w) = 3*w. Let p be c(0). Let k(b) be the third derivative of 0*b**3 + 0 + 1/12*b**4 - 2*b**2 + 0*b**5 - 1/60*b**6 + p*b. Determine y so that k(y) = 0.
-1, 0, 1
Let y be (-1 - (-15)/(-40)*-2)*0. Suppose y + 2/5*n**3 - 2/5*n + 0*n**2 = 0. Calculate n.
-1, 0, 1
Factor 0*r**2 + 0 + 1/4*r - 1/4*r**3.
-r*(r - 1)*(r + 1)/4
Factor 1/8*k**2 + 1/8*k - 1/8 - 1/8*k**3.
-(k - 1)**2*(k + 1)/8
Let z be ((-2)/(-8))/((-1)/(-4)). Let g be 2/6*0/z. Solve -1/4*y**2 + 1/4 + g*y = 0 for 