et v(q) be the third derivative of q**6/120 + q**5/60 - 5*q**4/24 + q**3/2 - 11*q**2. Factor v(y).
(y - 1)**2*(y + 3)
Let p(h) be the second derivative of -1/6*h**2 + 1/15*h**5 - 1/18*h**4 + 1/30*h**6 + 0 - 5*h - 2/9*h**3. Suppose p(y) = 0. What is y?
-1, -1/3, 1
Let a be 6/(-24) + 13/4. Find y, given that 26*y**2 - 22*y**2 - 1 - a*y + 0*y = 0.
-1/4, 1
Let n(i) = -3*i**3 - 2*i**2 + i. Let z be n(1). Let p be z/6 + 35/30. Factor -p + 1/2*g**2 + 0*g.
(g - 1)*(g + 1)/2
Let s = -2/7 - -15/28. Let t(a) = -a + 1. Let q be t(1). Factor -s + q*p + 1/4*p**2.
(p - 1)*(p + 1)/4
Let y(d) be the second derivative of d - 1/6*d**3 - 1/12*d**4 + d**2 + 0. Factor y(r).
-(r - 1)*(r + 2)
Let 17*v + 2*v**2 - 17*v = 0. Calculate v.
0
Let n(d) = 90*d**3 - 272*d**2 + 135*d + 30. Let v(s) = -30*s**3 + 91*s**2 - 45*s - 10. Let h(c) = 6*n(c) + 17*v(c). Factor h(l).
5*(l - 2)*(l - 1)*(6*l + 1)
Let y(o) be the first derivative of -1/8*o**3 - 3/16*o**2 + 0*o + 5 + 3/32*o**4 + 3/40*o**5. Suppose y(u) = 0. Calculate u.
-1, 0, 1
Let d(a) be the third derivative of -a**6/320 - a**5/160 + 5*a**4/64 - 3*a**3/16 - 2*a**2 - 21*a. Factor d(h).
-3*(h - 1)**2*(h + 3)/8
Let d(y) = -y**2 - 11*y - 7. Let j be d(-10). Factor 2*l**2 - 18*l + 18*l - 2*l**j.
-2*l**2*(l - 1)
Let d = -288/5 + 58. Suppose r - 5*r + 8 = 0. Factor -d + 4/5*s - 2/5*s**r.
-2*(s - 1)**2/5
Let x be (-2)/10*10/(-66). Let q(d) be the second derivative of 0 - x*d**3 + 0*d**2 + 1/165*d**6 + 1/110*d**5 - d - 1/66*d**4. What is m in q(m) = 0?
-1, 0, 1
Factor 28/5*s**2 - 4/5*s**3 - 64/5 - 32/5*s.
-4*(s - 4)**2*(s + 1)/5
Let s = 141610/87 - 3771/29. Let v = 1511 - s. Find n such that v*n - 6*n**4 - 8/3 + 20*n**3 - 74/3*n**2 = 0.
2/3, 1
Let x(r) be the second derivative of -r**5/5 + 4*r**4/3 - 13*r. Factor x(u).
-4*u**2*(u - 4)
Let b be -1 - 13/((-156)/30). Factor 0 + 0*f + b*f**5 - 9/2*f**4 - 3/2*f**2 + 9/2*f**3.
3*f**2*(f - 1)**3/2
Let f(w) = -w**3 + w**2 - w. Let q(a) = 16*a**4 - 7*a**3 - 16*a**2 + 9*a - 1. Let i be 2/3*18/(-4). Let l(v) = i*f(v) - 3*q(v). Suppose l(h) = 0. Calculate h.
-1, 1/4, 1
Suppose 5*s = 2*i + 6, 4*s - 3*s = 2. Factor -1/4*j**i + 0 - 1/2*j.
-j*(j + 2)/4
Let n(m) be the second derivative of m**4/4 + 2*m. Let x be n(-1). Factor -4 - x + 4*i**2 - 2*i**4 + 5.
-2*(i - 1)**2*(i + 1)**2
Let n be -6 + 49/14 - (-9)/2. Solve -3/4*w**n + 9/4 + 3/2*w = 0 for w.
-1, 3
Factor b**3 - 4*b - 4 + 0*b**2 + 1/4*b**4.
(b - 2)*(b + 2)**3/4
Suppose -21 = -5*x - 1. Let z(m) = -m - 4. Let f be z(-6). Factor -5*l**2 + 4*l**2 + 3*l**x - f*l**4.
l**2*(l - 1)*(l + 1)
Factor 4*j**2 - 6 + 53*j**3 + 5*j - 4*j - 52*j**3.
(j - 1)*(j + 2)*(j + 3)
Let h(s) be the first derivative of 0*s**4 + 0*s + 0*s**2 - 2/45*s**5 + 2/27*s**3 - 8. Factor h(k).
-2*k**2*(k - 1)*(k + 1)/9
Let f be 2/(-32)*8/(-30). Let j(p) be the third derivative of -f*p**5 + 0*p**3 - 4*p**2 + 0 + 0*p**4 + 0*p + 1/120*p**6. Solve j(s) = 0 for s.
0, 1
Let u be (18/5)/(56/70). Determine q, given that -1/2*q**2 - u - 3*q = 0.
-3
Let t = 46 - 26. Suppose 0 = 26*r - 21*r - t. Factor 0 - d**3 - 1/3*d + 1/3*d**r + d**2.
d*(d - 1)**3/3
Let j(o) = -3*o**3 - o**2 + 2*o + 2. Let u be j(-1). Determine f, given that 4/7*f**3 + 4/7*f**u - 6/7*f + 2/7*f**5 - 6/7*f**4 + 2/7 = 0.
-1, 1
Let a(w) be the third derivative of -1/108*w**4 + 4*w**2 + 0*w**3 + 1/540*w**6 + 0 + 0*w - 1/945*w**7 + 1/270*w**5. Find u such that a(u) = 0.
-1, 0, 1
Let o(d) be the third derivative of -5*d**2 + 1/600*d**6 + 1/60*d**4 + 1/60*d**5 + 0*d**3 + 0*d + 0 - 1/560*d**8 - 1/210*d**7. Suppose o(q) = 0. Calculate q.
-1, -2/3, 0, 1
Let c(q) = q**3 + 3*q**2 + 2*q + 8. Let j be c(-4). Let w = -12 - j. Factor -1/4*t**5 + 1/4*t**w + 1/2*t**3 + 1/4 - 1/2*t**2 - 1/4*t.
-(t - 1)**3*(t + 1)**2/4
Let g(x) = -x**3 + 11*x**2 + 3. Suppose 1 = 3*f - 32. Let b be g(f). Factor 0 - 4/5*c**2 + 2/5*c**b + 2/5*c.
2*c*(c - 1)**2/5
Let l(t) = 3*t + 19. Let h be l(-5). Let z(p) be the first derivative of -3/2*p**h + 3/5*p**5 + 0*p + 0*p**2 - 3 + p**3. Solve z(q) = 0.
0, 1
Suppose 3 = b - 4*q - 9, -3*b = q + 3. Let t(l) be the third derivative of 0*l - 1/12*l**4 - 2*l**2 - 2/3*l**3 + b + 1/30*l**5. Solve t(n) = 0 for n.
-1, 2
Let -4/13*y**2 + 4/13 - 2/13*y + 2/13*y**3 = 0. Calculate y.
-1, 1, 2
Let u(l) = -l**4 - l**3 - l**2 + l - 1. Let x(c) = 16*c**4 + 24*c**3 + 38*c**2 - 14*c + 22. Let v(j) = 44*u(j) + 2*x(j). Factor v(d).
-4*d*(d - 2)*(d + 1)*(3*d + 2)
Let b(z) = z**2 + 2*z - 6. Let h be b(2). Find d such that -2/7*d - 2/7*d**4 - 2/7 + 4/7*d**h + 4/7*d**3 - 2/7*d**5 = 0.
-1, 1
Suppose 18/11*k - 4/11 - 20/11*k**2 + 24/11*k**4 - 10/11*k**5 - 8/11*k**3 = 0. Calculate k.
-1, 2/5, 1
Find z, given that 2/7*z + 6/7*z**2 + 2/7*z**4 + 0 + 6/7*z**3 = 0.
-1, 0
Let q(m) be the first derivative of -m**6/360 - m**5/120 + m**3/3 + 2. Let u(y) be the third derivative of q(y). Factor u(p).
-p*(p + 1)
Let w(r) be the third derivative of r**6/1440 + r**5/480 - r**4/48 + 5*r**3/6 + 3*r**2. Let y(c) be the first derivative of w(c). Solve y(v) = 0 for v.
-2, 1
Suppose 11 = 3*z + 2. Let r(q) be the second derivative of -1/36*q**4 + 0*q**2 + 0*q**z + 0 + 2*q. Solve r(i) = 0.
0
Factor 14*i**2 - 45 - 11 + 154*i + 38*i.
2*(i + 14)*(7*i - 2)
Factor -8*j - 1/2*j**2 - 32.
-(j + 8)**2/2
Let f(k) be the second derivative of -k**6/195 - 3*k**5/65 - k**4/6 - 4*k**3/13 - 4*k**2/13 + 18*k. Factor f(s).
-2*(s + 1)**2*(s + 2)**2/13
Let s(z) be the first derivative of 2/5*z**5 - 4/3*z + 5/3*z**2 - 5/6*z**4 - 2/9*z**3 - 5. Determine i so that s(i) = 0.
-1, 2/3, 1
Suppose 2*c = 2 + 2. Factor -7*i**c + 0*i**4 + 3*i**4 + 4*i**2.
3*i**2*(i - 1)*(i + 1)
Let c(b) = -b**2 + 5*b - 6. Let a be c(3). Let t(u) be the second derivative of a*u**2 + 0 + 1/21*u**3 - u + 1/105*u**6 - 1/70*u**5 - 1/42*u**4. Solve t(p) = 0.
-1, 0, 1
Let t(b) = 3*b - 4. Let n be t(2). Let f(d) = -d - 5. Let h be f(-5). Factor h*y**2 + 4*y**n - 3*y**2 + y.
y*(y + 1)
Let k be (10/(-4) - -2)*-6. Suppose k = 3*x - 3*o, -4*o + 29 + 2 = 3*x. Factor 0 + 2/3*m**2 + 0*m**3 - 2/3*m**4 + 1/3*m**x - 1/3*m.
m*(m - 1)**3*(m + 1)/3
Factor 2*i**3 + 2*i**2 + 4*i - 8 - 4*i**3 + 4*i.
-2*(i - 2)*(i - 1)*(i + 2)
Let u be (36/7)/(74/14 - 5). Let y(s) be the first derivative of -6*s**3 + u*s**2 - 24*s + 3/4*s**4 + 2. Factor y(c).
3*(c - 2)**3
Let g = -437 + 20977/48. Let j(v) be the second derivative of 1/8*v**2 + 1/12*v**3 + g*v**4 + 0 - v. Factor j(d).
(d + 1)**2/4
Let o = 3935/7 + -561. Suppose -o*s**2 - 4/7 - 10/7*s - 2/7*s**3 = 0. What is s?
-2, -1
Let c be (-29)/(-9) - (-28)/(-126). Let a(v) be the second derivative of 1/10*v**5 + 0 - v - 1/6*v**4 + 1/15*v**6 + 0*v**2 - 1/3*v**c. What is h in a(h) = 0?
-1, 0, 1
Let x(j) be the second derivative of j**6/6 + 3*j**5/20 - 11*j**4/6 - 2*j**3 + 4*j**2 + 10*j. Suppose x(h) = 0. What is h?
-2, -1, 2/5, 2
Suppose -18 = -5*x + 7. Suppose x*a + c = 6*c, 5*c = 2*a. Factor 1/3*m + 2/3*m**4 + 0*m**3 - 1/3*m**5 - 2/3*m**2 + a.
-m*(m - 1)**3*(m + 1)/3
Let k be -1 + 3 + (315/(-14))/15. Factor 0 + k*v**2 - 1/2*v**3 + 0*v.
-v**2*(v - 1)/2
Let a = 370/287 + -6/41. Solve -a*h + 8/7 + 2/7*h**2 = 0 for h.
2
Let f(h) be the second derivative of -10*h**6/3 + 4*h**5 - 4*h**4/3 - 10*h. Let f(j) = 0. What is j?
0, 2/5
Let y be ((-1)/(-2))/(2/8). Suppose p - 21 = -y*p. Solve 4*r**2 - 2*r**4 - p + 5 + 0 = 0.
-1, 1
Let k(s) be the second derivative of -s**7/105 - 2*s**6/25 - 13*s**5/50 - 2*s**4/5 - 4*s**3/15 + 4*s. Factor k(g).
-2*g*(g + 1)**2*(g + 2)**2/5
Let g = -2 + 4. Let h = 6 - g. Determine i, given that i**4 + 0*i**2 + i**2 - 2*i**h = 0.
-1, 0, 1
Let b(w) be the third derivative of -2*w**2 + 1/156*w**4 + 1/780*w**6 + 0 - 1/195*w**5 + 0*w + 0*w**3. Factor b(l).
2*l*(l - 1)**2/13
Let b = 1 + 4. Let w(k) = k**2 - 6*k. Let u(h) = h**2 - 7*h. Let x(s) = b*u(s) - 6*w(s). Factor x(p).
-p*(p - 1)
Factor 21*q**4 + 124*q**2 - 2*q**3 + 5*q**3 - 124*q**2.
3*q**3*(7*q + 1)
Suppose -8 = -4*g - 0*g. Let q(k) be the second derivative of 1/6*k**4 + 0 - 1/3*k**3 - g*k + 1/10*k**5 - k**2. Factor q(u).
2*(u - 1)*(u + 1)**2
Let c(l) = l**2 - 15*l - 18. Let i(k) = -k**2 + 29*k + 36. Let j(b) = -5*c(b) - 3*i(b). Factor j(x).
-2*(x + 3)**2
Let n(q) be the first derivative of 4*q**3 - 8*q**2 + 4*q - 18. Factor n(x).
4*(x - 1)*(3*x - 1)
Let j(b) = -b - 3. Let r be j(-6). Let z(t) be the first derivative of 1/12*t**