 2 + 1/3*f**3. Let n(i) be the third derivative of t(i). Factor n(p).
-2*(p - 2)*(p - 1)
Let w(i) = i**3 + 33*i**2 + 5*i + 165. Let u be w(-33). Factor u - 1/3*o**2 + 1/3*o**3 + 0*o.
o**2*(o - 1)/3
Let u be (8/(-10))/((-6)/15). Solve 21*b**3 + 7*b**2 + 8*b**2 - 12*b**u + 3*b**2 = 0.
-2/7, 0
Let y(p) = -4*p**4 - 8*p**2 + 6*p - 6. Let i(l) = 9*l**4 + 17*l**2 - 13*l + 13. Let k(x) = 6*i(x) + 13*y(x). Determine h, given that k(h) = 0.
-1, 0, 1
Suppose 3*y - 7 = 5. Suppose 4*m - y*o - 32 = 0, 6*m + 4*o = 4*m + 4. Factor x**3 - m*x + 4*x + x**3.
2*x*(x - 1)*(x + 1)
Suppose -59*w = -78*w. Factor -5/4*l**2 + 5/4*l**4 + 5/2*l**3 - 5/2*l + w.
5*l*(l - 1)*(l + 1)*(l + 2)/4
Let o be -3 - (1 + (-808)/4). Suppose -86*f**3 - 82*f**4 - 122*f**3 - o*f**4 - 32*f**2 + 196*f**5 = 0. What is f?
-2/7, 0, 2
Let k be (-8)/(-51)*(-9)/48*-4. Factor 0 + 2/17*t**2 + k*t.
2*t*(t + 1)/17
Let p(j) be the third derivative of -7*j**6/660 - 13*j**5/165 - 5*j**4/33 + 8*j**3/33 + 39*j**2. Find b, given that p(b) = 0.
-2, 2/7
Let l be (-40)/(-8)*1/4. Factor v**2 + l*v + 1/2 + 1/4*v**3.
(v + 1)**2*(v + 2)/4
Let b(n) be the second derivative of -7*n**5/20 - 3*n**4/2 + 2*n**3 - n**2 + 7*n. Let l(h) be the first derivative of b(h). Factor l(o).
-3*(o + 2)*(7*o - 2)
Let m(g) be the third derivative of -3*g**8/728 + 16*g**7/455 - 97*g**6/780 + 47*g**5/195 - 11*g**4/39 + 8*g**3/39 + 26*g**2. Find f, given that m(f) = 0.
2/3, 1, 2
Let y be (4 - 27/6) + (-2)/(-4). Factor 1/3*b + 1/3*b**2 + y - 1/3*b**3 - 1/3*b**4.
-b*(b - 1)*(b + 1)**2/3
Suppose 17 = 8*v + 1. Factor 4/3*p - 2/9 - 2*p**v.
-2*(3*p - 1)**2/9
Let t(y) be the second derivative of -y**4/54 + 4*y**3/27 - 5*y. Solve t(m) = 0.
0, 4
Suppose -3*q - 3*q + 12 = 0. Let h(m) be the second derivative of -q*m + 1/105*m**6 + 1/70*m**5 - 1/42*m**4 - 1/21*m**3 + 0 + 0*m**2. What is g in h(g) = 0?
-1, 0, 1
Let s(w) be the second derivative of 1/20*w**6 - 3/8*w**5 + 3/2*w**2 - 7/4*w**3 + 0 + 9/8*w**4 - 4*w. Factor s(o).
3*(o - 2)*(o - 1)**3/2
Let r = -4 + 7. Factor -r*f**4 + 5*f**4 + 4*f**5 + f**5.
f**4*(5*f + 2)
Suppose 6*f = 3*f - 7*f. Factor f + 3/2*a - 3/2*a**3 + 3/2*a**4 - 3/2*a**2.
3*a*(a - 1)**2*(a + 1)/2
Let p(y) be the first derivative of y**5/10 + y**4/4 - y**2/2 - y/2 - 4. What is g in p(g) = 0?
-1, 1
Let j(u) = -17*u**5 + u**4 + 3*u**2 + 3*u + 3. Let r(w) = -188*w**5 + 10*w**4 + 34*w**2 + 34*w + 34. Let c(i) = 68*j(i) - 6*r(i). Find d, given that c(d) = 0.
0, 2/7
Suppose 0*q - 1/2*q**5 + 0*q**2 + 1/2*q**4 + 0*q**3 + 0 = 0. Calculate q.
0, 1
Let q(s) be the first derivative of -s**6/3 + s**4/2 - 11. Factor q(l).
-2*l**3*(l - 1)*(l + 1)
Let t(w) be the first derivative of 2 - 4*w + 1/30*w**4 + 0*w**2 - 1/15*w**3. Let p(h) be the first derivative of t(h). Suppose p(a) = 0. Calculate a.
0, 1
Factor 13*u - 9*u + 2*u**2 - 2*u**3 + 0*u**2.
-2*u*(u - 2)*(u + 1)
Let i(m) = -m**2 - 7*m + 2. Let z(q) = -q**3 - 7*q**2 + 8*q - 7. Let j be z(-8). Let b be i(j). Factor -2*p**5 + p**4 + 3*p**5 - 2*p**5 + b*p**3.
-p**3*(p - 2)*(p + 1)
Let y be 2/4 - (-1)/(-2). Solve y*p**2 + p - p**2 - 5*p + 5*p = 0.
0, 1
Let f be ((-57)/(-15) - 1) + 1/5. Let u(a) be the second derivative of -1/30*a**5 + 0 - a + 0*a**4 + 0*a**f + 0*a**2 + 1/45*a**6. Solve u(l) = 0 for l.
0, 1
Let y(s) = -27*s - 105. Let d be y(-4). Factor -3*c**2 + 3/2*c + d - 3/2*c**3.
-3*(c - 1)*(c + 1)*(c + 2)/2
Let f(r) = -r**3 - 4*r**2 + 3*r - 7. Let g be f(-5). Find p, given that 8/7*p**2 - 10*p**g + 8/7*p + 0 = 0.
-2/7, 0, 2/5
Let z(y) be the second derivative of -y**4/12 - y**3/6 - y**2/2 + 3*y. Let q(x) = 13*x**2 - x + 3. Let n(w) = -q(w) - 3*z(w). Factor n(m).
-2*m*(5*m - 2)
Suppose 4*x = -7*s + 2*s + 2, 2*s - 8 = -4*x. Solve -3*g**x + 5*g**2 - 3*g**2 - 4*g + g + 4*g**2 = 0 for g.
0, 1
Factor 4/5*u - 2/5*u**2 - 2/5.
-2*(u - 1)**2/5
Let t = 100 - 100. Factor -4/5*r**2 + t*r + 4/5.
-4*(r - 1)*(r + 1)/5
Suppose -5 + 5 = -3*s. Suppose -2/5*h + 0 + 2/5*h**3 + s*h**2 = 0. Calculate h.
-1, 0, 1
Factor 4/7*g + 1/7*g**4 - 2/7*g**3 + 4/7 - 3/7*g**2.
(g - 2)**2*(g + 1)**2/7
Let d(n) be the first derivative of -n**8/1050 + n**7/700 + n**6/900 - 5*n**3/3 - 3. Let f(h) be the third derivative of d(h). Factor f(j).
-2*j**2*(j - 1)*(4*j + 1)/5
Let 2/3*g**2 + 0*g - 2/3 = 0. Calculate g.
-1, 1
Let s(b) be the second derivative of 2/21*b**3 + 0 - 1/7*b**2 - 1/42*b**4 + 4*b. Factor s(v).
-2*(v - 1)**2/7
Let d = 3 - 7. Let r = 6 + d. Factor -2*j**2 + j**2 + 3*j**r - 2.
2*(j - 1)*(j + 1)
Let i be (((-78)/(-36))/(-13))/(2/(-3)). Suppose 1/4*y**3 + i*y**2 + 0 + 0*y = 0. What is y?
-1, 0
Let h(i) be the third derivative of -i**4/24 + 5*i**3/2 + 5*i**2. Let m be h(11). Let -2*j**4 - 3*j**3 + 3*j**2 + 3*j + j**m + j**4 - 3*j**4 = 0. What is j?
-1, 0, 1
Factor 2/5*m + 2/5*m**5 + 0 + 12/5*m**3 - 8/5*m**4 - 8/5*m**2.
2*m*(m - 1)**4/5
Suppose -5*o - 4*t = 66, t - 3*t = o + 18. Let r be 25/10*(-2)/o. Factor r + 3/2*s + 1/2*s**3 + 3/2*s**2.
(s + 1)**3/2
Factor 3*u**3 + 2*u**5 + 15*u**3 - 4*u**5 + 6*u - 16*u**2 - 6*u**3.
-2*u*(u - 1)**3*(u + 3)
Let x = 304 - 304. Let x*g - 1/6*g**2 + 1/6 = 0. Calculate g.
-1, 1
Let r(n) be the first derivative of n**6/660 - n**5/66 + 2*n**4/33 - 4*n**3/33 + n**2/2 - 7. Let g(m) be the second derivative of r(m). Solve g(s) = 0.
1, 2
Let o be (-2 + 1)/1*-1. Let f be (o + (-6)/15)*5. Find a, given that -1/2*a**2 + 1/2*a**f + 1/2 - 1/2*a = 0.
-1, 1
Let z(q) be the first derivative of 2*q**3 + 7*q**2/2 - 6*q + 1. Let l(v) = -5*v**2 - 6*v + 5. Let i(c) = 7*l(c) + 6*z(c). Factor i(y).
(y - 1)*(y + 1)
Suppose 16*h - 7*h**2 - 30 - 81*h + 31*h**2 - 15*h**3 + 46*h**2 = 0. Calculate h.
-1/3, 2, 3
Let x(d) be the third derivative of d**6/540 - d**4/36 - d**3/6 - d**2. Let j(f) be the first derivative of x(f). Factor j(h).
2*(h - 1)*(h + 1)/3
Let x(y) be the second derivative of 3/8*y**4 + 1/120*y**6 + 0*y**2 + 1/2*y**3 + 1/10*y**5 + 0 + y. Let g(t) be the second derivative of x(t). Factor g(l).
3*(l + 1)*(l + 3)
Find v, given that 0*v + 0 + 1/7*v**2 = 0.
0
Let j = 20 - 15. Let d(w) be the second derivative of 0 + 1/9*w**4 - 2/45*w**6 - 1/60*w**j + 1/18*w**3 + 0*w**2 + w. Factor d(q).
-q*(q - 1)*(q + 1)*(4*q + 1)/3
Let x be (3/27)/(10/(-12) - -1). Determine j so that -4/3*j - 2/3*j**2 - x = 0.
-1
Let i(z) be the first derivative of z**3 - 1 - 3 + 3 + 7*z - 6*z**2 + 2*z. Factor i(v).
3*(v - 3)*(v - 1)
Let q = -5/187 - -202/561. Factor 0 - 1/3*g - q*g**2.
-g*(g + 1)/3
Factor 1/4 - 7/8*s - 9/8*s**2.
-(s + 1)*(9*s - 2)/8
Let n(h) = -8*h**2 + 20*h + 22. Let t(f) = -6*f**2 + 20*f + 22. Let x(r) = -4*n(r) + 6*t(r). Factor x(z).
-4*(z - 11)*(z + 1)
Let a(c) be the first derivative of c**2/2 - 12*c + 1. Let o be a(12). Solve 8/9 + o*i - 2/3*i**2 - 2/9*i**3 = 0 for i.
-2, 1
Let t(a) = -a**3 - 2*a**2 + a + 6. Let d(l) = 2*l**3 + 4*l**2 - 2*l - 11. Let s(c) = -4*d(c) - 7*t(c). What is r in s(r) = 0?
-2, -1, 1
Let j(u) be the first derivative of 2*u**3/13 + 5*u**2/13 + 4*u/13 + 12. Find a, given that j(a) = 0.
-1, -2/3
Let z(d) be the first derivative of d**5/20 + d**4/2 + 2*d**3 + 4*d**2 - 2*d + 1. Let c(n) be the first derivative of z(n). What is x in c(x) = 0?
-2
Suppose -3*q = -6*q. Let a = 1/2 - q. Find k such that 0*k**2 + 0*k + 0 + a*k**3 = 0.
0
Suppose 3*k - 2*j - 18 + 2 = 0, -8 = k + 2*j. Let q(m) be the third derivative of 0*m - k*m**2 + 0 + 2/27*m**3 - 1/270*m**5 + 1/108*m**4. Factor q(h).
-2*(h - 2)*(h + 1)/9
Let z(x) = 7*x**3 - 2*x**2 + 6*x + 8. Let p(j) = 15*j**3 - 4*j**2 + 13*j + 17. Let q(r) = -6*p(r) + 13*z(r). Let n be q(0). Factor 1/4*u**n - 1/2*u + 1/4.
(u - 1)**2/4
Let h(n) be the second derivative of -16/15*n**3 - 4/15*n**4 + 0 + 0*n**2 - 1/50*n**5 - n. Determine l, given that h(l) = 0.
-4, 0
Let b be (-4 - -3)*(-3 + 1). Let j(l) be the second derivative of 2*l**b + l + 0 + l**3 + 1/6*l**4. What is y in j(y) = 0?
-2, -1
Suppose -12 - 12 = 4*n. Let o = -3 - n. Solve -2/11*x**o + 6/11*x**2 + 2/11 - 6/11*x = 0 for x.
1
Let d(y) be the second derivative of 0*y**2 - 1/70*y**5 + 1/147*y**7 - 1/105*y**6 + 0*y**3 + 0 + 1/42*y**4 - y. Factor d(b).
2*b**2*(b - 1)**2*(b + 1)/7
Let l(x) be the second derivative of x**4/3 + 2*x**3 + 2*x - 9. Factor l(d).
4*d*(d + 3)
Let w(b) be the second derivative of 1/12*b**3 + 3*b - 1/8*b**2 + 0*b**4 - 1/40*b**5 + 0 + 1/120*b**6. Factor w(h).
(h - 1)**3*(h + 1)/4
