 -5*z = u - 19. Factor 4 + 33*y + 15*y**4 + 26*y**3 + b*y**2 + 8*y**3 + 2 + 17*y**z.
3*(y + 1)**3*(5*y + 2)
Find x, given that -2*x**3 + 2*x + 2/3*x**2 + 2/3*x**4 - 4/3 = 0.
-1, 1, 2
Let n(h) be the second derivative of h**7/280 - h**5/80 + 2*h**2 - 2*h. Let l(f) be the first derivative of n(f). Factor l(r).
3*r**2*(r - 1)*(r + 1)/4
Factor 3*k**2 + 2*k + 31*k**3 - 14*k**3 - 16*k**3.
k*(k + 1)*(k + 2)
Let x = 9 + -14. Let s = x + 7. Factor -8*q + 8*q - 2*q + 5*q**s.
q*(5*q - 2)
Let b be (-3)/4 + (-11)/(-4). Let c = 0 + b. Let -2*g**4 + 6*g + 3*g - 12*g**c + 8*g**3 - 2 - g = 0. Calculate g.
1
Suppose -5*b = 3*i, 5 - 20 = 3*i. Solve 10*k**2 + 0*k**3 + 3*k**b + 3*k - 4*k**2 = 0 for k.
-1, 0
Let j(a) be the third derivative of -a**6/120 - a**5/120 + a**4/24 + a**3/12 + 4*a**2. Factor j(i).
-(i - 1)*(i + 1)*(2*i + 1)/2
Let r = -927 - -927. Suppose u - 1/2*u**3 + r - 1/2*u**2 = 0. Calculate u.
-2, 0, 1
Let x(r) be the first derivative of -2*r**5/5 + 4*r**4 + 6*r**3 - 26. Factor x(c).
-2*c**2*(c - 9)*(c + 1)
Suppose 1 = 5*b + 11. Let h = 0 - b. Solve -7*f - 2 + f**2 - h + 3*f + 14*f**2 = 0 for f.
-2/5, 2/3
Let c(o) be the first derivative of -o**8/504 + o**6/90 - o**4/36 - o**2 + 2. Let g(r) be the second derivative of c(r). Factor g(i).
-2*i*(i - 1)**2*(i + 1)**2/3
Let v(z) be the first derivative of -2*z**5/35 + z**4/7 - 8. Determine o so that v(o) = 0.
0, 2
Let l = -19 + 21. Let z = 18 + -13. Factor -k**z + 8*k**l - 8*k**2.
-k**5
Suppose 0 - 1/6*p - 1/6*p**2 = 0. What is p?
-1, 0
Let d(z) be the second derivative of -z**6/20 + z**4/4 - 3*z**2/4 - 5*z. Determine m so that d(m) = 0.
-1, 1
Let q(o) be the first derivative of o**6/15 - 8*o**5/25 + 3*o**4/5 - 8*o**3/15 + o**2/5 - 9. Factor q(a).
2*a*(a - 1)**4/5
Suppose 5*u = 4*u + 6. Let q(g) be the second derivative of -3*g + 1/10*g**5 + 0*g**2 + 0*g**4 + 1/15*g**u + 0 + 0*g**3. Let q(l) = 0. Calculate l.
-1, 0
Let q(s) be the first derivative of 0*s - 2 + 1/60*s**5 + 0*s**3 + s**2 + 1/24*s**4. Let f(y) be the second derivative of q(y). Factor f(k).
k*(k + 1)
Let p = -15 - -17. Factor 0*x**p + 0*x - 1/6*x**3 + 0 - 1/6*x**4.
-x**3*(x + 1)/6
Suppose 0 = -v + 4*q - 5, q = 2*v - 2*q. Let t(g) be the first derivative of 0*g - 2 + 1/12*g**v + 1/8*g**2. Find x such that t(x) = 0.
-1, 0
Let n(t) = t**3 + 9*t**2 + t + 12. Let y be n(-9). Factor -2 - 2*b**2 + 3*b**2 + 1 - b**y + b.
-(b - 1)**2*(b + 1)
Let y be 90/2*28/2. Suppose -a + 127 = -2*o, -4*o = 4*a - y + 122. What is x in -a*x**5 - 12*x**2 - 78*x**3 - 48*x**5 + 8*x - 8*x**2 + 265*x**4 = 0?
-2/7, 0, 2/5, 1
Suppose 0 = -4*s + 4*p, 2*p + 3 = 1. Let j = s - -3. Factor 18*a - j - 109/2*a**2 - 49/2*a**4 + 63*a**3.
-(a - 1)**2*(7*a - 2)**2/2
Let c(u) = -2*u**2 + 3*u + 4. Let z be c(3). Let y be 0/z*(2 - 1). Suppose 0*m - 8*m**5 + 14/3*m**3 - 4/3*m**2 + 14/3*m**4 + y = 0. What is m?
-2/3, 0, 1/4, 1
Let b(d) be the second derivative of -3*d + 1/42*d**4 - 1/7*d**3 + 2/7*d**2 + 0. What is k in b(k) = 0?
1, 2
Let x be (-112)/(-18) + (-4)/18. Suppose 0 = 2*j - 0*j - x. Factor -4*a - 7*a**3 + a**j + 3*a**4 + a**4 - 2*a**4 - 10*a**2 + 2*a**5.
2*a*(a - 2)*(a + 1)**3
Factor j**2 - 19*j**3 + 0*j**2 - 4*j**4 + 7*j**2 + 23*j**3.
-4*j**2*(j - 2)*(j + 1)
Let i(f) be the third derivative of 0*f - 1/120*f**5 + 0 - 1/24*f**4 - 1/12*f**3 - 3*f**2. Factor i(k).
-(k + 1)**2/2
Let w(n) = -4*n**3 - 2*n**2 + 4*n - 4. Let g be w(2). Let j be 2/(-4) + g/(-48). Factor 0 - 1/4*q + j*q**2.
q*(q - 1)/4
Let h be ((-10)/15)/((-2)/6). Solve 4*v + h*v**4 - 3*v**3 + 0*v**3 - 2*v**2 - 2*v + v**3 = 0.
-1, 0, 1
Let x(t) be the first derivative of -t**7/56 + t**6/60 - t**3 + 3. Let i(z) be the third derivative of x(z). Factor i(o).
-3*o**2*(5*o - 2)
Factor 4 - 52*n**4 + 68*n**3 - 5*n**2 - 2*n + 14*n**5 - 25*n**2 - 2*n**2.
2*(n - 1)**4*(7*n + 2)
Let m(i) be the first derivative of 2/7*i - 2/21*i**3 + 2 + 1/7*i**2 - 1/14*i**4. Find l, given that m(l) = 0.
-1, 1
Let y(q) be the third derivative of 1/28*q**4 - 4*q**2 - 1/140*q**6 + 1/490*q**7 + 0*q - 1/14*q**3 + 0 + 0*q**5. Factor y(j).
3*(j - 1)**3*(j + 1)/7
Determine v, given that -11 + v**4 - 2*v**3 + 6 + 5 = 0.
0, 2
Let b(v) be the third derivative of v**5/30 - v**3/3 + v**2. Factor b(i).
2*(i - 1)*(i + 1)
Suppose -88*t + 95*t = 0. Let j be (-2)/(-4)*(-4)/(-9). Factor -2/9*i + 0 + t*i**2 + j*i**3.
2*i*(i - 1)*(i + 1)/9
Factor -1/2 + 11/4*x**2 + 5/4*x + x**3.
(x + 1)*(x + 2)*(4*x - 1)/4
Let r(l) = 3*l**5 + 11*l**4 + 27*l**3 + 23*l**2 - 26*l - 38. Let y(k) = -k**5 - k**4 + k + 1. Let j(s) = r(s) + 2*y(s). Suppose j(p) = 0. Calculate p.
-3, -2, 1
Let r(y) be the second derivative of 0 + 0*y**3 + 0*y**2 + 0*y**4 - 2*y + 1/75*y**6 + 1/50*y**5. Find a, given that r(a) = 0.
-1, 0
Suppose -4*v + 15 = -3*l, 3*v + 0 = 3*l + 12. Suppose -v = -2*f + f. Factor 4*q + 0*q**2 + f*q**2 - 2 - 5*q**2.
-2*(q - 1)**2
Determine c, given that -1/3*c**3 + 5/3*c**2 - 2*c**4 + 2/3*c + 0 = 0.
-2/3, -1/2, 0, 1
Suppose 0 = -5*t + 5*n - 25, 4*t + 7*n = 2*n + 16. Let h = 3 + t. Factor -4*k - 8*k**h + 6*k**3 + k + 4 + k.
2*(k - 1)**2*(3*k + 2)
Let f(m) be the first derivative of -m**3 + 3/5*m**5 - 6 + 0*m + 3/2*m**2 - 3/4*m**4. Determine r so that f(r) = 0.
-1, 0, 1
Suppose -d - 8*d**5 + 4*d**2 - 4*d**4 + 0*d**5 + 0*d**5 + 12*d**3 - 3*d = 0. What is d?
-1, 0, 1/2, 1
Let t(b) be the third derivative of -1/30*b**4 + 2*b**2 + 0 + 0*b + 0*b**3 - 3/50*b**5 - 7/300*b**6. Solve t(x) = 0 for x.
-1, -2/7, 0
Let i(x) = -3*x**2 - 2. Let c(p) = 5*p**2 + 3. Let u(y) = -5*c(y) - 8*i(y). Solve u(r) = 0.
-1, 1
Let i(m) be the third derivative of m**5/300 + m**4/15 + 8*m**3/15 - 6*m**2. Factor i(c).
(c + 4)**2/5
Let d = -11 + 15. Let l be 2 + ((-16)/6)/d. Find n such that 8/3*n**4 + 2/3*n + 0 + l*n**3 - 2*n**5 - 8/3*n**2 = 0.
-1, 0, 1/3, 1
Let n(y) be the third derivative of y**9/60480 + y**8/20160 - y**5/60 + y**2. Let h(p) be the third derivative of n(p). Let h(c) = 0. What is c?
-1, 0
Let d = 19 + -37/2. Let s(x) be the third derivative of 3/10*x**5 + d*x**4 + 0 + x**2 + 1/3*x**3 + 1/15*x**6 + 0*x. Solve s(m) = 0 for m.
-1, -1/4
Let 0*w + 6/5*w**3 + 0 - 2/5*w**5 + 0*w**4 + 4/5*w**2 = 0. Calculate w.
-1, 0, 2
Let y(w) be the second derivative of -2*w**6/15 + 2*w**5/5 - 4*w**3/3 + 2*w**2 - 7*w. Factor y(a).
-4*(a - 1)**3*(a + 1)
Let i = -107 + 537/5. Let l(q) be the first derivative of i*q - 4/15*q**3 - 1/15*q**6 + 2/25*q**5 + 1 - 1/5*q**2 + 1/5*q**4. What is d in l(d) = 0?
-1, 1
Let x(t) be the second derivative of -t**7/126 + t**6/45 - t**5/60 - t. Suppose x(q) = 0. What is q?
0, 1
Let r = 1 - -7. Suppose -2 = 3*f - r. Factor -4*s + 2*s**4 + s**3 + 7*s**2 - s**f + 2*s - 7*s**3.
2*s*(s - 1)**3
Let z = 11 + -8. Suppose 0*k**3 + 5*k**3 - 4*k**z - k**4 - k + k**2 = 0. What is k?
-1, 0, 1
Let k be (0/2)/(3/((-9)/12)). What is o in 0*o**3 + 1/4*o**5 + 0*o + 0 + k*o**2 + 1/4*o**4 = 0?
-1, 0
Let d be 6/4 + 4/8. Suppose 5*l - 3*s = 19, -3*l + d*l + 3 = -s. Let -k**2 - 3*k**4 + 11*k**4 + 2*k**2 + 4*k**5 + l*k**3 = 0. Calculate k.
-1, -1/2, 0
Factor 9/5*g**2 - 4/5 + 16/5*g.
(g + 2)*(9*g - 2)/5
Let f(v) be the third derivative of -v**5/6 + v**4/3 - 4*v**3/15 - 4*v**2. Find i such that f(i) = 0.
2/5
Let c = 92/105 + -10/21. Factor -c*f + 1/5*f**2 + 1/5*f**3 + 0.
f*(f - 1)*(f + 2)/5
Let t(y) be the first derivative of 14*y**5/15 - y**4/3 - 5. What is x in t(x) = 0?
0, 2/7
Let w be 6 + -2 + 21/(-6). Suppose -3/2*o + w*o**2 + 3/2*o**3 + 1/2*o**4 - 1 = 0. What is o?
-2, -1, 1
Let l be 18/48*2 + (-1)/4. Factor 2*f**3 - 9/2*f**2 + 3*f - l.
(f - 1)**2*(4*f - 1)/2
Let k(d) be the third derivative of d**8/784 + 2*d**7/245 + 3*d**6/140 + d**5/35 + d**4/56 + 3*d**2. Factor k(b).
3*b*(b + 1)**4/7
Let x be (-8)/(-5) - (-86)/215. What is w in 2/3*w**3 - 4/3 + 0*w**2 - x*w = 0?
-1, 2
Suppose 7 = 4*y - 1. Factor k + 3*k + 2*k**3 + y - 6*k - 2*k**2.
2*(k - 1)**2*(k + 1)
Let s(b) be the second derivative of -b**10/18900 + b**9/9450 - b**8/16800 + 7*b**4/12 + 7*b. Let r(v) be the third derivative of s(v). Factor r(f).
-2*f**3*(2*f - 1)**2/5
Let w(n) be the second derivative of n**5/20 + n**4/6 + 6*n. Factor w(y).
y**2*(y + 2)
Let y(d) be the third derivative of d**8/7840 - d**7/2940 + d**6/2520 + d**5/30 + 3*d**2. Let a(p) be the third derivative of y(p). Let a(f) = 0. What is f?
1/3
Let u(x) = -x**3 + 9*x**2 - 6*x - 1.