**2 + 1 - 2/5*w**5 + w**4. Find c such that i(c) = 0.
0, 1
Let m(l) = 5*l**5 - 2*l**4 - l**3 + 2. Let u(q) = 16*q**5 - 7*q**4 - 2*q**3 + 7. Let s(w) = 7*m(w) - 2*u(w). Factor s(k).
3*k**3*(k - 1)*(k + 1)
Let g(i) be the first derivative of 2*i**5/15 + i**4/6 - 4*i**3/3 - 4*i**2/3 + 16*i/3 - 2. Factor g(s).
2*(s - 2)*(s - 1)*(s + 2)**2/3
Let m(n) be the first derivative of 8/21*n**3 + 0*n - 1 + 4/7*n**2 + 1/14*n**4. Factor m(o).
2*o*(o + 2)**2/7
Let y(k) be the first derivative of k**5 + 25*k**4/2 + 160*k**3/3 + 80*k**2 - 40. Factor y(u).
5*u*(u + 2)*(u + 4)**2
Let i(p) be the first derivative of -2*p**3/3 + 2*p**2 + 16*p - 23. Factor i(w).
-2*(w - 4)*(w + 2)
Factor 4/3*h + 2/3*h**2 - 16/3.
2*(h - 2)*(h + 4)/3
Let r(u) be the first derivative of -u**3/12 - u**2/8 - 12. Factor r(b).
-b*(b + 1)/4
Let x = 104/23 - 18697/4140. Let k(d) be the third derivative of 0*d**3 + 0 - x*d**5 + 0*d**4 - 1/360*d**6 - 2*d**2 + 0*d. Determine q, given that k(q) = 0.
-1, 0
Let s(h) be the third derivative of -h**8/2520 - h**7/1575 + h**6/900 + h**5/450 + 17*h**2. Let s(u) = 0. What is u?
-1, 0, 1
Let f(j) = -j + 7*j - j**2 - j + 3. Let l be f(5). Factor -6*c**2 - l*c - c + 3 - 1.
-2*(c + 1)*(3*c - 1)
Suppose 0 = -2*g + 6*g - 40. Let o = g + -10. Solve 0*c + 0 + 0*c**4 + o*c**2 - 1/2*c**3 + 1/2*c**5 = 0 for c.
-1, 0, 1
Let p = 52 + -16. Let h be 40/18 - 8/p. Determine b so that -b**3 + 4*b**2 - h*b - 2*b**3 + b**3 = 0.
0, 1
Let m(p) be the second derivative of 1/30*p**4 - 2/15*p**3 - p + 0 + 0*p**2. Find a, given that m(a) = 0.
0, 2
Suppose 0*t - 16 = 4*t - 4*j, -t = -2*j + 8. Suppose -k = -3*s + 9, 2*k + 4*s = -4 + 26. Factor c**k - 1/2*c**4 + t*c**2 - c + 1/2.
-(c - 1)**3*(c + 1)/2
Let s(j) = -5*j**3 - 4*j**2 + 5*j + 4. Let f(u) = -11*u**3 - 8*u**2 + 10*u + 9. Let o(p) = 6*f(p) - 13*s(p). Determine q, given that o(q) = 0.
1, 2
Suppose 0 = 6*b - 3*b - 12. Find f such that -2 + 18 + 3*f**2 - 12*f - b = 0.
2
Let c be (-6)/(-4)*42/9. Suppose -6*n + c*n - 3 = 0. Solve 1 + 8*s**2 - 11/2*s - 7/2*s**n = 0.
2/7, 1
Factor -125*j**4 - 5*j + 24*j + 25*j**3 + 12*j**2 + 68*j**2 + j.
-5*j*(j - 1)*(5*j + 2)**2
Suppose 0 = 3*q + 3 + 6. Let k be q/18 + (-38)/(-12). Find l, given that k*l**2 + 1 + l**3 + 6 - 6 + 3*l = 0.
-1
Let q(i) be the second derivative of -i**6/45 + 7*i**5/60 + i**4/6 + 7*i**3/6 + 3*i. Let j(m) be the second derivative of q(m). Suppose j(p) = 0. What is p?
-1/4, 2
Suppose -5*c - 4 = -c. Let j(w) = w**3 - w**2 + w - 1. Let b(z) = -108*z**5 - 162*z**4 - 32*z**3 + 36*z**2 + 20*z - 4. Let i(l) = c*b(l) + 4*j(l). Factor i(k).
2*k*(2*k - 1)*(3*k + 2)**3
Let f(u) be the third derivative of u**9/1512 - u**7/140 + u**6/90 + 5*u**3/6 + u**2. Let p(z) be the first derivative of f(z). Find i, given that p(i) = 0.
-2, 0, 1
Let g(s) be the second derivative of 1/9*s**3 + 0*s**4 - 1/30*s**5 + 0 - 4*s + 0*s**2. Solve g(l) = 0.
-1, 0, 1
Let s(l) be the first derivative of -6*l**3/7 - 16*l**2/7 + 8*l/7 + 19. Factor s(h).
-2*(h + 2)*(9*h - 2)/7
Suppose 5*k - 5 = -2*y, 3*k = -y + 4*y - 18. Factor 6*o - 2 - y*o**2 - 2*o**2 + o**2 + 0*o**3 + 2*o**3.
2*(o - 1)**3
Let y(t) be the second derivative of t**4/20 + 3*t**3/10 + 3*t**2/5 - 12*t. Factor y(m).
3*(m + 1)*(m + 2)/5
Let l(a) = a**3 + a**2 + a. Let z(n) = -46*n**3 - 56*n**2 + 76*n - 16. Let j(i) = -4*l(i) + z(i). Solve j(r) = 0 for r.
-2, 2/5
Suppose -4*w + 149 = 17. Determine s so that -s**2 - 3*s**2 - 3*s + 27*s**3 - w*s**4 + 12*s**5 + 3*s**2 - 2*s**2 = 0.
-1/4, 0, 1
Let k be 7/((-35)/15) - 16/(-5). Factor -1/5*p**2 - k*p**4 + 0 + 2/5*p**3 + 0*p.
-p**2*(p - 1)**2/5
Let z(r) be the third derivative of r**8/28 + 9*r**7/70 + 3*r**6/20 + r**5/20 - 2*r**2. Factor z(b).
3*b**2*(b + 1)**2*(4*b + 1)
Let k be (-2723)/33 - 2/(-11). Let u = 83 + k. Factor 1/3*y**2 + y + u.
(y + 1)*(y + 2)/3
Let b = -9 + 9. Suppose -m + b*m = -2. Solve 4*y + 0*y + 2 + 0*y + 2*y**m = 0 for y.
-1
Let i(r) be the first derivative of 2*r**5/5 - r**4 + 2*r**3/3 - 25. Factor i(f).
2*f**2*(f - 1)**2
Suppose -18 = -179*n + 170*n. Suppose 0*y**3 + 0 + 0*y**n + 3/2*y**4 + 0*y = 0. What is y?
0
Factor 0 + 3*z**4 + 0*z - 3/2*z**5 + 0*z**2 + 0*z**3.
-3*z**4*(z - 2)/2
Let u = 6 + -4. Suppose -4*n = -n + 5*z + 4, 0 = 5*n + 5*z. Suppose -3 + n*h**u - 1 + 11*h - 13*h = 0. Calculate h.
-1, 2
Suppose 3*s + 3*q + 18 = -0*s, -3*s = -3*q + 18. Let t = -4 - s. Factor -1/5*x + 0 + 1/5*x**t.
x*(x - 1)/5
Let u(p) be the third derivative of p**5/30 + p**4/3 + 4*p**3/3 + 35*p**2. Determine h, given that u(h) = 0.
-2
Let n be ((-28)/(-30) + (-9)/15)*0. Let t be (-8)/84*14/(-6). Factor -2/3*s + t*s**2 + n.
2*s*(s - 3)/9
Let c(q) be the second derivative of -2*q**7/63 + q**5/5 + 2*q**4/9 - 2*q. Factor c(r).
-4*r**2*(r - 2)*(r + 1)**2/3
Let x = -346/3 + 116. Let m**3 - x*m**2 - 1/3*m**4 + 0 + 0*m = 0. Calculate m.
0, 1, 2
Find d, given that 18*d**2 + 1479 - 1485 - 16*d - 17*d = 0.
-1/6, 2
Solve -8*h**2 + h + 5*h**3 - 5*h - h**3 + 8 = 0.
-1, 1, 2
Let n(m) be the first derivative of -3*m**8/112 - 4*m**7/35 - 3*m**6/20 + m**4/8 - 2*m**2 + 7. Let r(f) be the second derivative of n(f). Factor r(w).
-3*w*(w + 1)**3*(3*w - 1)
Let h be 52*-6*8/36. Let a = h - -70. Suppose -5/3*l + 5/3*l**3 + a*l**2 - 2/3 = 0. What is l?
-1, -2/5, 1
Let t be 5/(80/(-68)) - -5. Solve 3/2*a**4 + 0*a**3 - 3/2*a**2 + 0 + t*a**5 - 3/4*a = 0.
-1, 0, 1
Let p = 5 + -1. Let f(q) be the third derivative of 0*q + 1/21*q**p + 0 - 4/21*q**3 - 1/210*q**5 + q**2. Find i such that f(i) = 0.
2
Let b be (-3)/6 - (-5116)/(-2328). Let i = -3/97 - b. Find u such that 8/3 + i*u + 10/3*u**3 - 26/3*u**2 = 0.
-2/5, 1, 2
Let c be (136/(-140) - -1)*(-3 - -4). Let o(q) be the second derivative of 0*q**2 + 1/42*q**4 + 0*q**3 + 1/105*q**6 + 0 - 2*q - c*q**5. Factor o(t).
2*t**2*(t - 1)**2/7
Let r(h) be the third derivative of h**8/168 - 2*h**7/105 + h**5/15 - h**4/12 - 9*h**2. Factor r(l).
2*l*(l - 1)**3*(l + 1)
Let 26 - 2*f**2 - 26 - 2*f**3 = 0. Calculate f.
-1, 0
Factor 9*z**3 - 3*z**4 + 6*z**4 + 40*z**2 + 3*z - 31*z**2.
3*z*(z + 1)**3
Suppose 4 = 3*j - 2*j. Let d(y) be the first derivative of 1/6*y**6 - 2 + 0*y + 2/5*y**5 + 0*y**2 - 2/3*y**3 - 1/4*y**j. Factor d(a).
a**2*(a - 1)*(a + 1)*(a + 2)
Let x(j) = j**2 - j + 1. Let n(z) = 4*z**3 - 3*z**2 + 4*z - 4. Let l(o) = -3*n(o) - 12*x(o). Factor l(g).
-3*g**2*(4*g + 1)
Let n be (-30)/(-9) + (-4)/(-6). Suppose n*f + 2*q - 15 = -3*q, 2*q - 6 = -3*f. Determine d, given that -1/3*d**3 - 2/3*d**2 + f - 1/3*d = 0.
-1, 0
Let w(f) be the second derivative of -1/15*f**4 + 4/15*f**3 - 2/5*f**2 - 4*f + 0. Find i, given that w(i) = 0.
1
Let j(b) be the third derivative of b**8/672 - b**7/420 - b**6/240 + b**5/120 + 6*b**2. Suppose j(p) = 0. Calculate p.
-1, 0, 1
Let h(p) be the first derivative of p**4 + 4*p**3 + 6*p**2 + 4*p + 15. Factor h(b).
4*(b + 1)**3
Factor x - 1/2*x**2 - 1/2.
-(x - 1)**2/2
Solve -2 - 14/3*n - 10/3*n**2 - 2/3*n**3 = 0 for n.
-3, -1
Suppose 8*r = 13 + 11. Let f(g) be the second derivative of -g**2 + 1/10*g**5 + 1/6*g**4 + 0 - g - 1/3*g**r. Factor f(j).
2*(j - 1)*(j + 1)**2
Let o(y) be the first derivative of 7*y**6/1440 + y**5/30 + y**4/24 - y**3/3 + 2. Let s(a) be the third derivative of o(a). Factor s(j).
(j + 2)*(7*j + 2)/4
Suppose 6*f - 3*f - 8 = -4*p, -8 = -4*p + 4*f. Factor 0*a**p - 3/4*a + 1/4*a**3 - 1/2.
(a - 2)*(a + 1)**2/4
Let b(h) be the first derivative of -h**5/20 - h**4/16 + h**3/6 - 10. Find s such that b(s) = 0.
-2, 0, 1
Suppose 4*h + h + 17*h = 0. Find o such that -2/3*o + h + 4/3*o**2 - 2/3*o**3 = 0.
0, 1
Let z(y) be the third derivative of y**5/60 + y**4/24 - y**3/3 - 37*y**2. Factor z(v).
(v - 1)*(v + 2)
Suppose -v + 0*v = -28*v. Factor v - 3/7*w**2 + 0*w + 1/7*w**3.
w**2*(w - 3)/7
Factor 12*y**2 - 4*y**2 - 4*y - 9*y**2 - 3*y**2.
-4*y*(y + 1)
Suppose 0 + 1/3*x**4 + 0*x + 0*x**3 - 1/3*x**2 = 0. Calculate x.
-1, 0, 1
Let c = -2/307 - -636/3377. Let o = 8/77 + c. Solve o*g**2 - 4/7*g + 0 = 0 for g.
0, 2
Let l(o) be the third derivative of 0*o + 0 + 0*o**4 + 3*o**2 + 1/1050*o**7 + 0*o**3 + 1/1680*o**8 - 1/300*o**5 - 1/600*o**6. Factor l(m).
m**2*(m - 1)*(m + 1)**2/5
Let g(r) be the second derivative of -r**7/126 - r**6/15 - 13*r**5/60 - r**4/3 - 2*r**3/9 - 18*r. What is a in g(a) = 0?
-2, -1, 0
Let f(o) = -o**2 - 7*o + 8. Let b be f(-8). Factor 0 + b*c**2 + 2/