5 + 2 + 26/3*t**2 + 38/3*t**3. Factor d(x).
(x + 1)*(x + 2)*(5*x + 2)**2/3
Let 1/2*a + 1/2*a**2 + 0 = 0. Calculate a.
-1, 0
Let i(v) = v**3 - v**2 + v - 1. Let w(g) = 4*g**4 - 23*g**3 + 43*g**2 - 3*g - 21. Let r(d) = -3*i(d) + w(d). Factor r(y).
2*(y - 3)**2*(y - 1)*(2*y + 1)
Let a(m) be the second derivative of m**6/120 - 2*m. Factor a(x).
x**4/4
Let g(f) = f**5 + 3*f**4 - 4*f**3 + 5*f**2. Let n(t) = t**5 + 5*t**4 - 6*t**3 + 7*t**2. Let q(v) = 7*g(v) - 5*n(v). Suppose q(l) = 0. Calculate l.
0, 1
Let n(z) be the first derivative of z**6/10 + 4*z**5/25 - 2*z**4/5 - 2*z**3/5 + z**2/2 + 2*z/5 + 19. Let n(c) = 0. What is c?
-2, -1, -1/3, 1
Suppose -3*c + 15 = 2*c. Suppose -5*j - 11 = -2*v, v + 2 = c*v + 4*j. Determine h so that -4/3*h**2 + 2/3*h**v + 0*h + 0 = 0.
0, 2
Factor 2/5*m**2 + 4/5*m + 2/5.
2*(m + 1)**2/5
Let x(j) be the first derivative of j**6/48 + j**5/8 + 5*j**4/16 + 5*j**3/12 + 5*j**2/16 + j/8 - 6. Suppose x(n) = 0. Calculate n.
-1
Let l be (-14)/77 - 35/(-11). Factor -30 + 8*k**l + 12*k**2 + 8*k + 0*k**3 + 2*k**4 + 32.
2*(k + 1)**4
Let f(b) be the second derivative of b**6/2340 + b**5/390 + b**4/156 + b**3/3 + 6*b. Let o(q) be the second derivative of f(q). Factor o(y).
2*(y + 1)**2/13
Suppose -3*x + 2 = -13. Suppose 20 = -4*f, x*y = 2*f - 4*f - 5. Factor 24*u**2 + u + 2*u + 6*u + y + 16*u**3.
(u + 1)*(4*u + 1)**2
Suppose 4*i + 0*i = 48. Suppose 2*c + 2*c - 28 = 3*z, 2*c - i = z. Factor -1/2*s**2 + 1/2*s**c + 1/2*s**3 + 0*s - 1/2*s**5 + 0.
-s**2*(s - 1)**2*(s + 1)/2
Let r(c) = 4*c - 2. Let o be r(1). Determine t, given that 14*t**2 - 3*t**3 - 20*t**o + 3 - 3*t**3 + 3*t**4 + 3*t + 3*t**5 = 0.
-1, 1
Factor -10/13*a - 2/13*a**3 - 8/13*a**2 - 4/13.
-2*(a + 1)**2*(a + 2)/13
Suppose 0*z = z - 2. Find n such that -4 + 12*n + n**z - 14*n + 5 = 0.
1
Let o(t) be the first derivative of -t**6/6 + 3*t**5/20 + 13*t**4/16 - 17*t**3/12 + 3*t**2/8 + t/2 + 1. What is d in o(d) = 0?
-2, -1/4, 1
Let a(m) be the first derivative of -5*m**4/12 + 4*m**3/3 - 3*m**2/2 + 2*m/3 + 16. Factor a(v).
-(v - 1)**2*(5*v - 2)/3
Let w be 0 + 1 + (-1)/(-1). Suppose -i = -1, 0 = 5*h + w*i - 12 - 0. Suppose -9*r**3 - 4*r**2 + 4 - 4*r**3 + r**3 - h*r**3 + 14*r = 0. What is r?
-1, -2/7, 1
Let c(s) be the first derivative of s**5/90 - s**3/27 - 5*s + 4. Let f(x) be the first derivative of c(x). Suppose f(y) = 0. Calculate y.
-1, 0, 1
Let n be (-26)/(-6) + 6/(-18). Suppose 2*z - n = 4. Factor 12*l - l**5 - 12*l + 2*l**z - l**3.
-l**3*(l - 1)**2
Let c = 26/3 - 76/9. Determine z, given that -c + 0*z + 2/3*z**2 - 4/9*z**3 = 0.
-1/2, 1
Let x(i) = -i**2 + 7*i - 4. Let o be x(6). Solve -3*y**o - 2*y**3 - 3*y**3 + 4*y**2 + 4*y**3 = 0 for y.
0, 1
Let z(y) be the second derivative of 1/6*y**4 + y + 0*y**2 + 11/135*y**6 + 1/6*y**5 + 1/63*y**7 + 0 + 2/27*y**3. Find s such that z(s) = 0.
-1, -2/3, 0
Let t(i) = 2*i**2 - 4*i - 3. Let n(s) = 4*s**2 - 2 - 1 + 4 - 5*s**2 + 2*s. Suppose -2 = 5*v + 8. Let o(j) = v*t(j) - 5*n(j). Factor o(b).
(b - 1)**2
Let c(a) be the second derivative of a**6/15 + 2*a**5/5 + 5*a**4/6 + 2*a**3/3 - 7*a. Suppose c(h) = 0. What is h?
-2, -1, 0
Suppose 16 - 1 = 3*v. Suppose 3*h - 20 = -h, q - v*h = -23. Factor 2/5 + 6/5*w**q - 2/5*w**3 - 6/5*w.
-2*(w - 1)**3/5
Let c(x) be the third derivative of -x**6/360 + x**4/72 - 8*x**2. Factor c(n).
-n*(n - 1)*(n + 1)/3
Let h(c) be the first derivative of -c**4/5 - 5*c**3/3 - 13*c**2/5 - c + 32. What is r in h(r) = 0?
-5, -1, -1/4
Let h(c) be the third derivative of c**7/1260 - c**6/360 - 7*c**5/360 - c**4/36 - 26*c**2. Determine w so that h(w) = 0.
-1, 0, 4
Let h = -10 - -13. Solve 8 - 3*w**2 + 12*w - 8*w**3 - 4*w - 3*w**2 + 0*w**h - 2*w**4 = 0 for w.
-2, -1, 1
Suppose 2 + 8 = 2*k. Suppose -5*s**5 + 9*s**k + 15*s + 30*s**2 + 30*s**3 + 15*s**4 - s**5 + 3 = 0. Calculate s.
-1
Let d be (8 - 3 - -3) + -5. Factor l + 1/3 + 1/3*l**d + l**2.
(l + 1)**3/3
Let z be (-70)/15 + 42/7. Factor -z*c**2 - 2/3*c**3 + 0 - 2/3*c.
-2*c*(c + 1)**2/3
Factor -27*z + 4*z**2 - 8*z**2 - 20 - 8*z + 11*z.
-4*(z + 1)*(z + 5)
Let y(k) be the third derivative of -k**8/42 - 2*k**7/15 - 73*k**6/240 - 43*k**5/120 - 11*k**4/48 - k**3/12 - 33*k**2 + k. Factor y(a).
-(a + 1)**3*(4*a + 1)**2/2
Let i(l) be the second derivative of -l**7/56 + 3*l**5/40 - l**3/8 - 18*l. Factor i(o).
-3*o*(o - 1)**2*(o + 1)**2/4
Let j(y) be the first derivative of y**9/1512 - y**7/210 + y**5/60 - 2*y**3/3 + 3. Let x(a) be the third derivative of j(a). Find l, given that x(l) = 0.
-1, 0, 1
Let d be (-4)/34 + 664/(-136) + 7. Solve -1/5*b + 0 - 1/5*b**d = 0 for b.
-1, 0
Let i = 31/6 - 9/2. Let a(z) be the first derivative of 1/2*z**4 + 1/3*z**2 + 10/9*z**3 - i*z - 1. Determine c so that a(c) = 0.
-1, 1/3
Let j(m) = 5*m**5 - 2*m**4 - 7*m**3 + 7*m**2 + 5*m - 2. Let g(b) = 10*b**5 - 5*b**4 - 15*b**3 + 15*b**2 + 10*b - 5. Let r(y) = -3*g(y) + 5*j(y). Factor r(i).
-5*(i - 1)**3*(i + 1)**2
Let f(d) be the first derivative of -3 - 3/10*d**2 - 4/15*d**3 + 1/5*d. Factor f(n).
-(n + 1)*(4*n - 1)/5
Let i(o) be the second derivative of -10*o + 0*o**2 - 2/3*o**3 - 1/3*o**4 + 0. Factor i(v).
-4*v*(v + 1)
Let g = 1 + 3. Determine m, given that -44*m**3 + m**4 + 50*m**3 + 2*m**g - 3*m**5 - 6*m**2 + 3 - 3*m = 0.
-1, 1
Solve 8*g**5 + 55*g**4 + 36*g**2 - 19*g**4 + 8*g - 8*g**3 + 64*g**3 = 0.
-2, -1, -1/2, 0
Let w be 1 + (-4)/(-6)*3. Suppose -3*s + u = 3*u, -w*u = s. Factor s*z**3 + 0 + 0*z**2 + 0*z - 2/13*z**5 + 2/13*z**4.
-2*z**4*(z - 1)/13
Let o(j) be the first derivative of j**5/30 + j**4/6 + j**3/3 - j**2/2 - 5. Let h(t) be the second derivative of o(t). Let h(r) = 0. What is r?
-1
Let l(v) be the second derivative of 3/4*v**4 + 0*v**2 - 3/10*v**6 + 1/4*v**5 + 0 - 1/6*v**7 + 1/3*v**3 - 8*v. Find o such that l(o) = 0.
-1, -2/7, 0, 1
Let r(o) be the second derivative of o**8/40320 - o**7/7560 + o**6/4320 - o**4/4 - o. Let w(x) be the third derivative of r(x). Factor w(s).
s*(s - 1)**2/6
Suppose y + 1 = z - 2, 0 = -y + 4*z - 12. Suppose 2 = -n + 5. Factor 7*c**4 + y - c**5 + n*c**5 - 1 - 2*c + 8*c**3 + 2*c**2.
(c + 1)**4*(2*c - 1)
Let j(o) = o**3 - 11*o**2 - 13*o + 14. Let w be j(12). Determine q, given that 3*q**4 + 0*q**5 - 3*q**3 - q**5 - 4*q**w + 5*q**2 = 0.
0, 1
Let l(z) be the second derivative of z**8/3360 - z**7/1680 + 5*z**3/6 + 4*z. Let b(x) be the second derivative of l(x). Find q, given that b(q) = 0.
0, 1
Let o(l) = l**3 - 4*l**2 - 5*l. Let n be o(5). Let a = 4 + -2. Factor 0*i**a + 2*i**2 + n*i**2.
2*i**2
Let f(w) be the second derivative of -3*w**5/20 - w**4/2 + 3*w**3/2 - 38*w. Factor f(x).
-3*x*(x - 1)*(x + 3)
Let y(o) be the second derivative of 0*o**2 + 0 - 1/9*o**4 - 1/60*o**5 - 2/9*o**3 - 4*o. Factor y(r).
-r*(r + 2)**2/3
Let c(b) be the first derivative of -b**8/168 + b**7/105 + b**2/2 + 3. Let m(k) be the second derivative of c(k). Suppose m(o) = 0. Calculate o.
0, 1
Let o(h) be the first derivative of -1/2*h**3 + 0*h**2 + 2*h + 1/8*h**4 - 9. Factor o(t).
(t - 2)**2*(t + 1)/2
Factor 9*k**3 - k**4 + 6*k**2 + 12*k - 12*k + 4*k**4.
3*k**2*(k + 1)*(k + 2)
Let g(q) = q**2 - 1. Let d(h) = 2*h**3 - 5*h**2 - 2*h + 5. Suppose s + 2*s - 3*o - 3 = 0, 4*s + 2*o = -8. Let m = 2 - s. Let p(i) = m*g(i) + d(i). Factor p(u).
2*(u - 1)**2*(u + 1)
Let h(c) be the second derivative of -1/2*c**2 - 1/12*c**4 - 1/3*c**3 + 0 + 8*c. Determine n, given that h(n) = 0.
-1
Let b(x) be the third derivative of -x**7/420 - x**6/80 - x**5/60 + 7*x**2. Factor b(f).
-f**2*(f + 1)*(f + 2)/2
Suppose -5*q + 10 = -5*o, 0 = -0*q - 2*q + o + 4. Factor 0*v - 2/3*v**q + 8/3*v**3 + 0 - 2*v**4.
-2*v**2*(v - 1)*(3*v - 1)/3
Let b be (-2)/(-5) - 3*(-3)/(-60). Factor b*r**2 + 1/4*r + 0.
r*(r + 1)/4
Let d = -49 + 92. Let m = d + -257/6. Let -1/6 + 1/6*u + 1/6*u**2 - m*u**3 = 0. Calculate u.
-1, 1
Find b, given that 1/2*b**4 + 0 - 9/2*b + 15/2*b**2 - 7/2*b**3 = 0.
0, 1, 3
Let u(y) = 3*y - 3*y + 20*y**5 - 8*y**2 + 4*y**3 + 2*y**2 - 32*y**4. Let r(p) = 7*p**5 - 11*p**4 + p**3 - 2*p**2. Let h(a) = 14*r(a) - 5*u(a). Factor h(i).
-2*i**2*(i - 1)**3
Let t(y) = -y + 36. Let f be t(0). Suppose -5*i - 2*o + f = 0, -2*i + 9 = 3*o - 12. Suppose 2*k**3 - 5*k**2 + 0*k**3 + 2 + 11*k**2 + i*k = 0. What is k?
-1
Let w(o) = 2*o**4 + 2*o**3 - 6*o - 2. Let j(t) = 2*t**4 + t**3 - 7*t - 2. Let n(h) = -2*j(h) + 3*w(h). Find m such that n(m) = 0.
-