- 5. Suppose 9 = 4*s + y. Determine l so that -4*l + 4*l**s - 5*l + 3*l + 2 = 0.
1/2, 1
Let c(g) be the second derivative of -g**7/60 - g**6/15 - g**5/20 + g**4/6 + 2*g**3/3 + g. Let j(f) be the second derivative of c(f). Factor j(y).
-2*(y + 1)**2*(7*y - 2)
Let a(c) = c**5 + 3*c**4 + 3*c**3 - 3*c**2 + 2*c. Let d(b) = -b**5 - b**4 - b**3 + b**2 - b. Let v(l) = -a(l) - 2*d(l). Let v(o) = 0. What is o?
-1, 0, 1
Suppose -6 - 16 = -3*l + 2*x, 3*l = 4*x + 32. Let 0 - 1/3*f**3 + 2/3*f**5 + f**l - f**2 - 1/3*f = 0. What is f?
-1, -1/2, 0, 1
Let m(o) be the second derivative of 1/30*o**6 - 1/20*o**5 - o + 0*o**2 + 0 - 1/12*o**4 + 1/6*o**3. Find i such that m(i) = 0.
-1, 0, 1
Let b = 14 + -11. Factor 7*c**2 - 4*c + 3*c - b*c**2.
c*(4*c - 1)
Let t = 24 - 18. Let s = t + -17/3. Find f such that -s*f**3 + f**2 - 4/3 + 0*f = 0.
-1, 2
Suppose 0*u + 12 = 4*u + 4*c, 12 = 4*u + 2*c. Factor -14/5*v**u - 18/5*v**2 - 4/5*v + 0.
-2*v*(v + 1)*(7*v + 2)/5
Let n(x) = 5*x**2. Let u be n(1). Let s(j) be the second derivative of 0 - j - 1/18*j**3 + 1/60*j**u - 1/36*j**4 + 1/90*j**6 + 0*j**2. Let s(h) = 0. What is h?
-1, 0, 1
Determine j so that 8*j**3 + 12*j**2 + 2*j**3 + 4*j + 2*j**3 + 4*j**4 = 0.
-1, 0
Factor 1/4*j - 1/4*j**4 + 3/4*j**3 + 0 - 3/4*j**2.
-j*(j - 1)**3/4
Let b be (8/56)/((-2)/(-12)). Factor 8/7*h**2 - 2/7 - b*h.
2*(h - 1)*(4*h + 1)/7
Let q(n) be the first derivative of 1/9*n**3 + 1/5*n**5 + 0*n**2 + 1/4*n**4 + 3 + 1/18*n**6 + 0*n. Factor q(h).
h**2*(h + 1)**3/3
Find m, given that -9*m**2 - 1/4*m**4 - 5/2*m**3 - 27/2*m - 27/4 = 0.
-3, -1
Let y(d) be the second derivative of -7*d**6/120 + d**5/40 + 7*d**4/48 - d**3/12 - 5*d. Factor y(w).
-w*(w - 1)*(w + 1)*(7*w - 2)/4
Let u(m) be the second derivative of 343*m**5/110 - 98*m**4/11 + 112*m**3/11 - 64*m**2/11 - 13*m. Factor u(r).
2*(7*r - 4)**3/11
Let b(l) be the third derivative of -l**10/75600 + l**8/8400 - l**6/1800 - l**4/12 + l**2. Let a(z) be the second derivative of b(z). Factor a(h).
-2*h*(h - 1)**2*(h + 1)**2/5
Let j = -274/5 - -55. Let d(h) be the third derivative of -8*h**3 - h**2 - 6/5*h**5 + 0 + 0*h + j*h**6 + 4*h**4 - 1/70*h**7. Factor d(c).
-3*(c - 2)**4
Factor 0 + 0*s - 4/7*s**4 - 16/7*s**3 - 16/7*s**2.
-4*s**2*(s + 2)**2/7
Let 28*t**3 - 5*t - 5*t**5 - 20*t**2 - 13*t**3 - 5*t**3 + 10*t**4 + 10 = 0. What is t?
-1, 1, 2
Let h = -435094/9 + 48401. Let t = h - 57. Find r such that -t*r**2 + 0*r + 0 - 2/9*r**4 + 4/9*r**3 = 0.
0, 1
Let a be (18/(-3))/((-2)/10). Suppose -31*z**3 + 2*z + a*z**3 - z = 0. What is z?
-1, 0, 1
Let s be (-3600)/624*(-4)/(-6) + 4. Factor 2/13*f**5 - 4/13*f**4 - s*f + 0*f**3 + 4/13*f**2 + 0.
2*f*(f - 1)**3*(f + 1)/13
Let s = -20231/72 + 281. Let j(h) be the third derivative of -2*h**2 + 0*h**6 + 0*h**3 + 0 + 0*h - s*h**4 + 1/90*h**5 - 1/315*h**7 + 1/1008*h**8. Factor j(q).
q*(q - 1)**3*(q + 1)/3
Let f = 3 - 1. Let v be (1/7)/(159/(-21) - -8). Determine z, given that v*z**3 - f*z**2 + 4*z - 8/3 = 0.
2
Let g be (-6)/(-3)*((-294)/(-48) + -5). Let 3/2*j - 1/4*j**2 - g = 0. What is j?
3
Suppose -2*f = -5*f + 30. Let k be (4/f)/(1/10). Factor -h**4 + 6*h**5 + 4*h**3 + 2*h**k - 11*h**4.
2*h**3*(h - 1)*(3*h - 2)
Suppose 2*m = -4 + 10. Let x = 3 + m. Factor -2*t**2 - x*t - 4 - 2*t - 4.
-2*(t + 2)**2
Let w(t) = -4*t**2 - 32*t + 12. Let i(j) = j - 1. Let r(c) = 20*i(c) + w(c). Factor r(x).
-4*(x + 1)*(x + 2)
Let n(c) be the third derivative of c**5/60 + 5*c**4/12 + 25*c**3/6 + 10*c**2. Factor n(z).
(z + 5)**2
Let l(j) be the second derivative of j**5/5 - j**4/3 - 8*j. Determine i so that l(i) = 0.
0, 1
Let x = 3329/4 - 832. Suppose 0 = 3*c - 14 + 5. Factor 1/2*v**2 + 0 + 1/4*v**c + x*v.
v*(v + 1)**2/4
Let b = 20/3 + -19/3. Determine q so that 2/3 + b*q - 1/3*q**2 = 0.
-1, 2
Solve 12*n**2 - 5*n**5 + 12*n**4 - 44*n**3 + 4*n**3 + 8*n**2 + 13*n**4 = 0.
0, 1, 2
Let c(n) be the second derivative of -n**6/15 + 2*n**5/5 - 2*n**4/3 + 45*n. Factor c(a).
-2*a**2*(a - 2)**2
Let b(z) = z**2 - 2*z - 4. Let t be b(4). Factor q**2 - 4*q - 7*q**2 + q**t + q**4.
2*q*(q - 2)*(q + 1)**2
Factor 2/3*n + 5/3*n**2 + 4/3*n**3 + 0 + 1/3*n**4.
n*(n + 1)**2*(n + 2)/3
Let y(j) be the first derivative of -4/15*j**3 + 13/10*j**4 + 2/5*j - 13/10*j**2 + 2/25*j**5 - 13/30*j**6 + 3. Let y(r) = 0. Calculate r.
-1, 2/13, 1
Let q be 13 - (2 - 0 - 4). Find o such that -23*o**2 - 7*o**2 + q*o**5 + 9*o**4 + 2*o**4 + 6 - 3*o + 13*o**4 - 12*o**3 = 0.
-1, 2/5, 1
Let o(m) = -4*m**4 + 32*m**3 - 20*m**2 - 8. Let a(v) = 3*v**4 - 21*v**3 + 13*v**2 + 5. Let j(n) = -8*a(n) - 5*o(n). Determine c so that j(c) = 0.
0, 1
Let f be -1 + -3 + (1672/18)/22. Factor f + 0*n - 2/9*n**2.
-2*(n - 1)*(n + 1)/9
Let r(v) be the first derivative of 2*v**6 - 4*v**5 - 7*v**4 + 28*v**3 - 32*v**2 + 16*v - 14. Suppose r(g) = 0. Calculate g.
-2, 2/3, 1
Let d(i) = i**4. Suppose -3*m + 4*h + 3 = 0, -3*m + 1 = h - 2. Let t(s) = -3*s**3 + 4*s. Let y(x) = m*d(x) + t(x). Factor y(u).
u*(u - 2)**2*(u + 1)
Let t(w) be the first derivative of 0*w**2 + 1/6*w**3 + 0*w - 1. Suppose t(c) = 0. Calculate c.
0
Let 1/9*y**3 + 1/9*y**4 - 2/9*y**2 + 0*y + 0 = 0. What is y?
-2, 0, 1
Suppose -4*g + 0*g = -236. Let s = -294/5 + g. Factor -s*k**4 + 1/5*k**3 + 1/5*k**2 - 1/5*k + 0.
-k*(k - 1)**2*(k + 1)/5
Suppose -t = 9 - 13. Factor -35*p**3 + 0 - 98/3*p**t - 4/3*p - 12*p**2.
-p*(2*p + 1)*(7*p + 2)**2/3
Let n = -48 - -51. Let l(j) be the third derivative of 1/48*j**4 + 0 - 1/240*j**6 + n*j**2 + 0*j + 0*j**5 + 0*j**3. Factor l(m).
-m*(m - 1)*(m + 1)/2
Let r = 15 - 8. Let h(w) = 4*w**3 + 10*w**2 + 4*w - 2. Let x(a) = -13*a**3 - 31*a**2 - 11*a + 7. Let o(i) = r*h(i) + 2*x(i). Solve o(l) = 0.
-3, -1, 0
Let a(u) = 21*u**3 + 11*u**2 - 16*u - 7. Let p(j) = 5*j**3 + 3*j**2 - 4*j - 2. Let i(h) = -2*a(h) + 9*p(h). Suppose i(q) = 0. Calculate q.
-2, -2/3, 1
Let y(b) be the first derivative of -b**7/1960 - b**6/210 - b**5/56 - b**4/28 + 5*b**3/3 + 6. Let s(h) be the third derivative of y(h). Factor s(m).
-3*(m + 1)**2*(m + 2)/7
Suppose -15 = -4*w - 11. Let m(f) be the first derivative of -1/6*f**2 + 1/9*f**3 - 1/3*f + 1/12*f**4 - w. Factor m(d).
(d - 1)*(d + 1)**2/3
Let r = 8 + -4. Suppose 0*h**2 + r*h - 3*h - 6 + 2*h + 3*h**2 = 0. What is h?
-2, 1
Suppose -3*k = 3*g - 18, -25 = -5*k - g + 5. Let z(w) be the first derivative of 0*w + 2/3*w**3 - 3/4*w**4 - 1/12*w**k - 1/4*w**2 + 2/5*w**5 - 2. Factor z(v).
-v*(v - 1)**4/2
Let n(t) = t**2 + 8*t + 2. Let v be n(-7). Let d = v - -5. Factor 1/4*m**2 + 1/4*m**3 - 1/2*m + d.
m*(m - 1)*(m + 2)/4
Let u be 2/4 + 36/24. Factor -5*t + 12*t**u + 2*t**3 - 6*t**3 - 16 + 5*t.
-4*(t - 2)**2*(t + 1)
Let w(b) be the first derivative of -b**4/14 + 2*b**3/21 + 2*b**2/7 - 43. Factor w(t).
-2*t*(t - 2)*(t + 1)/7
Factor 1/4*j**2 + 7/4*j + 3.
(j + 3)*(j + 4)/4
Suppose -4*l = 6*l - 20. Factor 3/5*p**l - 9/5*p + 6/5.
3*(p - 2)*(p - 1)/5
Let d(f) be the first derivative of -f**6/6 + 4*f**5/5 - 3*f**4/4 - 4*f**3/3 + 2*f**2 + 10. Factor d(l).
-l*(l - 2)**2*(l - 1)*(l + 1)
Let m(p) be the first derivative of -7*p**3/4 + 15*p**2/8 + 3*p/2 + 7. Find l, given that m(l) = 0.
-2/7, 1
Factor 0 + 6/7*j**4 - 10/7*j**3 + 4/7*j**2 + 0*j.
2*j**2*(j - 1)*(3*j - 2)/7
Let f(k) be the third derivative of -2/315*k**7 + 0*k**6 - 1/504*k**8 + k**2 + 1/36*k**4 + 0*k + 1/45*k**5 + 0*k**3 + 0. Factor f(d).
-2*d*(d - 1)*(d + 1)**3/3
Factor 9/7*u - 12/7*u**2 + 0 + 3/7*u**3.
3*u*(u - 3)*(u - 1)/7
Let l(q) = -q**5 - q**4 - q**2 - q - 1. Let r(h) = -8*h**4 - 4*h**3 + 16*h**2 + 12*h + 4. Let i(d) = -4*l(d) - r(d). Suppose i(s) = 0. Calculate s.
-2, -1, 0, 1
Let w(t) be the first derivative of 1/2*t**2 + 0*t + 3/4*t**4 - 3 - t**3 - 1/5*t**5. Suppose w(u) = 0. Calculate u.
0, 1
Let d(y) = -2*y**5 + y**5 + 2*y**5. Let m(t) = 6*t**5 + 6*t**4 + 4*t**3. Let c(x) = 4*d(x) - m(x). Factor c(g).
-2*g**3*(g + 1)*(g + 2)
Let w(i) be the third derivative of i**8/5760 - i**7/1260 + i**6/1440 + i**5/360 - i**4/3 - 9*i**2. Let d(s) be the second derivative of w(s). Factor d(g).
(g - 1)**2*(7*g + 2)/6
Suppose -12 = 3*r, l + 9 = -4*r - 7. What is x in -2/7*x**2 - 4/7*x**3 - 2/7*x**4 + l + 0*x = 0?
-1, 0
Let g be -2*9/(-6) + -1. Factor 0*m**2 - 5*m**2 + 3*m + 3*m**g + 4*m**2 - m**3.
-m*(m - 3)*(m + 1)
Let u = -6/53 + 242/265. Let u*v**4 + 0*v - 2/5*v**3 + 2/5*v**5 - 4/5*v**2 + 0 = 0. What is v?
-2, -1, 0, 1
Let a b