6*a**2. Find f, given that j(f) = 0.
-2, -1, 1
Suppose 8*a + 68 - 108 = 0. Factor -1/2 - i**3 - 1/2*i**4 + 1/2*i + i**2 + 1/2*i**a.
(i - 1)**3*(i + 1)**2/2
Let l(q) be the first derivative of -q**6/3 + 12*q**5/5 - 13*q**4/2 + 8*q**3 - 4*q**2 - 4. Solve l(k) = 0 for k.
0, 1, 2
Let q = 109/2 + -54. Determine k, given that q*k + 1/4 + 1/4*k**2 = 0.
-1
Factor -13 - 18*n - 3*n**2 + 4 - 6 - 12.
-3*(n + 3)**2
Solve 2/7*z**2 + 0 + 10/7*z**3 + 0*z = 0.
-1/5, 0
Let k(c) be the third derivative of -c**6/200 + c**5/50 - c**4/40 + 6*c**2. Factor k(s).
-3*s*(s - 1)**2/5
Let g(b) be the first derivative of -b**4/48 + b**2/8 - 3*b - 3. Let p(r) be the first derivative of g(r). Find d, given that p(d) = 0.
-1, 1
Let -8/7 + 0*d**2 - 4/7*d**3 + 12/7*d = 0. Calculate d.
-2, 1
Factor 3*f**2 - 1 + 23*f - 31*f - 2.
(f - 3)*(3*f + 1)
Let r = 17/108 + -3/20. Let d(x) be the third derivative of 1/540*x**6 + r*x**5 + 2*x**2 + 0 + 0*x**3 + 1/108*x**4 + 0*x. Factor d(n).
2*n*(n + 1)**2/9
Let w(c) = c**2 + 3*c + 2. Suppose -13 = 4*g - 1. Let k(u) = u**2 + 5*u + 4. Let b(t) = g*k(t) + 5*w(t). Factor b(f).
2*(f - 1)*(f + 1)
Let p be 2*-1 - ((0 - 3) + -1). Let t(y) be the second derivative of 0 - p*y - 1/6*y**4 + 1/6*y**3 + 1/20*y**5 + 0*y**2. Determine z, given that t(z) = 0.
0, 1
Let x = 93/7 - 13. Let u be (-100)/(-126) + (12/(-27))/2. Factor 2/7 + u*s + x*s**2.
2*(s + 1)**2/7
What is q in 9/7*q + 3/7*q**2 + 0 = 0?
-3, 0
Let j(q) be the first derivative of 4*q**3/3 - 4*q**2 + 4*q + 11. Factor j(z).
4*(z - 1)**2
Let d = 692/5943 - 6/283. Let c(i) be the first derivative of 1/7*i**2 + 0*i - d*i**3 + 3. Factor c(v).
-2*v*(v - 1)/7
Let l(a) = -7*a**5 - 21*a**4 - 50*a**3 - 76*a**2 - 51*a - 16. Let i(k) = -k**5 - k**4 + k. Let b(h) = -5*i(h) + l(h). Suppose b(z) = 0. Calculate z.
-2, -1
Let y(p) = p**5 + p**3 + 1. Let v(m) = 4*m**5 - 2*m**4 + 8*m**3 + 2*m**2 + 6. Let l(j) = v(j) - 6*y(j). Factor l(o).
-2*o**2*(o - 1)*(o + 1)**2
Let i be 0*(1 + -1 - 2)/(-4). Factor i - 4/7*g - 6/7*g**2 - 2/7*g**3.
-2*g*(g + 1)*(g + 2)/7
Suppose -3*i + 65 = -2*x - 3*x, -3*x - i - 25 = 0. Let d = -6 - x. Factor -f**2 + 2*f**5 - f**5 - 2*f**4 + 0*f**4 - f**d + 3*f**3.
f**2*(f - 1)**3
Suppose 5*t = -5*u - 85, 101 = -5*t + 4*u - 5*u. Let l(b) = b + 1. Let k(y) = -y**3 + 7*y + 7. Let s(z) = t*l(z) + 3*k(z). Factor s(f).
-3*f**3
Let b(o) = -3*o**3 + 6*o**2 + 9*o - 12. Let i(l) = -6*l**3 + 12*l**2 + 19*l - 25. Let a(x) = -13*b(x) + 6*i(x). Suppose a(q) = 0. What is q?
-1, 1, 2
Suppose -8*b + 11 + 5 = 0. Determine t, given that 0 - 2/5*t - 2/5*t**b = 0.
-1, 0
Let j = 115 - 113. Let s(h) be the third derivative of 4*h**j + 1/42*h**4 + 0*h + 1/21*h**3 + 0 + 1/210*h**5. Determine q, given that s(q) = 0.
-1
Factor 4/9 - 2/3*q + 2/9*q**2.
2*(q - 2)*(q - 1)/9
Let o be 2/(-8) - 711/(-2700). Let u(r) be the second derivative of 0*r**2 - 2*r + 0 + 0*r**3 + 3/100*r**5 - 1/60*r**4 - o*r**6. Find l such that u(l) = 0.
0, 1/2, 1
Let x(b) be the first derivative of -b**2/2 + 11*b + 2. Let d be x(9). Factor 10*i - 6 - 2*i - d*i**2 - 2.
-2*(i - 2)**2
Let t(x) = -6*x**3 - 10*x**2 - 8*x - 4. Let d(w) = -w**3 - 1. Let a(o) = -4*d(o) + t(o). Factor a(n).
-2*n*(n + 1)*(n + 4)
Let q = -4 + 0. Let t be ((-2)/q)/(1/3). Factor -1/2*x**2 - t*x - 1.
-(x + 1)*(x + 2)/2
Let s(c) be the second derivative of -1/24*c**4 + 0*c**2 + 0*c**3 + 1/24*c**6 + 3/80*c**5 - 5*c + 0. Suppose s(z) = 0. What is z?
-1, 0, 2/5
Let t(s) be the third derivative of -s**7/35 - s**6/40 + s**5/10 + s**4/8 + 6*s**2. Suppose t(w) = 0. What is w?
-1, -1/2, 0, 1
Let c = 48 + -30. Factor -29*l - 4*l**3 + 15*l + c*l.
-4*l*(l - 1)*(l + 1)
Let n(u) be the second derivative of u**8/336 - u**7/105 + u**6/120 + 5*u**2/2 + 5*u. Let m(t) be the first derivative of n(t). Factor m(f).
f**3*(f - 1)**2
Factor -53*f**3 - 58*f**3 + 5*f + 106*f**3 - 2*f**2 + 2.
-(f - 1)*(f + 1)*(5*f + 2)
Let o be (-2 - -2)*(-2)/4. Suppose o = -a - 5*c + 5 - 15, -2*a - 3*c + 1 = 0. Factor 3*j**2 - a*j**2 - 4*j + 2*j.
-2*j*(j + 1)
Let g(f) = f**3 - f**2 - f + 1. Let m(p) = 2*p**3 - 4*p**2 + 2*p + 8. Let i(d) = 4*g(d) - m(d). Determine a, given that i(a) = 0.
-1, 2
Let u = -579/2 - -290. Factor -4*x + 2 - u*x**3 + 5/2*x**2.
-(x - 2)**2*(x - 1)/2
Let z(l) be the second derivative of 1/5*l**2 - 2/15*l**3 - l + 1/30*l**4 + 0. Determine g, given that z(g) = 0.
1
Find t, given that 26/7*t**2 + 0 + 10/7*t**3 - 12/7*t = 0.
-3, 0, 2/5
Let j(i) be the first derivative of -3/2*i**2 + 0*i**3 - 1/60*i**5 + 2 - 1/24*i**4 + 0*i. Let n(f) be the second derivative of j(f). Factor n(t).
-t*(t + 1)
Let n(l) be the first derivative of 3*l**5/25 + l**4/4 + l**3/15 - l**2/10 + 6. Factor n(g).
g*(g + 1)**2*(3*g - 1)/5
Let r be 3 - (-3)/(-9)*3. Suppose 3*n + 2*w + 4 = 0, -2*n + 20 - 6 = -r*w. Let 0 - n*u**4 + 2/5*u**3 + 0*u + 0*u**2 + 8/5*u**5 = 0. Calculate u.
0, 1/4, 1
Let j(t) be the first derivative of t**6/120 + t**5/40 - t**3/12 - t**2/8 + 2*t + 1. Let d(k) be the first derivative of j(k). Factor d(h).
(h - 1)*(h + 1)**3/4
Let -3/2*v**4 - 1 - 1/2*v**3 - 3/2*v + 9/2*v**2 = 0. Calculate v.
-2, -1/3, 1
What is z in -21*z**2 - 16*z + 4*z**3 + 30*z**2 - 16 - 5*z**2 = 0?
-2, -1, 2
Factor -7/3*g**3 + 16/3*g**2 - 2 + 17/3*g.
-(g - 3)*(g + 1)*(7*g - 2)/3
Factor -4/7*k - 2/7*k**2 + 0.
-2*k*(k + 2)/7
Let k(g) be the first derivative of 27*g**4/16 + 29*g**3/4 + 9*g**2 + 3*g + 25. What is u in k(u) = 0?
-2, -1, -2/9
Let y(l) be the third derivative of l**5/180 + l**4/24 + l**3/9 + 13*l**2. Factor y(m).
(m + 1)*(m + 2)/3
Let g(k) be the second derivative of k**6/10 - 3*k**5/10 + k**3 - 3*k**2/2 + 8*k. Suppose g(i) = 0. What is i?
-1, 1
Let b(w) be the first derivative of w**6/150 + w**5/100 - w**4/20 - w**3/30 + w**2/5 + w - 2. Let t(l) be the first derivative of b(l). Solve t(m) = 0 for m.
-2, -1, 1
Suppose -1 = 5*m + 19. Let l be (m - 56/(-12))*3. Factor 12/5*g + 3/5*g**l + 12/5.
3*(g + 2)**2/5
Factor -2/5*b - 1/5*b**2 + 3/5.
-(b - 1)*(b + 3)/5
Let m(v) = -v**5 + v**3 + v**2 + v - 1. Let q(r) = 77*r**5 + 81*r**4 - 50*r**3 - 26*r**2 + 25*r - 7. Let f(g) = -4*m(g) + q(g). Let f(b) = 0. Calculate b.
-1, 1/3
Let n(u) be the third derivative of 0*u + 1/2*u**3 - 1/40*u**5 + u**2 + 0 + 1/16*u**4. Factor n(x).
-3*(x - 2)*(x + 1)/2
Let i(k) = -k + 11. Let j be i(6). Let c(r) be the third derivative of 0 + 0*r + 1/4*r**4 + 1/3*r**3 + r**2 + 3/40*r**j. Factor c(x).
(3*x + 2)**2/2
Let f = -2/49 - -59/245. Let v(j) be the first derivative of -2 - f*j**2 - 1/5*j**6 + 2/5*j**4 - 4/15*j**3 + 0*j + 4/25*j**5. Suppose v(i) = 0. What is i?
-1, -1/3, 0, 1
Let d(i) be the first derivative of -i**7/4620 - i**6/990 + 4*i**3/3 + 5. Let o(n) be the third derivative of d(n). Determine a so that o(a) = 0.
-2, 0
Suppose -2/5*t**4 + 0 - 2/3*t**3 - 2/15*t**2 + 2/15*t = 0. What is t?
-1, 0, 1/3
Let f be ((-8)/10)/((-2)/5). Suppose 5*d + 4*l = f*l + 25, -4*l = 5*d - 25. Factor -d*m**3 + 5*m**5 - 2*m + 0*m + 2*m**3 + 7*m**4 - 7*m**2.
m*(m - 1)*(m + 1)**2*(5*m + 2)
Let k(g) = -21*g**2 + 3*g + 18. Let t(i) = -6*i**2 + i + 5. Let j(d) = 5*k(d) - 18*t(d). Determine w, given that j(w) = 0.
0, 1
Let h(a) be the third derivative of -1/15*a**5 - 1/672*a**8 + 7/48*a**4 + 1/210*a**7 + 0 + 0*a + 6*a**2 + 1/120*a**6 - 1/6*a**3. Solve h(c) = 0.
-2, 1
Suppose -42*m + 43*m = 2. Factor 8/3*h - 2 - 2/3*h**m.
-2*(h - 3)*(h - 1)/3
Let t(h) be the third derivative of h**7/120 + h**6/120 + h**4/3 - 3*h**2. Let w(v) be the second derivative of t(v). Factor w(l).
3*l*(7*l + 2)
Let q = -5 + 5. Suppose i = 4*d - 8*d, q = 3*i. Let 2 - 15*v - 2*v**4 + d + 4*v**3 + 11*v = 0. Calculate v.
-1, 1
Let u(g) be the first derivative of -4*g - 5 - 4/9*g**3 + 8/3*g**2. What is h in u(h) = 0?
1, 3
Let a(v) be the second derivative of v**6/60 - v**5/15 + 2*v**2 + 3*v. Let m(u) be the first derivative of a(u). Factor m(r).
2*r**2*(r - 2)
Let u(y) be the first derivative of -5*y**3/9 - 5*y**2/2 + 20*y/3 - 12. Factor u(s).
-5*(s - 1)*(s + 4)/3
Factor 2*j**3 - 3*j**4 - j**2 + j**3 - 3*j**5 + 4*j**2.
-3*j**2*(j - 1)*(j + 1)**2
Suppose 6*s = 238 - 220. Find d, given that -1/4*d**s + 0*d + 0*d**4 + 0 + 1/4*d**5 + 0*d**2 = 0.
-1, 0, 1
Factor -4/5*t**2 - 8/5*t - 4/5.
-4*(t + 1)**2/5
Let g be (-1 + (3 - 2))/2. Let f(t) be the first derivative of 3/2*t**4 - 2*t**3 + g*t - 2/5*t**5 - 2 + t**2. Suppose f