 8*j(a) - o(a). Factor n(v).
-2*v**2
Let a = 466 - 466. Let d(p) be the third derivative of -9*p**2 + 0*p**5 - 1/120*p**6 + a*p + 0*p**4 + 0 + 0*p**3 - 1/210*p**7. Factor d(r).
-r**3*(r + 1)
Let u(z) be the first derivative of -z**3 - 3/8*z**4 + 0*z - 3/4*z**2 - 11. What is t in u(t) = 0?
-1, 0
Solve -48 - 16*p**2 - 4*p**3 - 24*p**2 + 62*p**2 - 14*p**2 + 44*p = 0 for p.
-3, 1, 4
Let x(k) = -k**3 - 2*k**2 - 2*k + 4. Let j be x(0). Solve -2 + 13*d**2 - 18*d**2 + j*d**2 - 3*d = 0.
-2, -1
Let o(y) be the second derivative of -125*y**4/3 - 168*y**3 - 8*y**2 + 292*y. Factor o(j).
-4*(j + 2)*(125*j + 2)
Let k(j) be the second derivative of j**6/480 - 3*j**5/80 + j**4/4 + 31*j**3/6 + 13*j. Let u(z) be the second derivative of k(z). Find d such that u(d) = 0.
2, 4
Let f = -133 + 7981/60. Let k(l) be the second derivative of f*l**5 + 3/2*l**2 - 6*l + 7/36*l**4 + 5/6*l**3 + 0. Factor k(m).
(m + 1)*(m + 3)**2/3
Let i(m) be the first derivative of 0*m + 0*m**2 - 2/3*m**3 + 12 + 3/2*m**4. Factor i(h).
2*h**2*(3*h - 1)
Let y(q) = -q + 2 - 3 - 2. Let o be y(-5). Factor -3*m**3 - 3*m**2 + 3*m + 9*m**2 + 3*m**4 - 9*m**o.
3*m*(m - 1)**2*(m + 1)
Let z be 31/(-4) + (1452/102 + -14)*34. Find i, given that -i**5 + 13/4*i**2 - 1/2 - 11/4*i**4 - z*i**3 + 5/4*i = 0.
-2, -1, 1/4, 1
Let 0 - 3*v**4 + 0*v + 3/2*v**3 + 0*v**2 = 0. What is v?
0, 1/2
Let g(i) be the third derivative of i**7/42 - i**6/4 - 11*i**5/12 + 5*i**4 + 70*i**3/3 - i**2 + 62. Solve g(u) = 0 for u.
-2, -1, 2, 7
Suppose 12*p - 13*p = 126. Let a = p + 126. Determine v, given that -2/9*v**4 + 2/9*v - 2/3*v**2 + 2/3*v**3 + a = 0.
0, 1
Let f(o) be the third derivative of -4/33*o**3 - 1/330*o**5 + 1/33*o**4 + 0 + 0*o + 3*o**2. Let f(r) = 0. Calculate r.
2
Let n(t) be the third derivative of t**7/2520 - t**6/180 + 11*t**4/8 - 41*t**2. Let a(u) be the second derivative of n(u). Let a(g) = 0. What is g?
0, 4
Let n(k) be the first derivative of k**7/1680 - k**6/720 + 5*k**3 - 2. Let u(y) be the third derivative of n(y). Let u(j) = 0. What is j?
0, 1
Let c(q) be the third derivative of q**8/36960 + q**7/4620 - q**5/165 - 5*q**4/24 - 20*q**2. Let w(v) be the second derivative of c(v). Factor w(g).
2*(g - 1)*(g + 2)**2/11
Let v = -10 - -21. Suppose -5*w = -4*z - 8, -5*w + 3*z + v = -0*z. Let 0*o - 2/11*o**5 + 0 + 0*o**2 + 2/11*o**w + 4/11*o**3 = 0. Calculate o.
-1, 0, 2
Let n be 1/3*(-900)/(-700). Find m such that -6/7*m**2 + 0 - 9/7*m**3 + n*m = 0.
-1, 0, 1/3
Let l(k) be the second derivative of -k**6/120 - k**5/50 - 43*k**3/6 + 14*k. Let r(m) be the second derivative of l(m). Solve r(t) = 0 for t.
-4/5, 0
Let l(z) = 4*z**4 + 20*z**3 + 28*z**2 + 12*z + 4. Let t(v) = 4*v**4 + 20*v**3 + 27*v**2 + 11*v + 5. Let s = -4 + -1. Let k(y) = s*l(y) + 4*t(y). Factor k(a).
-4*a*(a + 1)*(a + 2)**2
Let t(s) be the second derivative of -s**7/3 - 124*s**6/15 - 643*s**5/10 - 407*s**4/3 - 160*s**3/3 + 128*s**2 + s + 60. Determine m, given that t(m) = 0.
-8, -1, 2/7
Suppose -15*w = -9*w - 30. Let u(o) = -2*o**2 - 2*o + 4. Let m(f) = 2*f**2 + 3*f - 5. Let j(x) = w*u(x) + 4*m(x). Factor j(z).
-2*z*(z - 1)
Let r(t) be the second derivative of -18*t**5/35 + 25*t**4/42 - 4*t**3/21 - 358*t - 1. Let r(c) = 0. What is c?
0, 1/4, 4/9
Let f(c) be the third derivative of 5*c**8/168 - 5*c**7/12 + 29*c**6/16 - 5*c**5/3 - 5*c**4/3 + 482*c**2 - 2. Determine o so that f(o) = 0.
-1/4, 0, 1, 4
Let h(c) = -6*c**2 + 3. Let k(o) = o**2 + 11*o + 2. Let u be k(-11). Let a(y) = y**2 - 6*y**2 + y + 0*y + 4 - u*y**2. Let w(n) = -3*a(n) + 4*h(n). Factor w(z).
-3*z*(z + 1)
Let x(y) be the second derivative of -y**5/80 + 3*y**4/4 - 18*y**3 + 216*y**2 - 9*y - 1. Find q, given that x(q) = 0.
12
Factor 0 + 2/7*r**2 - 40/7*r.
2*r*(r - 20)/7
Suppose -5 = -9*h - 5. Let 18/5*z**4 + 0*z - 14/5*z**5 - 4/5*z**3 + 0*z**2 + h = 0. Calculate z.
0, 2/7, 1
Factor -3 - 2*y + 1775*y**3 + 4*y**2 + 1775*y**3 + 2*y**4 - 3548*y**3 - 3*y**4.
-(y - 3)*(y - 1)*(y + 1)**2
Suppose -x + 0*s = -5*s + 5, 2*x - 3*s - 18 = 0. Factor x*o**4 - 8*o**3 - 16*o**4 + o**5 + 6*o**3.
o**3*(o - 2)*(o + 1)
Let z = 553/690 - -42/115. Let u(r) be the second derivative of -2/5*r**5 + 0 + z*r**4 - 2/3*r**3 - 10*r - r**2. Determine k, given that u(k) = 0.
-1/4, 1
Let z(a) = 4*a**4 + a**3 - a**2 - a + 3. Let o(x) = 5*x**4 - 5*x**4 - 4*x**4 + 5*x**4 + 1. Let h(p) = 3*o(p) - z(p). Factor h(c).
-c*(c - 1)*(c + 1)**2
Factor 0*r + 0 - 5/2*r**2 - 1/6*r**5 + 29/6*r**3 - 13/6*r**4.
-r**2*(r - 1)**2*(r + 15)/6
Let g(o) be the second derivative of o**7/3 + 71*o**6/60 + 4*o**5/5 + o**4/6 - 78*o + 2. Determine w, given that g(w) = 0.
-2, -2/7, -1/4, 0
Suppose -l = 3*n + 3, -8*n = -4*n - 4*l - 12. Let t(o) be the second derivative of n - 1/4*o**4 - 4*o + 0*o**2 - 3/40*o**5 - 1/4*o**3. Factor t(h).
-3*h*(h + 1)**2/2
Let q(p) be the second derivative of 5/12*p**3 + 0 + 1/2*p**2 - 7/24*p**4 + p. Factor q(c).
-(c - 1)*(7*c + 2)/2
Suppose -49/3*h**2 + 5/3*h**4 - 100/3 - 1/3*h**5 + 17/3*h**3 - 160/3*h = 0. What is h?
-2, -1, 5
Let -70 - 32 + 270 - 52*i + 4*i**2 = 0. Calculate i.
6, 7
Let x(d) = -8*d**3 + 14*d**2 - 15*d - 3. Let y(q) = q**2 + 2*q + 1. Let s(h) = -x(h) - 3*y(h). Solve s(f) = 0 for f.
0, 1, 9/8
Let q(x) be the third derivative of -x**5/36 - 25*x**4/18 - 250*x**3/9 + 70*x**2. Factor q(c).
-5*(c + 10)**2/3
Suppose 4*j - 4 = 4. Determine k so that -4*k**5 + 0*k**5 - j*k**3 + 6*k**5 = 0.
-1, 0, 1
Let p(i) be the first derivative of 5*i**9/756 - i**8/24 - 31*i**7/672 - i**6/72 + 12*i**3 + 10. Let d(c) be the third derivative of p(c). Factor d(r).
5*r**2*(r - 4)*(4*r + 1)**2/4
Let g = -6 - -8. Suppose -g*s + 5*s - 36 = 0. Suppose -3*v + s - 11*v**2 + 11*v + 7*v**2 = 0. Calculate v.
-1, 3
Let m(u) be the first derivative of -28 + 3/20*u**4 - 18/5*u - 8/5*u**3 + 39/10*u**2. Solve m(r) = 0.
1, 6
Let c be 63/(5985/247)*(25 + 1). Factor 52/5*f - 2/5*f**2 - c.
-2*(f - 13)**2/5
Factor 21*i**4 + 4*i**2 - 32*i + 19*i**2 - 19*i**4 - 16*i**3 + 17*i**2.
2*i*(i - 4)*(i - 2)**2
Let i be (1*-5)/(7/7). Let r = 7 + i. Factor 1/5*k**4 + 0*k**r + 0 + 0*k - 1/5*k**5 + 0*k**3.
-k**4*(k - 1)/5
Let r(h) be the first derivative of -50*h**3/3 + 35*h**2/2 + 15*h + 29. Factor r(q).
-5*(q - 1)*(10*q + 3)
Let x(j) = j**2 + 436*j + 9688. Let g(c) = 2*c**2 + 437*c + 9686. Let k(m) = -4*g(m) + 3*x(m). Factor k(d).
-5*(d + 44)**2
Let t = 4275 + -4274. Factor 3/4*k**2 + t - 2*k.
(k - 2)*(3*k - 2)/4
Let k(w) be the first derivative of 175*w**6/2 + 299*w**5 + 1315*w**4/4 + 75*w**3 - 70*w**2 - 20*w + 290. Solve k(v) = 0.
-1, -2/15, 2/7
Find t such that 311*t - 33*t**3 - 168 - 177*t**2 - 105*t - 21*t**5 + 148*t + 48*t**5 + 21*t**4 - 24*t**5 = 0.
-7, -4, 1, 2
Determine r, given that 28/3*r**2 - 128/3*r + 64 - 2/3*r**3 = 0.
4, 6
Let h(j) be the first derivative of -j**4/4 + 4*j**3/3 + 7*j**2/2 - 10*j - 5. Find r, given that h(r) = 0.
-2, 1, 5
Let j = -177 + 83. Let u = -90 - j. Let -u - 4/3*x**2 - 16/3*x = 0. Calculate x.
-3, -1
Let q(y) be the second derivative of -y**7/735 + y**6/420 + y**2 + 10*y. Let j(w) be the first derivative of q(w). Let j(s) = 0. What is s?
0, 1
Let f(k) = 75*k**4 - 10*k**3 - 5*k**2 - 5*k + 5. Let s = 34 - 30. Let h(c) = -75*c**4 + 9*c**3 + 6*c**2 + 4*c - 4. Let b(v) = s*f(v) + 5*h(v). Factor b(q).
-5*q**2*(3*q + 1)*(5*q - 2)
Let r(a) = -a**4 - 2*a**3 + a**2 - 1. Let y(i) = 3*i**3 + 7*i**2 - 12*i + 1. Let d(g) = -3*r(g) - 3*y(g). Factor d(x).
3*x*(x - 2)**2*(x + 3)
Factor -8/17*b**3 - 6/17*b**2 - 2/17*b**4 + 0 + 0*b.
-2*b**2*(b + 1)*(b + 3)/17
Let h(u) = 2*u**3. Let p(k) = -21*k**3 + 195*k**2 + 12675*k + 274625. Let o(s) = -22*h(s) - 2*p(s). What is b in o(b) = 0?
-65
Let s(f) be the third derivative of f**6/720 + f**5/120 + 3*f**3/2 - 14*f**2. Let a(t) be the first derivative of s(t). Suppose a(q) = 0. What is q?
-2, 0
Suppose s - 5*u = -s + 56, 0 = -s + 4*u + 34. Suppose s*r - 19 - 35 = 0. Factor 13/4*h**2 + 27/4*h**r + 7/4*h**5 + 0 + 1/2*h + 23/4*h**4.
h*(h + 1)**3*(7*h + 2)/4
Let k = -268 - -805/3. Factor -4/3*h - 1 - k*h**2.
-(h + 1)*(h + 3)/3
Let c(b) = -b**4 + 90*b**3 - 1938*b**2 + 1849*b + 6. Let y(f) = 2*f**4 - 179*f**3 + 3875*f**2 - 3698*f - 10. Let t(r) = -5*c(r) - 3*y(r). Factor t(n).
-n*(n - 43)**2*(n - 1)
Determine u, given that 328329/4*u - 20903613/4 + 3/4*u**3 - 1719/4*u**2 = 0.
191
Let h(p) be the third derivati