- 5*i**4/84 + i**3/7 + 66*i**2. Factor h(a).
2*(a - 1)**2*(a + 3)/7
Let q(r) be the second derivative of 0 + 0*r**2 + 1/15*r**3 - 7*r + 1/30*r**4. Factor q(n).
2*n*(n + 1)/5
Suppose -14 = -3*y - j, 2*y = 5*y - j - 4. Factor 45*q**2 - y*q - 11*q**4 + 6*q**4 + 15*q**3 + 28*q.
-5*q*(q - 5)*(q + 1)**2
Let p(u) be the first derivative of -u**6/30 + u**5/3 - 2*u**4/3 - 5*u**2/2 + u + 19. Let h(n) be the second derivative of p(n). Factor h(d).
-4*d*(d - 4)*(d - 1)
Let x be 5 + (-26)/(-13) + (-66)/10. Factor -6/5*y**2 + 8/5*y**4 + x - 8/5*y**3 + 4/5*y.
2*(y - 1)**2*(2*y + 1)**2/5
Let t(l) = -l**4 - l**3 + l**2 - l. Let c(s) = -2*s**4 - 10*s**3 + 2*s**2 + 14*s. Let d(x) = c(x) + 2*t(x). Factor d(z).
-4*z*(z - 1)*(z + 1)*(z + 3)
Let g(w) be the second derivative of -6*w - 1/300*w**5 + 0 - 1/900*w**6 + 0*w**2 + 2/3*w**3 + 0*w**4. Let v(n) be the second derivative of g(n). Factor v(x).
-2*x*(x + 1)/5
Let d(w) be the third derivative of -w**6/360 + 31*w**5/15 - 1922*w**4/3 + 953312*w**3/9 - 876*w**2. Determine j so that d(j) = 0.
124
Suppose 0 = s + 4*u - 19, 3*s - 5*u + 10 + 1 = 0. Let v(y) be the first derivative of 2*y**s - 1 + 0*y + 3/2*y**2. Factor v(k).
3*k*(2*k + 1)
Let b(i) be the second derivative of -i**4/8 - 23*i**3/2 - 1587*i**2/4 + 2*i - 29. Solve b(g) = 0.
-23
Let n(d) be the first derivative of d**4/2 + 2*d**3 + 2*d**2 - 104. Let n(i) = 0. What is i?
-2, -1, 0
Suppose 22*v - 126 = -16. Suppose 5*q - 32*y - 6 = -29*y, 0 = -v*q + 4*y + 8. Factor -9/5*u**3 + 0*u + 9/5*u**4 + 3/5*u**2 + q - 3/5*u**5.
-3*u**2*(u - 1)**3/5
Let -5 - 299*z**4 - 40*z**2 - 1 + 6 - 65*z**3 + 269*z**4 - 5*z = 0. Calculate z.
-1, -1/6, 0
Let t(r) = r - 2. Let l be t(7). Suppose -o - l*k - 20 = -0*o, -3*o + 2*k + 8 = 0. Factor 4*m**2 + 5*m**4 + o*m**3 + 12*m**3 + 7*m**4 + 4*m**5.
4*m**2*(m + 1)**3
Let z(k) be the third derivative of k**7/30 + 17*k**6/12 - 127*k**5/60 - 25*k**4/12 - 255*k**2. Factor z(x).
x*(x - 1)*(x + 25)*(7*x + 2)
Factor -4/3*y**2 + 2/9*y**3 - 6*y + 0.
2*y*(y - 9)*(y + 3)/9
Let r be -1 + 0 - (-40)/8. Suppose -3*q = -r*v + v, 5*q = 4*v + 2. Factor -4*t**5 - 4*t + v*t**2 + 5*t + 3*t**5 - 2*t**4.
-t*(t - 1)*(t + 1)**3
Let l(u) be the first derivative of -3*u**3 - u**2 - 37. Factor l(d).
-d*(9*d + 2)
Let i(v) be the first derivative of v**6/6 + 2*v**5/5 - 3*v**4/4 + 433. Suppose i(p) = 0. What is p?
-3, 0, 1
Let p = -3/1204 + -14673/301. Let o = p - -49. Determine w, given that -o*w - 1/4*w**3 + 0 - 1/2*w**2 = 0.
-1, 0
Let h(z) be the second derivative of -z**7/756 - 8*z**6/405 - 13*z**5/135 - 4*z**4/27 - 3*z**3 - 29*z. Let t(k) be the second derivative of h(k). Factor t(s).
-2*(s + 2)*(s + 4)*(5*s + 2)/9
Find n, given that 81*n - 3/4*n**4 + 45/4*n**3 + 0 - 54*n**2 = 0.
0, 3, 6
Suppose -13*m + 27*m - 10*m = 0. Let n(g) be the second derivative of -3*g + 1/21*g**3 + 0 + 2/105*g**6 - 1/21*g**4 + 0*g**2 + m*g**5 - 1/147*g**7. Factor n(o).
-2*o*(o - 1)**3*(o + 1)/7
Let t be 2*(-1 - (-15)/12). Let a(j) be the second derivative of 0 + j - 1/2*j**4 - t*j**3 + 0*j**2 - 3/16*j**5 - 1/40*j**6. Solve a(r) = 0 for r.
-2, -1, 0
Let -1/3*j + 1/3*j**3 + 0 + 0*j**2 = 0. Calculate j.
-1, 0, 1
Let t(m) be the third derivative of m**8/1680 - 2*m**7/525 + m**6/600 + m**5/30 - m**4/30 - 4*m**3/15 + 5*m**2 - 1. Factor t(b).
(b - 2)**3*(b + 1)**2/5
Suppose -2*y + 4*y = 10. Find d such that 0*d**4 - 18*d**3 + 9 + 15*d - 6*d**2 + 443*d**y - 3*d**4 - 440*d**5 = 0.
-1, 1, 3
Suppose 19 = 13*v - 14*v - 3*i, -14 = 7*v + 4*i. Suppose -12/7*t**v + 3/7*t**3 + 9/7*t + 0 = 0. What is t?
0, 1, 3
Let h be ((-4)/16)/(324/(-32) - -9). Find s such that -h*s**5 + 0*s + 1/9*s**2 + 0 - 1/3*s**4 + 0*s**3 = 0.
-1, 0, 1/2
Let t(x) be the second derivative of -x**8/1008 + x**7/210 + x**6/360 - x**5/60 - 3*x**2 - 34*x. Let v(k) be the first derivative of t(k). Solve v(w) = 0 for w.
-1, 0, 1, 3
Suppose -5*d + 68 = 33. Let c(f) be the second derivative of 4*f + 1/105*f**d + 0*f**3 - 1/50*f**5 + 0 + 0*f**2 + 1/30*f**4 - 1/75*f**6. Factor c(l).
2*l**2*(l - 1)**2*(l + 1)/5
Factor 69/4 - 3/8*p**2 - 63/8*p.
-3*(p - 2)*(p + 23)/8
Let r be 59/((-10974)/12) + (-300)/(-806). Determine y so that 2/13*y + 2/13*y**5 - 4/13*y**3 - 2/13*y**4 - 2/13 + r*y**2 = 0.
-1, 1
Let z(j) = j**2 + 6*j + 5. Let v(t) = -4*t**2 - 19*t - 15. Let m(w) = -2*v(w) - 7*z(w). Factor m(k).
(k - 5)*(k + 1)
Factor 0 + 2/13*c - 2*c**3 + 14/13*c**4 + 10/13*c**2.
2*c*(c - 1)**2*(7*c + 1)/13
Let t(m) be the second derivative of 50*m**6/3 - 373*m**5/5 + 123*m**4 - 238*m**3/3 - 4*m**2 + 2*m - 51. Suppose t(w) = 0. What is w?
-2/125, 1
Suppose 0*y + 36 = 9*y. Let 2*t**y + 16*t - 3*t**3 - t**3 - 8*t**3 + 2*t**4 = 0. What is t?
-1, 0, 2
Let s(w) be the first derivative of w**3/12 - 3*w**2/2 + 9*w + 23. Let s(o) = 0. Calculate o.
6
Let q be (383/3)/((-35)/(-21)). Let v = 77 - q. Factor 2/5*l + 4/5 - v*l**2.
-2*(l - 2)*(l + 1)/5
Suppose -5*a + 17 = q, 2*a + 4*q = -2*a + 4. Suppose -4*y + 3*y = -a*h + 8, 12 = 3*y. Let -2/5*f**h + 0 - 2/5*f - 4/5*f**2 = 0. Calculate f.
-1, 0
Let v be (-225)/100*4/(-3). Find p, given that -2/9*p + 5/9*p**4 - p**v + 7/9*p**2 - 1/9*p**5 + 0 = 0.
0, 1, 2
Let v(h) be the second derivative of 5*h**7/42 + h**6/2 - h**5/4 - 35*h**4/12 + 10*h**2 - 2*h - 21. Suppose v(q) = 0. What is q?
-2, -1, 1
Suppose 2*n + l = 3*n + 2, 13 = -2*n - l. Let a(h) = 3*h**2 + 2*h - 5. Let o(b) = -b**2 + 1. Let s(d) = n*o(d) - a(d). Factor s(x).
2*x*(x - 1)
Let i(d) be the third derivative of -d**9/12096 - d**8/1344 - d**7/336 - d**6/144 - 11*d**5/30 + 37*d**2. Let g(v) be the third derivative of i(v). Factor g(c).
-5*(c + 1)**3
Let -3*b**5 + b**4 + 192 - 3*b**4 - 13*b**4 + 552*b - 168*b + 24*b**3 + 228*b**2 = 0. What is b?
-4, -2, -1, 4
Suppose 278 + 382 = -11*t. Let b be (-1 - 1)*t/330. Factor -b - 2/11*y + 2/11*y**2.
2*(y - 2)*(y + 1)/11
Factor 4 - 4*r**5 - 4 + 0*r**5 - 697*r**4 + 48*r**2 + 693*r**4 + 32*r**3.
-4*r**2*(r - 3)*(r + 2)**2
Let h(o) = o**5 - o**4 - o**3 - o. Let q(p) = -8*p - 3*p**4 + 17*p**3 - 12*p**5 + 4*p**2 + 11*p + 13*p**4. Let w(t) = -44*h(t) - 4*q(t). Factor w(x).
4*x*(x - 2)*(x - 1)*(x + 2)**2
Suppose 0 = -5*w + 3*l - 33, 3*w + 3*l = l - 16. Let s be (-46)/w - (-3)/9. Factor -q**3 + 3 + 6*q**2 - s*q + 4*q**4 - 5*q**4 + q**3.
-(q - 1)**3*(q + 3)
Factor -3*d**4 - 29*d - 79*d + 165*d**2 - 28*d**3 - 20*d**3 + 18*d - 24*d.
-3*d*(d - 2)*(d - 1)*(d + 19)
Let b(p) = -16*p**4 - 28*p**3 + 30*p + 18. Let f(n) = -n**5 + n**4 + n**3 - n**2 - n - 1. Let d(v) = -b(v) - 2*f(v). Solve d(i) = 0 for i.
-4, -2, -1, 1
Suppose v + i = 0, -2*v + 5*i = 2*i + 10. Let f(s) = 10*s**2 + 6*s - 13. Let k(q) = q**2 + q - 1. Let o(y) = v*f(y) + 18*k(y). Factor o(d).
-2*(d - 4)*(d + 1)
Let d be 4*28/(-8) + 0. Let u = d - -16. Find v, given that 4*v**5 - 3*v - 5*v**5 + u*v**3 + 5*v - 3*v = 0.
-1, 0, 1
Let v(x) be the second derivative of -x**5/5 - 14*x**4 - 54*x**3 - 80*x**2 + 137*x. What is n in v(n) = 0?
-40, -1
Suppose -3*y - 10 + 33 = b, 4*b - 50 = -5*y. Let r = y - -1. Determine i so that -6*i**2 - 3*i + 5*i + r*i**2 = 0.
-2, 0
Let v = 508 + -508. Let t(c) be the first derivative of -2/15*c**5 + 2 + v*c**2 + 0*c + 2/9*c**3 + 1/9*c**6 - 1/6*c**4. Factor t(r).
2*r**2*(r - 1)**2*(r + 1)/3
Let 0*x**2 - 39*x - 3*x**2 - 570 + 480 = 0. Calculate x.
-10, -3
Let n(h) = -5*h - 13. Let z be n(-3). Let -6 + 1 - r**4 + 4 + z*r**2 = 0. What is r?
-1, 1
Let j = -2/14285 - -85724/99995. Factor -9/7 + 18/7*i**3 + 15/7*i**4 + 3/7*i**5 - 3*i - j*i**2.
3*(i - 1)*(i + 1)**3*(i + 3)/7
Suppose 4*k - 6 = -22, -35 = -5*z + 5*k. Let y(m) be the first derivative of -1/15*m**5 + 8 + 2/9*m**z - 1/18*m**6 - 1/3*m - 1/6*m**2 + 1/6*m**4. Factor y(h).
-(h - 1)**2*(h + 1)**3/3
Let q(b) be the first derivative of -b**4/14 + 34*b**3/21 - 9*b**2 - 162*b/7 - 198. Factor q(r).
-2*(r - 9)**2*(r + 1)/7
Let g(l) be the third derivative of -l**8/84 - 18*l**7/35 + 29*l**6/15 - 2*l**5/15 - 19*l**4/2 + 58*l**3/3 + 199*l**2 + 2*l. Find i, given that g(i) = 0.
-29, -1, 1
Let k = 3 + 25. Let b be k/(-63) + 2/3. Let b*p**2 + 2/9*p**3 + 0*p + 0 = 0. What is p?
-1, 0
Let u(p) be the second derivative of -161*p**5/120 + 181*p**4/24 - 46*p**3/9 + p**2 + 28*p - 6. What is a in u(a) = 0?
2/23, 2/7, 3
Let u(r) be the third derivative of r**7/2100 + r**6/300 - 2*r**5/25 + 7*r**4/15 - 5*r**3/6 + 51*r**2. Let h(