t h(a) be the second derivative of -2*a**5/15 + 56*a**4/9 + 121*a**3/3 + 93*a**2 - 23*a + 19. Factor h(n).
-2*(n - 31)*(2*n + 3)**2/3
Let n(m) = -m**4 - 61*m**3 - 4*m**2 + 56*m. Let k(f) = -4*f**4 - 214*f**3 - 14*f**2 + 196*f. Let y(g) = -5*k(g) + 18*n(g). Factor y(a).
2*a*(a - 14)*(a - 1)*(a + 1)
Let l(c) be the second derivative of -5/2*c**4 + 27*c**2 + 3/20*c**5 + 6 + 7/2*c**3 - 11*c. What is m in l(m) = 0?
-1, 2, 9
Let -798/5*p**2 + 39*p**4 - 411/5*p + 603/5 - 3/5*p**5 + 414/5*p**3 = 0. What is p?
-3, -1, 1, 67
Let a be -47 + (-32 - (-8568)/108). Find i such that -16/3*i + a*i**2 + 64/3 = 0.
8
Suppose 63 - 158*y + 463*y - 150*y - 137*y - y**2 = 0. Calculate y.
-3, 21
Suppose 8*z - 3*z = 10. Suppose 10 = -9*s - 20*s + 10. Factor s - 6/7*k + 6/7*k**z.
6*k*(k - 1)/7
Let a(m) = m**2 - m + 2. Let x be a(2). Suppose -7 = -x*w + s + 5, 2*s + 10 = w. Factor -5/3*q**w - 10/3 - 5*q.
-5*(q + 1)*(q + 2)/3
Let r = 975 + -690. Factor 238 + 437 + 64*z + 220 + z**2 - 156 + r.
(z + 32)**2
Let d = 2595 + -2527. Suppose -70*r - t = -d*r - 3, 0 = 3*r - 3*t - 9. Factor -1/4*o**r - o - 3/4.
-(o + 1)*(o + 3)/4
Determine d, given that 2/5*d**3 + 132/5*d**2 + 496/5 + 504/5*d = 0.
-62, -2
Let v be 177/6 - (-1)/(-2). Suppose 5*b - v = -19. Factor 18*c**2 - 36*c**2 + 5*c - c**3 - c**4 + 2 + 21*c**b.
-(c - 2)*(c + 1)**3
Let j be ((-5)/(-450)*393)/((-8)/16) - -9. Suppose 0 + j*p - 2/5*p**2 + 2/15*p**3 = 0. What is p?
0, 1, 2
Let b be ((-12)/108)/(45/(-810)). Factor 332/9*f + 2/9*f**b + 13778/9.
2*(f + 83)**2/9
Let c(q) be the second derivative of 145*q + 0 + 48/25*q**5 - 19/3*q**4 + 16/5*q**3 + 56/5*q**2 - 2/15*q**6. Determine z so that c(z) = 0.
-2/5, 1, 2, 7
Let u = -409 - -419. Let y = u - 8. Factor -3/2*n**y - 6 - 15/2*n.
-3*(n + 1)*(n + 4)/2
Let m(f) be the third derivative of -f**8/672 + f**7/28 - 9*f**6/80 - 81*f**5/40 + 633*f**2. Solve m(s) = 0 for s.
-3, 0, 9
Let c(a) be the second derivative of -a**6/180 + 13*a**5/30 - 169*a**4/12 + a**3/3 - 4*a**2 - 11*a. Let t(m) be the second derivative of c(m). Factor t(l).
-2*(l - 13)**2
Let s be (-32)/3*153/68. Let h be 2/(96/210) - (-9)/s. Solve -2/3*m**3 + 2/3*m**2 - 1/3*m**5 - m**h + m + 1/3 = 0 for m.
-1, 1
Suppose 30 = 5*b + 5*l, -15 + 3 = -2*b - 4*l. Suppose 10 + 14 = b*d. Suppose 20*u + 12*u**2 - 4*u**3 + 8 - 7*u**4 + 2*u**d + u**4 + 0*u**4 = 0. Calculate u.
-1, 2
Let b = -215 + 212. Let l be 9/27 - (0 + b/(-15)). Determine n, given that l*n**4 + 0 + 4/15*n**3 - 2/15*n**2 - 4/15*n = 0.
-2, -1, 0, 1
Let v(j) be the third derivative of j**5/40 - 4*j**4 + 337*j**2 + 2*j. Solve v(w) = 0.
0, 64
Suppose -5*l = -l - 40. Let q be 35/2 - 5/l. Find i such that 6*i + 4*i**5 - 20*i**3 + 27*i - q*i = 0.
-2, -1, 0, 1, 2
Let m(z) be the third derivative of -z**7/1785 - 28*z**6/255 + 113*z**5/510 + 2*z**2 + 24. Solve m(x) = 0.
-113, 0, 1
Let z(a) be the third derivative of -a**7/3780 - 7*a**6/540 - 11*a**5/60 - 9*a**4/2 - 2*a**2 - 9*a. Let t(u) be the second derivative of z(u). Factor t(k).
-2*(k + 3)*(k + 11)/3
Let b(m) = -35*m**2 + 50*m + 40. Let v(k) = k**2 + k. Let o(p) = b(p) + 20*v(p). Let c(q) = -7*q**2 + 35*q + 20. Let w(z) = 5*c(z) - 3*o(z). Factor w(h).
5*(h - 4)*(2*h + 1)
Factor -1 - 69*g**2 + 9*g**2 + 56*g**2 - 60*g - 175.
-4*(g + 4)*(g + 11)
Let r(f) be the second derivative of f**6/3060 + 6*f**5/85 + 108*f**4/17 + 2*f**3/3 - 6*f**2 - 3*f - 37. Let b(g) be the second derivative of r(g). Factor b(u).
2*(u + 36)**2/17
Suppose 3*c - 6*s = 60, 2*c + 0 = -s + 5. Let t(r) be the third derivative of 0*r**3 + 1/30*r**c + 1/5*r**5 - 25*r**2 + 1/3*r**4 + 0*r + 0. Factor t(v).
4*v*(v + 1)*(v + 2)
Let d(y) = -y**3 + 2*y**2 - y. Let j(a) = -4*a**3 - 9*a**2 + 15*a - 2. Suppose -56 = 4*p - 4*u, 6*p - 3*u + 32 = 4*p. Let h(z) = p*d(z) - 5*j(z). Factor h(x).
5*(x - 1)*(x + 2)*(6*x - 1)
Let a(k) be the second derivative of 11*k**7/70 + k**6/45 + 27*k**3 + 2*k + 38. Let f(z) be the second derivative of a(z). Factor f(p).
4*p**2*(33*p + 2)
Let f(o) be the second derivative of -o**6/15 - 75*o**5/2 + 2659*o**4/6 - 1907*o**3 + 3438*o**2 - 2716*o. Suppose f(r) = 0. Calculate r.
-382, 1, 3
Factor 0 - 6134700/7*p**3 + 731051750/7*p**4 + 17160/7*p**2 - 16/7*p.
2*p*(715*p - 2)**3/7
Let m(h) be the second derivative of 13*h**7/105 + 41*h**6/75 - 163*h**5/50 - 689*h**4/30 - 38*h**3 - 72*h**2/5 - h + 626. Suppose m(d) = 0. Calculate d.
-3, -1, -2/13, 4
Suppose 85*u + 47*u = -0*u + 24*u. Let m(c) be the first derivative of u*c + 1/12*c**4 + 1/6*c**2 - 2/9*c**3 - 17. Suppose m(s) = 0. What is s?
0, 1
Suppose -10/7*w**5 + 74/7*w**2 + 86/7*w**3 + 2*w**4 - 16/7 - 4/7*w = 0. What is w?
-1, 2/5, 4
Factor -l**2 - 48*l + 77977 - 12*l - 77977 - 2*l**2.
-3*l*(l + 20)
Let d(h) be the third derivative of h**9/2160 + h**8/560 - h**7/105 - h**6/45 + 2*h**5/5 + 66*h**2. Let m(g) be the third derivative of d(g). Factor m(y).
4*(y - 1)*(y + 2)*(7*y + 2)
Let w = 1679543 - 1679541. Suppose 128/3*s - 2/3*s**w - 2048/3 = 0. What is s?
32
Let d(z) = 2*z**2 - z + 1. Let f(w) = -w**3 - 2*w**2 + 5*w - 10. Suppose 0 = -7*a + 3*a + 4. Let n(r) = a*f(r) + 4*d(r). Determine g, given that n(g) = 0.
-1, 1, 6
Solve -102/5*r**2 + 96/5*r**3 - 243/5*r + 42 + 3/5*r**5 + 36/5*r**4 = 0.
-7, -5, -2, 1
Suppose 4*p = 29*m - 27*m + 10, 3*m + 2*p = 17. Let a(v) = -10*v**3 - 4*v**2 - 3*v - 7. Let k(q) = -q**3 - q - 1. Let d(z) = m*a(z) - 21*k(z). Factor d(r).
-3*r*(r + 2)*(3*r - 2)
Let l(g) = 19*g**3 + 21*g**2 + 5*g - 29. Let q(b) = 7*b**3 + 7*b**2 + 2*b - 10. Let r(u) = -3*l(u) + 8*q(u). Find y, given that r(y) = 0.
-7, -1, 1
Let b(m) = -17*m**2 + 12216*m - 7490838. Let p(v) = 15*v**2 - 12220*v + 7490845. Let o(k) = -5*b(k) - 6*p(k). Determine r, given that o(r) = 0.
1224
Suppose 178*v - 25 = -4*c + 179*v, -5*v = -c + 11. Let x(u) be the first derivative of -24*u - c*u**2 + 21 + 3/4*u**4 + 2*u**3. Let x(z) = 0. Calculate z.
-2, 2
Let s(i) = 29*i + 443. Let v be s(-13). Suppose -31*p + v = 2*p. Factor -9/5*o**p - 13/5*o - 4/5.
-(o + 1)*(9*o + 4)/5
Let i(p) be the second derivative of 2/3*p**4 - 2/3*p**3 + 0 - 2*p**2 - 39*p. Factor i(g).
4*(g - 1)*(2*g + 1)
Let q(r) = 9*r**3 - 34*r**2 + 183*r - 35. Let i(w) = 8*w**3 - 36*w**2 + 184*w - 30. Let a(o) = 7*i(o) - 6*q(o). Factor a(n).
2*n*(n - 19)*(n - 5)
Factor -5276/3 - 6*g**2 + 23746/3*g.
-2*(g - 1319)*(9*g - 2)/3
Let q(i) = -i**3 - 222*i**2 - 1713*i - 6. Let h be q(-8). Factor -5*x**h + 2/3*x + 0.
-x*(15*x - 2)/3
Let x = 525 - 522. Let b(m) be the first derivative of 5 - 4/7*m**2 + 16/7*m + 1/21*m**x. Factor b(o).
(o - 4)**2/7
Let i(j) be the third derivative of -j**7/1680 + 11*j**6/480 + 127*j**5/480 + 53*j**4/48 + 9*j**3/4 - 4592*j**2. Factor i(k).
-(k - 27)*(k + 1)*(k + 2)**2/8
Let t(n) be the first derivative of 15 + 0*n + 12*n**3 + 9/5*n**5 + 33/4*n**4 + 6*n**2. Factor t(o).
3*o*(o + 1)*(o + 2)*(3*o + 2)
Let a(k) be the third derivative of -k**7/315 + 89*k**6/180 - 29*k**5/10 + 259*k**4/36 - 86*k**3/9 - 3*k**2 + 200. Factor a(w).
-2*(w - 86)*(w - 1)**3/3
Suppose 5*d + 20 = 3*b + 115, d - 6 = -2*b. Suppose a + 18 = 5*a - 2*x, 0 = -2*a - 4*x - d. Determine p so that -13*p**2 - 3*p - 20*p**2 + 32*p**2 - a*p = 0.
-5, 0
Let n(j) be the third derivative of j**5/330 - 5*j**4/132 - 12*j**3/11 + 12468*j**2. Factor n(a).
2*(a - 9)*(a + 4)/11
Let y(s) be the third derivative of -s**4/24 + 23*s**3/6 - 191*s**2. Let h be y(20). Determine w so that -w**h + 2/3*w**2 + 7/3*w + 2/3 = 0.
-1, -1/3, 2
Let c = 1/3 + 11/12. Let b be (-500)/(-200) + 5/(-2). Factor -1/4*z**5 + b*z + 0 - c*z**3 - 1/2*z**2 - z**4.
-z**2*(z + 1)**2*(z + 2)/4
Suppose 3*j = -2*j + 4*t + 158, -49 = -j - 5*t. Let u = 39 - j. Factor 13*v + 10*v + 10 - u*v**4 - 15*v**3 - 5*v**2 - 8*v.
-5*(v - 1)*(v + 1)**2*(v + 2)
Let j(h) be the first derivative of h**4/4 - 23*h**3/3 + 25*h**2 + 200*h - 6298. Factor j(k).
(k - 20)*(k - 5)*(k + 2)
Factor 761*s - 579121/2 - 1/2*s**2.
-(s - 761)**2/2
Let a(s) be the third derivative of -s**5/390 - 219*s**4/52 - 1310*s**3/39 + 4140*s**2. Suppose a(m) = 0. Calculate m.
-655, -2
Let y(i) = -8*i**2 - i + 96. Suppose -4*g - 10 = -5*f, -33 = 4*f + 2*g + 3*g. Let x(u) = 2*u**2 - 24. Let s(c) = f*y(c) - 9*x(c). Let s(o) = 0. What is o?
-3, 4
Let l(q) = 7*q**5 - 78*q**4 + 168*q**3 - 6*q**2 - 175*q + 74. Let m(g) = -2*g**5 + 2*g + 2. Let u(v) = l(v) + 5*m(v). 