*s**2. Factor k(z).
4*z**2*(z + 16)
Let a(b) be the third derivative of -b**5/270 - 11*b**4/36 - 62*b**3/27 + 1589*b**2. Factor a(n).
-2*(n + 2)*(n + 31)/9
Let 5*p**3 - p**3 + 829*p - 17*p**2 - 19*p**2 + 709*p - 1626*p = 0. Calculate p.
-2, 0, 11
Let u(y) be the first derivative of 9/2*y**4 + 24*y - 10/3*y**3 + 2/5*y**5 + 191 - 1/3*y**6 - 16*y**2. Find d such that u(d) = 0.
-2, 1, 3
Let g(n) be the second derivative of n**6/150 + 13*n**5/100 + n**4/12 - 229*n**3/30 + 21*n**2 + 7202*n. Suppose g(z) = 0. What is z?
-10, -7, 1, 3
Let l(y) be the second derivative of y**6/6 + 112*y**5 + 31360*y**4 + 14049280*y**3/3 + 393379840*y**2 + 4*y + 4. Solve l(j) = 0 for j.
-112
Let g(h) = -7*h**3 + 1435*h**2 - 688319*h + 109902239. Let b(l) = 3*l**3 + l**2 - 2*l. Let u(k) = -6*b(k) - 3*g(k). Suppose u(d) = 0. Calculate d.
479
Factor -84*f - 7186*f**2 + 3514*f**2 - 4*f**4 + 3596*f**2 + 12*f**3 + 80 + 72*f**3.
-4*(f - 20)*(f - 1)**2*(f + 1)
Suppose -26*j + 20*j + 24 = 0. Suppose 4*o = 3*w + 11, -j*w + 4*o + 5 = 13. Factor -32*l**2 + 64*l - 34 + 6*l**3 - 2*l**w + 34.
4*l*(l - 4)**2
Let d = -2422 + 2424. Let q be ((-12)/72)/(d/(-36)). Factor 12*u**q - 8*u**2 + 15/2*u**4 + 0*u - 25/2*u**5 + 0.
-u**2*(u + 1)*(5*u - 4)**2/2
Let f(w) be the first derivative of w**6/24 + w**5/16 - 49*w - 27. Let l(k) be the first derivative of f(k). Factor l(j).
5*j**3*(j + 1)/4
Suppose 8*u + 21 + 99 = 4*r, -2*r + 67 = -3*u. Factor -6*v**2 - 242/3 + r*v.
-2*(3*v - 11)**2/3
Suppose -696 - 150 = -9*l. Let y be 88 - l - (-1 + 78/(-14)). Factor y*w**2 - 20/7 + 16/7*w.
4*(w - 1)*(w + 5)/7
Let o(f) = 3. Let r(m) = m**2 - m + 1. Let y = -20 - -38. Let j = y - 19. Let b(t) = j*o(t) + r(t). Find l such that b(l) = 0.
-1, 2
Suppose s + 3*d = 2, -3*s + 14*d + 17 = 12*d. Suppose -5*o + s = -4*r - 211, -o = 4*r - 24. Factor 38/5*z**2 + 32*z + 2/5*z**3 - o.
2*(z - 1)*(z + 10)**2/5
Let d = 465 - 453. Suppose -3*u = 4*m - d, 4*u = 9*u - 20. Factor 0*p + m + 2/15*p**3 + 8/15*p**2.
2*p**2*(p + 4)/15
Let n(k) be the second derivative of k**5/60 + 49*k**4/18 + 102*k**3 - 4860*k**2 + 2891*k. Factor n(s).
(s - 10)*(s + 54)**2/3
Let w be 8299/(-1677) - 15/(-3). Let j(v) be the second derivative of -21/130*v**5 + 0 + w*v**3 - 18*v - 1/78*v**4 + 0*v**2. Let j(o) = 0. What is o?
-1/3, 0, 2/7
Factor -20172*z + 123*z**2 - 1/4*z**3 + 1102736.
-(z - 164)**3/4
Let -5 + 27/2*p - 1/2*p**4 - 25/2*p**2 + 9/2*p**3 = 0. What is p?
1, 2, 5
Let u(a) be the third derivative of 0*a**7 + 0 + 1/336*a**8 + 30*a**2 + 0*a**4 + 0*a**5 + 0*a + 0*a**6 + 0*a**3. Suppose u(o) = 0. Calculate o.
0
Let w(c) = -c**3 + 3*c. Let n(o) = -16*o**3 + 20*o**2 - 8*o. Suppose 28*l + 62 = 6. Let f(v) = l*n(v) + 28*w(v). Determine b, given that f(b) = 0.
0, 5
Suppose r - 6*r + 20 = 0. Factor 43*t - 43*t - 3*t**3 + 0*t**2 + r - 7*t**2.
-(t + 1)*(t + 2)*(3*t - 2)
Let f(l) be the first derivative of -2*l**5/65 + 57*l**4/13 - 1400*l**3/13 + 1078*l**2 - 63798*l/13 - 1792. Factor f(u).
-2*(u - 93)*(u - 7)**3/13
Let d(l) be the first derivative of 3*l**5/10 + 9*l**4/2 + 21*l**3/2 - 147*l**2/2 - 729. Factor d(z).
3*z*(z - 2)*(z + 7)**2/2
Suppose 38*p + p - 664 = 233. Let h(f) be the first derivative of -1/12*f**3 + 1/32*f**4 + 0*f + 0*f**2 + p. Factor h(z).
z**2*(z - 2)/8
Let p(a) be the third derivative of 47*a**8/168 - 236*a**7/105 + 127*a**6/20 - 98*a**5/15 + a**4/3 + 38*a**2 + a. What is j in p(j) = 0?
0, 1/47, 1, 2
Let w(b) be the first derivative of 14*b**5/15 - 2203*b**4/6 - 3374*b**3/3 - 3485*b**2/3 - 1268*b/3 + 7224. Find n, given that w(n) = 0.
-1, -2/7, 317
Let b(i) be the second derivative of -i**4/9 + 320*i**3/9 - 632*i**2/3 - 3*i + 26. Let b(t) = 0. Calculate t.
2, 158
Let i(j) be the second derivative of 1/4*j**4 - 63/2*j**3 + 63*j - 96*j**2 + 0. Find a, given that i(a) = 0.
-1, 64
Let d be ((-21)/(-28) - -42) + -42. Suppose 3*c - 4*c + 3 = 0. Find y, given that -d*y**c + 3/4*y**4 + 0*y + 1/4*y**2 - 1/4*y**5 + 0 = 0.
0, 1
Let z(d) be the second derivative of d**9/20160 + 3*d**8/8960 + d**7/1680 - 13*d**4/4 - 7*d + 3. Let m(a) be the third derivative of z(a). Solve m(g) = 0 for g.
-2, -1, 0
Determine a so that -297 - 21*a**3 - 2*a**4 - 37054*a - a**4 + 36568*a + 123*a**3 - 84*a**2 = 0.
-1, 3, 33
Let y(b) = -b**2 + 2*b + 3. Let p = 12 + -9. Let q(u) = p*u - u + 3*u**2 - 4*u**2 + 2. Let g(v) = -3*q(v) + 2*y(v). Factor g(r).
r*(r - 2)
Let k(m) = 6*m**5 + 10*m**4 - 10*m**3 - 7*m - 7. Let a(x) = -x**5 - x**4 + 2*x**3 + x + 1. Let t(w) = 21*a(w) + 3*k(w). Let t(c) = 0. Calculate c.
-1, 0, 4
Suppose -7*m + 9*m = 0. Suppose m = 2*a - 2*g, -g = 6*a - 2*a - 10. Factor 3 + 5 - 8 + a*n**2 - 2*n**3.
-2*n**2*(n - 1)
Let g(i) = -9*i**2 + 1096*i + 10598. Let l be g(-9). Suppose 0 - 1/8*f**l - 1/2*f**3 + 3*f**2 + 4*f - 3/4*f**4 = 0. What is f?
-4, -2, 0, 2
Let y(h) = -4*h**3 - 338*h**2 + 166*h - 332. Let u be y(-85). Factor 0 - 1/2*s**3 + u*s + 3*s**2.
-s*(s - 8)*(s + 2)/2
Let k be 6/9 + -1604*4/(-72). Let x = 886/9 - k. Solve 1/3*b**2 + 169/3 - x*b = 0 for b.
13
Suppose -470*b**2 + 56*b**4 + 638*b**2 - 3*b**5 - 213*b**3 - 20*b**4 + 12*b**4 + 432*b = 0. What is b?
-1, 0, 4, 9
Let t(g) be the second derivative of 1/80*g**5 - 3 + 1/6*g**4 + 17/24*g**3 - 8*g + 5/4*g**2. Factor t(c).
(c + 1)*(c + 2)*(c + 5)/4
Let s(h) = -2*h**4 - h**3 + h**2 + 6*h - 2. Let d(l) = -16*l**4 - 42*l**3 - 54*l**2 + 8*l - 12. Let o(w) = d(w) - 6*s(w). Determine v so that o(v) = 0.
-7, -1, 0
Factor 10140*x - 11296 - 2122 - 5*x**3 - 2520*x**2 + 3258.
-5*(x - 2)**2*(x + 508)
Let o(g) = -g**3 + 5*g + 5. Let k be o(-2). Let d(v) be the first derivative of -v**4 - 64*v + 23 + 0 + 64*v + 16*v**k - 72*v**2. Factor d(b).
-4*b*(b - 6)**2
Suppose 7*q - 2*q = -10. Let y be (-3 + (-13)/(-4))/(q/(-24)). Determine s so that -52*s**3 + 24*s**2 - 311*s**4 + 212*s**4 - 2*s**y - 21*s**5 = 0.
-4, -1, 0, 2/7
Determine t, given that -54/5 - 12/5*t - 2/5*t**4 + 12/5*t**3 + 56/5*t**2 = 0.
-3, -1, 1, 9
Let m = -1130733/4 + 282684. What is n in 1/4*n**2 + m*n - 9/2 = 0?
-6, 3
Let v = -49895 + 49897. Suppose 1 - 3/2*j - 1/2*j**v - 1/2*j**4 + 3/2*j**3 = 0. Calculate j.
-1, 1, 2
Let v = -366 - -376. Suppose 6*i - 2*i = 3*x + 23, -28 = -2*i - 4*x. What is b in -v + 3*b**2 - 15*b + 3*b**3 - 4 - i + 31 = 0?
-3, 1
Let b(c) be the third derivative of -c**8/252 - 2*c**7/315 + 4*c**6/15 - 8*c**5/9 - 8*c**4/9 + 32*c**3/3 + c**2 + 2*c - 133. Let b(k) = 0. What is k?
-6, -1, 2
Let 940*p**2 + 1/4*p**5 + 5104*p - 8*p**4 + 7744 + p**3 = 0. What is p?
-4, 22
Let c(m) be the third derivative of -1/6*m**5 - 3/8*m**4 - 13/480*m**6 + 0 + m - 1/840*m**7 + 131*m**2 + 0*m**3. Factor c(t).
-t*(t + 2)**2*(t + 9)/4
Let z(y) be the first derivative of -y**4/14 + 10*y**3/7 + 51*y**2 + 406*y - 1688. Solve z(k) = 0 for k.
-7, 29
Let a(f) be the second derivative of f**7/42 - 14*f**6/15 - 13*f**5/2 + 13*f**4/3 + 131*f**3/2 - 144*f**2 + 4048*f. Let a(z) = 0. Calculate z.
-3, 1, 32
Let c(m) be the first derivative of 3/13*m**2 - 20/13*m - 1/13*m**4 + 56 - 1/39*m**6 - 12/65*m**5 + 32/39*m**3. Solve c(j) = 0 for j.
-5, -2, -1, 1
Let 0 + 594/5*y**2 - 236/5*y + 4/5*y**4 - 246/5*y**3 = 0. What is y?
0, 1/2, 2, 59
Suppose t = 6*g - g + 6, -4*g - 5 = -t. Let h be -2 - (t/(-4) - 690/184). Determine n, given that 10/7*n**3 - 4/7*n + 0 + 6/7*n**h = 0.
-1, 0, 2/5
Let o(r) be the second derivative of -4*r**5/15 + 49*r**4/9 - 280*r**3/9 + 64*r**2/3 + 6250*r. Suppose o(h) = 0. Calculate h.
1/4, 4, 8
Let x(c) be the third derivative of 1/280*c**7 + 19/480*c**6 + 0*c**3 + 0 - 7/96*c**4 + 0*c - 57*c**2 - 1/16*c**5. Factor x(b).
b*(b - 1)*(b + 7)*(3*b + 1)/4
Let i = -210 - -213. Solve -5*a**i + 2*a**3 + 2*a**2 + 3*a**2 - 7*a**2 + a = 0 for a.
-1, 0, 1/3
Let l(r) be the third derivative of 0 + 1/780*r**6 + 5/13*r**3 + 23/156*r**4 + 3/130*r**5 - 175*r**2 + 0*r. Determine b so that l(b) = 0.
-5, -3, -1
Let o(g) be the second derivative of g**8/4480 - 11*g**7/1680 + 13*g**6/240 - g**5/5 - 67*g**4/6 + 258*g. Let y(k) be the third derivative of o(k). Factor y(w).
3*(w - 8)*(w - 2)*(w - 1)/2
Suppose 8*q - 10*q = -3*j + 4, 2*j - q = 2. Let p(v) be the second derivative of 7*v + 0 - 14/15*v**6 - v**5 + j*v**2 + 2/3*v**4 + 0*v**3. Factor p(k).
-4*k**2*(k + 1)*(7*k - 2)
Factor -312*z + 7*z**4 + 1582*z**2 + 771*z**3 + 8*z**4 - 918*z**2 - 1138*z**2.
3*z*(z - 1)*(z + 5