 569. Let z be j(-4). Let r(d) be the first derivative of -2/5*d**z + 22/3*d**3 + d**4 - 13 - 72*d - 12*d**2. Factor r(l).
-2*(l - 3)**2*(l + 2)**2
Let a(t) = -13*t**4 - 7*t**3 + 25*t**2 + 12*t - 7. Let d(k) = -4*k**4 - 2*k**3 + 8*k**2 + 4*k - 2. Let u(z) = 4*a(z) - 14*d(z). Factor u(x).
4*x*(x - 2)*(x + 1)**2
Suppose -6*d + 1014 = 996. Let n(m) be the second derivative of 0*m**2 - 1/80*m**5 + 0*m**d + 0*m**6 + 7*m + 1/168*m**7 + 0 + 0*m**4. Let n(i) = 0. Calculate i.
-1, 0, 1
Factor 3 - 27/4*p + 3/2*p**2.
3*(p - 4)*(2*p - 1)/4
Let l be -1714*-6*(-5)/240. Let a = l - -215. Find n, given that -a*n**2 + 3/8*n**3 + 0 + 3/8*n = 0.
0, 1
Let 15/7*t**2 + 0 - 2/7*t = 0. Calculate t.
0, 2/15
Let v(t) be the third derivative of -t**7/735 - 3*t**6/140 - 13*t**5/210 + 15*t**4/28 + 50*t**3/21 - 47*t**2. Let v(w) = 0. What is w?
-5, -1, 2
Suppose -8 + 44 = 4*d + 4*v, 2*d - 28 = -4*v. Suppose 7*t - 25 + d = 0. Solve 0*m + 0*m**2 + 2/9*m**4 + 2/9*m**t + 0 = 0.
-1, 0
Let n(l) be the first derivative of -2/45*l**5 + 0*l - 32/27*l**3 + 7/18*l**4 - 6 + 4/3*l**2. Find v, given that n(v) = 0.
0, 2, 3
Let g(q) = -q**3 + q**2 + 6*q - 3. Let d be g(3). Let o be (-34)/d - 126/21. Solve -4/3*x**4 + 4/3 - x**2 - 13/3*x**3 + o*x = 0.
-2, -1/4, 1
Let g(y) be the second derivative of y**5/4 - 5*y**4 - 150*y. Find s, given that g(s) = 0.
0, 12
Let w(n) be the first derivative of -n**4/16 + n**3 - 6*n**2 + 8*n + 21. Let l(f) be the first derivative of w(f). Factor l(r).
-3*(r - 4)**2/4
Factor -7542*z**3 - 526*z**2 - 845*z - 540*z**4 - 1248*z**2 - 20*z**5 + 3637*z**3 + 292*z**2 - 2028*z**2.
-5*z*(z + 13)**2*(2*z + 1)**2
Let r(z) = -3*z + 23. Let s be r(7). Solve 0 + 1/3*o**s + 1/3*o = 0 for o.
-1, 0
Let d be (-3 - -1)/((-900)/120). Factor -2/15*k + 0 - 2/15*k**3 + d*k**2.
-2*k*(k - 1)**2/15
Let l be 1/(-3)*(0 + -3). Solve l - 1 + d**3 + d**2 = 0.
-1, 0
Let y be ((-1)/(-3))/((-1)/(-12)). Suppose 2*a - 3*r - 17 = -4*r, -a - y*r = 2. Find n such that 3*n**3 + a*n**2 + n + 4*n - n - 8 = 0.
-2, 2/3
Let d(o) = -o**3 - 8*o**2 - 8*o - 7. Let x be d(-7). Suppose -5*k - 2*l + 4*l + 16 = 0, x = l + 3. Solve 97*h**k - 2*h**3 + 0*h**4 - 2*h**4 + 2*h - 95*h**2 = 0.
-1, 0, 1
Let i = -18/19 + 55/38. Let a(l) be the second derivative of 3/2*l**2 + l - 1/2*l**3 + 0 + 3/10*l**5 - 1/14*l**7 - i*l**4 + 1/10*l**6. What is s in a(s) = 0?
-1, 1
Let h(x) be the second derivative of 5*x**2 + 0 - 15*x + 5/6*x**3 - 1/4*x**5 - 5/6*x**4. Determine w so that h(w) = 0.
-2, -1, 1
Let n be (6/(-4) - 0)*(-752)/540. Let s = -8/9 + n. Factor -16/5*q**3 - s*q**4 + 0 - 4/5*q - 14/5*q**2.
-2*q*(q + 1)**2*(3*q + 2)/5
Let p(x) be the first derivative of 1/16*x**4 - 1/4*x**2 + 0*x - 1/12*x**3 + 25. Factor p(l).
l*(l - 2)*(l + 1)/4
Let b(r) be the second derivative of 3*r**5/10 + 4*r**4/9 - r**3 - 8*r**2/3 + 2*r + 38. Find h, given that b(h) = 0.
-1, -8/9, 1
Let m = 181 - 177. Suppose n + 5*u = -20, -3*n - u = -0*n + m. Let 3/5*g**2 + n*g + 0 = 0. Calculate g.
0
Suppose -4*a + 8 = -4*b, -5*a = 2*b - 20 + 3. Suppose 4*c + v + a*v - 32 = 0, 2*v - 28 = -5*c. Factor -c*q**3 - 2*q**4 + 2*q**2 - 5*q**2 + 0*q**2 + q**2.
-2*q**2*(q + 1)**2
Let y(c) = 8*c**3 + 4*c**2 + 5*c - 12. Let r(d) = -29*d**3 - 15*d**2 - 21*d + 48. Let l(p) = -6*r(p) - 22*y(p). Factor l(t).
-2*(t - 2)**2*(t + 3)
Let w = 351 + -351. Let x(j) be the second derivative of w - 6*j + j**5 + 4/3*j**3 + 7/3*j**4 + 0*j**2. Factor x(c).
4*c*(c + 1)*(5*c + 2)
Let f = 4 - 12. Let w = f - -19. Find q, given that -w*q**2 - 36*q**5 - 8*q - 4 - 32*q**2 + 62*q**2 + 35*q**3 - 24*q**4 = 0.
-1, -1/2, 2/3
Let m(s) be the second derivative of s**4/27 + 10*s**3/27 - 4*s**2/3 + 608*s. Suppose m(i) = 0. Calculate i.
-6, 1
Let h(g) be the second derivative of -g**5/10 - g**4/3 + g**3 - 9*g + 5. Let h(x) = 0. Calculate x.
-3, 0, 1
Let v(d) be the third derivative of -4*d**2 + 0 + 0*d - 4/33*d**3 + 1/33*d**4 - 1/330*d**5. Determine q, given that v(q) = 0.
2
Let w(q) = -37*q - 24. Let a be w(-8). Let l be (a/22)/2 + 22/(-121). Let 6*j**3 + 3/5 + l*j**2 + 3/5*j**5 + 3*j**4 + 3*j = 0. What is j?
-1
Let m(q) = 15*q**3 - 315*q**2 + 305*q - 75. Let z(t) = -16*t**3 + 316*t**2 - 305*t + 75. Let w(c) = -4*m(c) - 5*z(c). Factor w(i).
5*(i - 15)*(2*i - 1)**2
Let t(z) be the second derivative of -z**4/3 + 4*z**3/3 - 2*z**2 - 472*z. Suppose t(w) = 0. Calculate w.
1
Let o be (-102)/(-42) + (-9)/21. Determine f, given that 2*f**5 + 3*f**2 - 8 - o*f**3 + 11*f**2 - 607*f - 6*f**4 + 607*f = 0.
-1, 1, 2
Determine w, given that 0*w + 0 - 3/2*w**5 - 3*w**4 + 0*w**2 - 3/2*w**3 = 0.
-1, 0
Let f = 1041 + -1039. Let o(t) be the first derivative of 2/5*t - 1/5*t**f - 2/15*t**3 + 1 + 1/10*t**4. Factor o(b).
2*(b - 1)**2*(b + 1)/5
Let w(q) = -q**2 + 8*q - 9. Let h be w(6). Factor 2*x - 2*x**4 + x**3 + 1 + x**4 - 9*x**h + 6*x**3.
-(x - 1)*(x + 1)**3
Find t such that -10/3*t**4 - 18*t**3 - 42*t**2 + 0 - 36*t - 2/9*t**5 = 0.
-6, -3, 0
Suppose 37 = 2*s - 5*h, 4*h + 1 = -3*s - 1. Suppose 40 = 2*x - c, 0 = -2*c + s*c + 16. Factor 6 + 7*f + x*f**3 + 2*f - 21*f**3.
-3*(f - 2)*(f + 1)**2
Let d(r) = -10 + 2 + 9 + r + r**4 - r**2. Let a(v) = -18*v**4 - 48*v**3 - 78*v**2 - 69*v - 21. Let h(g) = -a(g) - 9*d(g). Factor h(s).
3*(s + 1)*(s + 2)**2*(3*s + 1)
Let z(w) = -3*w**3 - 9*w**2 + 33*w - 23. Let d(q) = 8*q**3 + 17*q**2 - 65*q + 45. Let p(t) = -2*d(t) - 5*z(t). Factor p(l).
-(l - 5)**2*(l - 1)
Suppose -10*h = -138 + 8. Suppose -3*c = h*c - 2*c. Factor c - 2*x**2 - 4/3*x.
-2*x*(3*x + 2)/3
Let u(r) = 2*r - 4. Let v be u(4). Suppose -2*n + 0*n = -4. Solve 2*x**3 + x**2 + 2*x**5 + 4*x**v - x**n = 0 for x.
-1, 0
Suppose -11*j + 10*j = -24. Let y = j - 21. Factor 8*x**3 - 3*x - 3*x**5 - x**3 - x**y.
-3*x*(x - 1)**2*(x + 1)**2
Let f = -24 + 28. Let x(t) = -2*t**3 + 8*t**2 + 28*t + 12. Let a(u) = u**3 + u**2 - u + 1. Let z(p) = f*a(p) + x(p). Suppose z(l) = 0. Calculate l.
-2
Determine r so that 7/3*r**3 + 4/3 + 20/3*r + 23/3*r**2 = 0.
-2, -1, -2/7
Let d be -1 + -3 + -9 + 15. Let 3 - 2 - 5 + 2 + d*s**2 = 0. Calculate s.
-1, 1
Factor -100/3*h - 4/3*h**3 - 56/3*h**2 - 16.
-4*(h + 1)**2*(h + 12)/3
Let g be (-8 - -14)/(1 + 1). Suppose -5*t + 2 = -88. Factor 22*x**2 + 2*x**4 - t*x**2 - 2*x**3 - 4*x**g.
2*x**2*(x - 2)*(x - 1)
Factor -256*w + 14*w**2 - 19*w**2 + 136*w.
-5*w*(w + 24)
Factor -136 + 2*n**5 - 2*n**3 + 268 - 132 + 4*n**2 - 4*n**4.
2*n**2*(n - 2)*(n - 1)*(n + 1)
Let a(q) be the second derivative of -9*q**6/5 + 3*q**5/5 + 143*q**4/18 - 16*q**3/9 - 64*q**2/3 - 423*q. Factor a(l).
-2*(l - 1)**2*(9*l + 8)**2/3
Let o(l) = -l**4 - 5*l**3 - 4. Let w(h) = -2*h**3 - h**2 - 1. Let n(t) = o(t) - 4*w(t). Factor n(p).
-p**2*(p - 4)*(p + 1)
Factor 7/5*t + 13/5*t**4 + 3/5*t**5 + 18/5*t**2 + 22/5*t**3 + 1/5.
(t + 1)**4*(3*t + 1)/5
Let o be ((-3)/6)/((-5)/390). Let -48*a**4 + 20*a + 22*a**2 + o*a**2 + 25*a**3 + 53*a**4 - 21*a**2 = 0. Calculate a.
-2, -1, 0
Factor 2/7*k**5 + 4/7 + 8/7*k**3 + 4/7*k**2 - 8/7*k**4 - 10/7*k.
2*(k - 2)*(k - 1)**3*(k + 1)/7
Let h(y) be the third derivative of 0 + 1/7*y**3 - 15*y**2 + 1/56*y**4 + 0*y + 1/490*y**7 - 3/140*y**5 - 1/280*y**6. Suppose h(d) = 0. Calculate d.
-1, 1, 2
Let a(w) be the third derivative of 0 - 5*w**2 - 4*w**4 + 0*w - 1/40*w**6 - 16*w**3 - 1/2*w**5. Suppose a(r) = 0. What is r?
-4, -2
Solve -11 - d**3 - 150*d + 35 + 2*d**3 - 5*d**2 + 17*d**2 + 185*d = 0 for d.
-8, -3, -1
Suppose -19*h = -14*h - 10. Factor 7*l**h - 5*l**2 + 6*l**3 + 7*l**4 + 2*l**2 - 5*l**4.
2*l**2*(l + 1)*(l + 2)
Let s be 553/2844*39/14 - (-1)/8. What is h in -4/3*h**4 + 0*h - 1/3*h**5 - 5/3*h**3 + 0 - s*h**2 = 0?
-2, -1, 0
Let x(z) be the third derivative of -z**9/60480 - z**8/10080 + 7*z**5/30 - z**2. Let g(a) be the third derivative of x(a). Suppose g(q) = 0. Calculate q.
-2, 0
Let z be 603/134*8/18. Find l such that 0 + 0*l + 3/4*l**z = 0.
0
Let u(j) = 15*j**3 - 15*j**2 + 3*j + 15. Let k(z) = -z**3 + z**2 - 1. Suppose 0 = -7*p + 10*p + 3. Let d(v) = p*u(v) - 18*k(v). Factor d(a).
3*(a - 1)**2*(a + 1)
Let l = 78 - 76. Factor -5*y**l + 21*y**2 - y**2 + 5*y**3 + 12*y - 2*y.
5*y*(y + 1)*(y + 2)
Let n(u) be the third derivative of 16/9*u**3 + 1/315*u**7 - u**2 + 0*u + 0 + 8/9*u**4 + 2/45*u**6 + 4/15*u**5. Find o, given that n(o) = 0.
-2
Let q be 5/(75/6) + (-5)/(150/2). Factor 1/3*f + 0*f**2 + 0 - q*f**3.
-f*(f - 1)*(f + 1