4)/2)). Determine a, given that -3*a**4 - a**2 - 6*a**3 + 15*a**3 - p*a**2 - 3*a**2 = 0.
0, 1, 2
Let j(r) = 7*r**3 - 3*r**2 + 2*r - 3. Let i(k) = -6*k**3 + 2*k**2 + 2. Let s(q) = 3*i(q) + 2*j(q). Factor s(d).
-4*d*(d - 1)*(d + 1)
Let s(x) be the third derivative of x**8/231840 - x**7/57960 - x**6/4140 - 11*x**5/60 + 15*x**2. Let c(r) be the third derivative of s(r). Factor c(y).
2*(y - 2)*(y + 1)/23
Factor 72*c - 10*c**2 + 8*c**2 - 5*c**2 + 10*c**2.
3*c*(c + 24)
Let f be (-54)/162*144/(-66). Determine j, given that 2*j**3 - f - 18/11*j**2 - 48/11*j = 0.
-1, -2/11, 2
Factor 14/5 + 3*s + 1/5*s**2.
(s + 1)*(s + 14)/5
Let t = 1377 + -9609/7. Find k such that 0 - t*k**2 - 9/7*k - 18/7*k**4 - 36/7*k**3 - 3/7*k**5 = 0.
-3, -1, 0
Let q(t) be the second derivative of -3*t**5/20 + 5*t**4/4 - 4*t**3 + 6*t**2 - 67*t. Factor q(o).
-3*(o - 2)**2*(o - 1)
Let b be (-5 - -3)/(3/(3/2)). Let j(x) = 3*x**4 + 3*x**3 - 9*x**2. Let g(o) = -o**3 + o**2. Let u(y) = b*j(y) - 9*g(y). Factor u(t).
-3*t**3*(t - 2)
Let k(s) be the first derivative of s**6/480 - s**5/8 + 25*s**4/8 + 43*s**3/3 - 17. Let f(g) be the third derivative of k(g). Factor f(v).
3*(v - 10)**2/4
Let m(k) = k**3 - 23*k**2 + 23*k - 12. Let s be m(22). Factor 5*v**3 - 15*v**2 + 2*v - s*v + 8*v.
5*v**2*(v - 3)
Let n(h) = h**3 - h**2 - 4*h + 7. Let g be n(2). Determine c, given that c**g + 0*c**3 + 6*c**3 - 3*c**3 + 8*c**2 + 4*c = 0.
-1, 0
Factor 2*a**4 - 10*a**2 - 139*a**3 + 76*a**2 + 288*a**3 - 129*a**3 + 72*a.
2*a*(a + 3)**2*(a + 4)
What is c in 49*c + 9*c**4 - 6*c**5 - 33*c**2 + 24*c**3 - 67*c + 14*c**4 + 10*c**4 = 0?
-1, -1/2, 0, 1, 6
Let i be ((-2)/(-6)*-1)/((-604)/3624). Solve -20/3*d - 16/3 + 20/3*d**3 + 4/3*d**4 + 4*d**i = 0 for d.
-4, -1, 1
Let 78/5*y**3 + 64/5*y**2 + 0 + 8/5*y = 0. What is y?
-2/3, -2/13, 0
Factor -9*q + 1/4*q**2 + 81.
(q - 18)**2/4
Let m(w) = 5*w**3 - 182*w**2 + 338*w + 2. Let y(l) = 110*l**3 - 4005*l**2 + 7435*l + 45. Let o(b) = -45*m(b) + 2*y(b). Solve o(s) = 0.
0, 2, 34
Let v = 5 - 2. Solve -4*p**3 + 3*p**3 + 5*p**v - 28*p**2 + 20*p**2 = 0.
0, 2
Factor -7*b - 4*b**3 - 2*b**2 + b**3 - 43*b**2 + 169*b.
-3*b*(b - 3)*(b + 18)
Factor -3/2 + 3/2*x**2 + 4/3*x - 4/3*x**3.
-(x - 1)*(x + 1)*(8*x - 9)/6
Let f(q) = 3*q**3 + 3*q**2 + 9*q - 11. Let t(n) = -n**3 + n**2 - 2*n + 1. Let k(b) = -5*f(b) - 20*t(b). Solve k(z) = 0 for z.
-1, 1, 7
Determine r so that -21*r**4 + 903*r**2 - 8*r**5 - 240*r + 100 - 844*r**2 + 52*r**3 + 10*r**5 = 0.
-2, 1/2, 2, 5
Let b(h) = h**3 + 9*h**2 + 8*h. Let m be b(-8). Factor 10/9*z**2 + m + 4/9*z.
2*z*(5*z + 2)/9
What is s in 1/2*s**3 + 0 + 0*s - 1/2*s**5 + 13/2*s**4 - 13/2*s**2 = 0?
-1, 0, 1, 13
Let i = 827/129 - -11/43. Let d be (-25)/(-12) + 6/(-8). Factor -16/3*k**2 - d*k**3 - 8/3 - i*k.
-4*(k + 1)**2*(k + 2)/3
Let w(f) be the third derivative of f**5/10 + 37*f**4/60 - 8*f**3/15 + 38*f**2. Factor w(c).
2*(3*c + 8)*(5*c - 1)/5
Let c(a) = -7*a**2 - 3*a. Let r(q) = -3*q**2 + 5*q. Let s(d) = -3*d**2 + 4*d. Let p(f) = 5*r(f) - 6*s(f). Let y(w) = 2*c(w) + 5*p(w). What is i in y(i) = 0?
0, 1
Let t(z) be the third derivative of z**6/40 - 9*z**5/20 + 15*z**4/8 + 25*z**3/2 - 3*z**2 - 26*z. What is h in t(h) = 0?
-1, 5
Let w(z) be the second derivative of z**9/40320 + z**8/2560 + z**7/448 + 3*z**6/640 + 9*z**4/4 + 34*z. Let p(q) be the third derivative of w(q). Factor p(i).
3*i*(i + 1)*(i + 3)**2/8
Factor 6*j - 3/2*j**2 + 18.
-3*(j - 6)*(j + 2)/2
Let v(t) be the third derivative of 0 + 1/1680*t**8 + 3/40*t**4 + 0*t - 1/300*t**6 + 1/25*t**5 + 12*t**2 - 2/525*t**7 + 0*t**3. Find f, given that v(f) = 0.
-1, 0, 3
Let s(i) = -i**2 + 2*i - 3. Let r(j) = -j**4 + 15*j**3 - 56*j**2 + 80*j - 34. Let n(b) = -2*r(b) - 4*s(b). Find c, given that n(c) = 0.
1, 2, 10
Let s(i) = 9*i**3 - 128*i**2 + 560*i - 441. Let a(l) = -3*l**3 + 43*l**2 - 187*l + 147. Let m = -99 + 106. Let r(g) = m*a(g) + 2*s(g). Factor r(q).
-3*(q - 7)**2*(q - 1)
Let v(m) = -m**4 + 20*m**3 - 117*m**2 - 147*m + 3. Let g(u) = -2*u**4 + 41*u**3 - 235*u**2 - 293*u + 5. Let d(w) = -3*g(w) + 5*v(w). Factor d(z).
z*(z - 12)**2*(z + 1)
Let h(q) be the second derivative of -q**4/84 - 73*q**3/42 - 36*q**2/7 - 485*q. Determine x, given that h(x) = 0.
-72, -1
Let a(i) be the second derivative of 5*i**4/12 + 50*i**3/3 - 110*i**2 + 194*i. Suppose a(s) = 0. Calculate s.
-22, 2
Let t(z) = -6*z**3 - 8*z**2 + 6*z + 8. Let a(m) = m**3 + 2*m**2 - 1. Let j(w) = 8*a(w) + t(w). Factor j(i).
2*i*(i + 1)*(i + 3)
Let 22*u**2 - 16*u**3 + 4*u**4 - 12 + 17*u - u - 14*u**2 = 0. Calculate u.
-1, 1, 3
Let u = 315 - 2519/8. Let k(i) be the third derivative of 10*i**2 + 0 - 1/240*i**5 - 1/24*i**4 - u*i**3 + 0*i. Factor k(l).
-(l + 1)*(l + 3)/4
Suppose 12 = 473*z - 471*z. Let k(r) be the third derivative of 0 + 0*r - 1/105*r**7 - 2*r**2 + 0*r**5 + 0*r**3 + 0*r**4 + 0*r**z. Find f such that k(f) = 0.
0
Let p = -2 + -5. Let z(i) = -3*i**2 + 3*i. Let r be ((-6)/(-5))/(2/(-5)). Let x(l) = l**3 + 5*l**2 - 6*l. Let t(k) = p*z(k) + r*x(k). Factor t(m).
-3*m*(m - 1)**2
Let f(q) be the second derivative of -q**6/75 + q**5/50 + 2*q**4/15 - 4*q**3/15 - 72*q. Factor f(w).
-2*w*(w - 2)*(w - 1)*(w + 2)/5
Let n(k) be the first derivative of -100*k**3/3 - 615*k**2/2 - 2025*k - 7. Let v(b) = 9*b**2 + 56*b + 184. Let m(r) = 4*n(r) + 45*v(r). Factor m(f).
5*(f + 6)**2
Let z(i) = -64*i + 4*i**3 + 40 + 86*i**4 - 9 - 296*i**2 - 7 - 8. Let a(d) = -17*d**4 - d**3 + 59*d**2 + 13*d - 3. Let n(v) = -16*a(v) - 3*z(v). Factor n(u).
2*u*(u - 2)*(u + 2)*(7*u + 2)
Let l be (-6)/((-360)/42)*4/56. Let r(c) be the second derivative of 7*c - 1/4*c**2 + 0 - 1/20*c**5 - 1/84*c**7 - 1/12*c**4 + 1/4*c**3 + l*c**6. Factor r(n).
-(n - 1)**4*(n + 1)/2
Let a(r) be the second derivative of r**4/84 - 11*r**3/42 + 9*r**2/7 + 235*r - 1. Factor a(o).
(o - 9)*(o - 2)/7
Let w(p) = 15*p**3 - p + 1. Let l be w(-3). Let j = l + 6017/15. Factor 2/15 - j*z**2 - 2/15*z + 2/15*z**3.
2*(z - 1)**2*(z + 1)/15
Let j be (-2 - 18/(-4))/((-213)/(-568)). Let d(a) be the first derivative of -4*a**2 + 8 - j*a**3 + 12*a. Factor d(l).
-4*(l + 1)*(5*l - 3)
Suppose 3*m - 14 = -x, m + 2 = -4*x + 2*x. Suppose -482 - m*r**2 + 482 - 2*r**3 + 8*r = 0. Calculate r.
-4, 0, 1
Suppose -5*k = 2*j + 9, -k + 2 + 1 = 2*j. Factor 10*r**3 - 2*r**j - 4*r**3 - r**3.
3*r**3
Suppose -5*b = 7*b - 60. Let x(q) be the third derivative of 0*q + 7*q**2 - 5/12*q**4 + 7/30*q**b + 0 - 2/3*q**3. Factor x(u).
2*(u - 1)*(7*u + 2)
Let o(t) be the second derivative of t**6/210 + t**5/35 + t**4/21 - 38*t - 1. Factor o(d).
d**2*(d + 2)**2/7
Let f(u) be the second derivative of -51*u - 1/180*u**6 - 1/12*u**4 + 0*u**3 + 1/24*u**5 + 0 + 0*u**2. Find p, given that f(p) = 0.
0, 2, 3
Suppose -67*s = 8*s - 75. Factor 1/4*m**2 + 0*m - s.
(m - 2)*(m + 2)/4
Let t(g) be the first derivative of -25 + 30*g**2 + 23*g**3 + 9/2*g**4 - 12*g. Factor t(j).
3*(j + 2)**2*(6*j - 1)
Let t(p) be the third derivative of p**5/90 + p**4/6 + p**3 - 8*p**2 - 2. Factor t(a).
2*(a + 3)**2/3
Let q(x) = x**2 - 3*x - 2. Let b be q(4). Factor 864*n + 838 + 24*n**3 - 397 + 824 + 216*n**b + n**4 + 31.
(n + 6)**4
Let q(g) = -g**3 + 2*g**2 + 11*g - 7. Let z be q(4). Suppose z*w = -12 + 12. Factor 1/2*a**2 - 1/2 + w*a.
(a - 1)*(a + 1)/2
Let b(w) = w**2 + 3*w - 1. Let z(d) = 772*d + 38420. Let h(p) = 4*b(p) + z(p). Find u, given that h(u) = 0.
-98
Factor -107*k**2 + 28 + 53*k**2 + 52*k**2 + 33 + 10*k + 39.
-2*(k - 10)*(k + 5)
Let u(y) be the second derivative of y**4/42 + 52*y**3/7 + 6084*y**2/7 + 8*y - 2. Solve u(w) = 0.
-78
Suppose 0 = 2*v - 19 + 55. Let k be 5/3*v/(-6). Factor k*p**3 + 5*p + 3*p**2 - 33*p**2 - 40*p**3.
-5*p*(p + 1)*(7*p - 1)
Let a(u) be the second derivative of u**4/16 - 33*u**3/4 + 3267*u**2/8 + 32*u. Determine m, given that a(m) = 0.
33
Suppose -2714*w = -2725*w. What is j in w - 9/2*j**2 + j = 0?
0, 2/9
Let y be 3 + (-297)/88 - (-58)/112. What is a in -2/7*a**4 + 0*a**3 + 0 - y*a + 1/7*a**5 + 2/7*a**2 = 0?
-1, 0, 1
Let q = -33 - -47. Let d be 10/q - 4/(-28). Suppose 9/7*x**2 - 3/7*x**4 - 24/7*x + 12/7 + d*x**3 = 0. What is x?
-2, 1, 2
Let a(u) be the second derivative of -u**9/24192 - u**8/13440 + u**7/1344 - u**6/960 + 8*u**3 + 49*u. Let s(y) be the second derivative of a(y). Factor s(p).
-p**2*(p - 1)**2*(p + 3)/8
Let h(s) be the first derivative of s**8/6720 +