be the second derivative of j**5/16 - 5*j**4/6 - 25*j**3/6 - 71*j. Factor t(x).
5*x*(x - 10)*(x + 2)/4
Let y(j) = -j**2 + 3*j + 1. Let q(k) = 4*k**3 + 304*k**2 + 1752*k + 2560. Let x(w) = q(w) - 4*y(w). Suppose x(z) = 0. What is z?
-71, -3
Suppose -4*n + 68 = s, 0 = -s - s - 4*n + 120. Determine t, given that -3*t**2 - s*t**3 + 4*t + 60*t**3 + 13*t**2 + 2*t**4 = 0.
-2, -1, 0
Factor -6*b + 2/9*b**3 + 20/9*b**2 - 8.
2*(b - 3)*(b + 1)*(b + 12)/9
Let d(s) = s**3 + 9*s**2 + 7*s - 6. Let p be (-6)/4*(-16)/(-3). Let j be d(p). Find c such that 3*c**2 + c + 0*c**2 - 2*c**j + 0*c = 0.
-1, 0
Let x be ((22/20)/11)/(12/136). Let w(o) be the first derivative of -7/3*o**4 - 22/9*o**3 - 4/3*o**2 + 2 - 1/3*o - 2/9*o**6 - x*o**5. Let w(k) = 0. What is k?
-1, -1/4
Let w(s) be the third derivative of -7*s**7/180 - 7*s**6/36 + s**5/30 + 10*s**4/9 - 16*s**3/9 + 12*s**2. Find m, given that w(m) = 0.
-2, 4/7
Let x(b) be the second derivative of -b**4/4 - 23*b**3/2 + 36*b**2 - 378*b. Factor x(r).
-3*(r - 1)*(r + 24)
Suppose 18*z + 238 - 274 = 0. Factor -3/8 - 9/8*u**z + 15/8*u - 27/8*u**3.
-3*(u + 1)*(3*u - 1)**2/8
Let n(y) = -8*y**4 + 20*y**3 - 42*y**2 - 98*y + 176. Let s(v) = 7*v**4 - 21*v**3 + 41*v**2 + 99*v - 176. Let p(w) = 5*n(w) + 6*s(w). Find l such that p(l) = 0.
-2, 2, 11
Let b be (-1371)/(-18) + 2/(-12). Suppose 5*z - b = a, 5*z - 80 = 6*a - a. Factor -z*d**3 - 4*d**5 - 20*d**4 - 13*d**2 - 23*d**2 - 21*d**3 + 8*d**2 - 8*d.
-4*d*(d + 1)**3*(d + 2)
Let c(b) be the third derivative of -b**6/120 + b**5/12 + 7*b**4/12 + b**3/2 + 9*b**2. Let p be c(7). Factor 4*f**3 - 2*f**3 + 3*f - 4*f**3 - f**p.
-3*f*(f - 1)*(f + 1)
Suppose 79 - 3 = 19*b. Let z(c) be the second derivative of 0*c**3 - 1/3*c**b - 3*c + 1/10*c**5 + 0*c**2 + 0. Factor z(s).
2*s**2*(s - 2)
Let o(j) be the third derivative of -j**6/960 + j**5/160 - 5*j**3/3 - 7*j**2. Let l(s) be the first derivative of o(s). Find p, given that l(p) = 0.
0, 2
Suppose -5*x + 14 = -3*m, m + x - 5 - 1 = 0. Factor -4*i**3 + 0*i**m - 6*i**2 + 10*i**2.
-4*i**2*(i - 1)
Let c(u) = 5*u**3 + 30*u**2 + 65*u. Let v(s) = s + 590 - 590. Let q(l) = c(l) - 20*v(l). Factor q(b).
5*b*(b + 3)**2
Let -3*b**2 + 92*b + 22*b - 168*b + b**2 = 0. Calculate b.
-27, 0
Let k(p) = p**4 + 2*p. Let j(v) = 2*v**4 + 5*v. Let b(w) = 2*j(w) - 5*k(w). Determine r so that b(r) = 0.
0
Let x(y) be the first derivative of 3*y**5/5 + 3*y**4 - 28*y**3 + 48*y**2 - 338. Solve x(n) = 0.
-8, 0, 2
Let q(u) be the first derivative of -u**4/4 + 14*u**3/3 - 12*u**2 + 2*u + 42. Let x be q(12). Factor 0 + 3/5*v**x + 9/5*v**3 + 9/5*v**4 + 0*v + 3/5*v**5.
3*v**2*(v + 1)**3/5
Let h(u) = u**4 - 8*u**3 - u**2 - 4*u. Let x(q) = -8*q**4 + 70*q**3 + 8*q**2 + 34*q. Let k(l) = 52*h(l) + 6*x(l). Factor k(v).
4*v*(v - 1)*(v + 1)**2
Let v be 46/115*2/4. Factor 1/5 + 0*w**2 - 2/5*w + 2/5*w**3 - v*w**4.
-(w - 1)**3*(w + 1)/5
Factor 2*k**3 + 75 + 8*k**2 + 2*k - 71 + 8*k.
2*(k + 1)**2*(k + 2)
Let q(c) be the first derivative of -c**6/48 - c**5/40 + c**4/32 + c**3/24 + 9. Let q(a) = 0. Calculate a.
-1, 0, 1
Let 56/19*c - 120/19*c**3 - 108/19*c**2 + 50/19*c**4 - 6/19 = 0. What is c?
-1, 1/5, 3
Suppose 2*n + 0*c - 28 = 4*c, 4*c = 3*n - 36. Factor 5*h**4 - 2*h**3 + 5*h**4 - n*h**4.
2*h**3*(h - 1)
Let y(o) be the third derivative of -o**5/150 + 11*o**4/10 - 363*o**3/5 + 5*o**2 - 1. Suppose y(f) = 0. Calculate f.
33
Let p be (-544)/(-256) + (-9)/8 + 1. Determine h so that -2/9*h**p + 0*h + 2/9*h**3 + 0 = 0.
0, 1
Suppose 18*r - 16*r = 0. Factor 10*i + 0*i**2 + 7 + 2*i**2 + 1 + r*i**2.
2*(i + 1)*(i + 4)
Determine z, given that -4/7*z - 4/7*z**2 + 48/7 = 0.
-4, 3
Determine x, given that 26/9*x - 2/9*x**2 - 28/3 = 0.
6, 7
Let k(g) = 2*g**4 - g**3 - g**2 + g - 1. Let c(v) = 42*v**4 - 372*v**3 + 3495*v**2 - 11085*v - 3015. Let f(a) = c(a) - 15*k(a). Factor f(u).
3*(u - 10)**3*(4*u + 1)
Let j(n) be the second derivative of 0*n**2 + 0 + 0*n**3 + 2/15*n**4 + 8/105*n**7 + 16*n + 2/25*n**6 - 9/25*n**5. Determine x so that j(x) = 0.
-2, 0, 1/4, 1
Let p(x) be the second derivative of 5/6*x**3 - 29*x - 1/4*x**5 + 5*x**2 + 1/6*x**6 + 0 - 5/4*x**4. Let p(j) = 0. Calculate j.
-1, 1, 2
Suppose -4*w - 355*f - 7 = -358*f, -2*w + 4*f = 16. Suppose -1/4*m**w - 7/2*m - 49/4 = 0. Calculate m.
-7
Suppose 3*u - 54 + 42 = 0. Let q(r) be the first derivative of 1/5*r**2 + 1/10*r**u - 4/15*r**3 + 0*r + 10. Factor q(d).
2*d*(d - 1)**2/5
Let f(k) = 8*k**5 + 24*k**4 + 40*k**3 + 24*k**2 + 4*k. Let a(b) = b**5 + b**4 - b + 4*b**2 + 9*b**2 + b**3 - 14*b**2. Let d(i) = 4*a(i) - f(i). Factor d(x).
-4*x*(x + 1)**3*(x + 2)
Suppose 0 = -5*w - 5*j - 25, 2*w - w + 5*j + 9 = 0. Let r be 45/10*w/(-6). Factor 0 + 3 + 3*k**2 - 9 + 0 - r*k.
3*(k - 2)*(k + 1)
Let b be 1/(3 + (-28)/8) - -4. Suppose -4*l - b*t + 8 = 0, -3*t - 2 = 10. Factor -2/3*w**2 + 0*w + w**3 - 1/3*w**l + 0.
-w**2*(w - 2)*(w - 1)/3
Suppose 2*q = -q + 4*q. Solve -12*m + q*m - 4*m**2 + 51*m**4 - 13*m**2 + 81*m**3 - 7*m**2 - 42*m**5 = 0 for m.
-1, -2/7, 0, 1/2, 2
Let b(p) = -3*p**3 - 13*p**2 - 7*p + 1. Suppose 2*z + 10 = 16. Let j(n) = n**2 + n + 1. Let o(y) = z*j(y) - 3*b(y). What is s in o(s) = 0?
-4, -2/3, 0
Factor -102/7 - 202/7*u + 2/7*u**3 - 14*u**2.
2*(u - 51)*(u + 1)**2/7
Let h = -11012 + 11014. Factor 0 - 2/5*d**h + 8/5*d.
-2*d*(d - 4)/5
Let d(p) be the second derivative of -p**4/28 - 6*p**3/7 - 30*p**2/7 + 283*p. Factor d(x).
-3*(x + 2)*(x + 10)/7
Let b(h) be the second derivative of -h**5/20 + h**4/3 - h**3/2 + 3*h**2/2 + h. Let u be b(3). Factor 0*f**3 + f + 12*f**2 + f + u*f**3 + 10*f.
3*f*(f + 2)**2
Let q(v) = v**3 - 29*v**2 + 167*v + 21. Let x be q(21). Let j(m) be the first derivative of x*m + 0*m**2 - 8 + 4/3*m**3. Factor j(w).
4*w**2
Let k(d) be the third derivative of 13*d**2 + 0 + 0*d + 1/60*d**5 + 2/3*d**4 + 32/3*d**3. Solve k(q) = 0.
-8
Let y be 1 + 0/((-2)/(-1)). Let k = 3 + y. Factor -3*x**k - x**3 + 2*x**4 + 2*x**4.
x**3*(x - 1)
Let u(q) be the second derivative of -q**6/195 + 2*q**5/65 + 5*q**4/78 + q - 10. Suppose u(v) = 0. Calculate v.
-1, 0, 5
Let s(o) be the first derivative of 64/3*o**3 + 10*o**2 - 16/5*o**5 + 0*o - 38 - 17*o**4. Solve s(j) = 0 for j.
-5, -1/4, 0, 1
Let c be (-12)/(-18) - (26/3)/((-48)/16). Let c + 8/3*h + 4/9*h**2 = 0. Calculate h.
-4, -2
Let z(d) be the first derivative of -d**5/140 - d**4/84 + d**3/42 + d**2/14 - 11*d - 9. Let j(u) be the first derivative of z(u). Factor j(i).
-(i - 1)*(i + 1)**2/7
Let k be (1 + (-4 - -5))*1. Suppose 0 = 3*l - 5*v - 0*v - 96, 21 = l + k*v. Let -l*s**5 - 435 + 33*s**3 + 435 - 12*s**2 + 18*s**4 - 12*s = 0. Calculate s.
-2/3, 0, 1
Let i(l) = l**2 + 16*l + 42. Let y be i(-13). Factor -1 - 5/4*c**2 + 2*c + 1/4*c**y.
(c - 2)**2*(c - 1)/4
Solve 0 + 3/8*q**2 - 9/4*q + 3/2*q**3 + 3/8*q**4 = 0.
-3, -2, 0, 1
Factor 4*i**5 - 880*i - 480 - 7*i**5 - 126*i**3 - 560*i**2 + 8*i**5 + 6*i**3 + 10*i**4.
5*(i - 6)*(i + 2)**4
Factor 484/3*k + 4/3*k**3 + 0 + 88/3*k**2.
4*k*(k + 11)**2/3
Let o(g) be the second derivative of g**5/4 - 70*g**4 + 7840*g**3 - 439040*g**2 + 129*g. Factor o(z).
5*(z - 56)**3
Let a = 1088 + -1083. Let l(c) = 2*c**2 + c - 5. Let z be l(-6). Factor b**3 + z*b**a + 4*b**4 - 60*b**5 - 2*b**4.
b**3*(b + 1)**2
Let w = 312 - 165. Let i be w/70 - 4/(-10). Find m such that -5/2*m**2 + 0 + i*m**4 - m**5 + 0*m**3 + m = 0.
-1, 0, 1/2, 1, 2
Let k(d) be the third derivative of 0*d + 0*d**3 + 0*d**4 + 0 + 34*d**2 + 0*d**6 - 1/525*d**7 + 0*d**5. Let k(m) = 0. What is m?
0
Let j(u) be the first derivative of 9*u - 2*u**3 + 6*u**2 - 4 + 1/4*u**4. Let g(l) be the first derivative of j(l). Determine m so that g(m) = 0.
2
Determine d, given that -72 + 58*d**2 + 47*d**2 - 107*d**2 - 74*d = 0.
-36, -1
Suppose 0 = -64*x + 71*x - 392. What is t in 5*t**4 - x*t**3 + 4*t**5 + 53*t**3 - 2*t**5 = 0?
-3, 0, 1/2
Determine b so that 12/5 - 8*b**5 - 22/5*b - 126/5*b**2 + 114/5*b**4 + 62/5*b**3 = 0.
-1, -2/5, 1/4, 1, 3
Let b(k) be the first derivative of -2*k**7/15 + k**6/6 + 16*k**5/15 + 2*k**4/3 - 4*k**2 + 9. Let p(u) be the second derivative of b(u). Solve p(h) = 0.
-1, -2/7, 0, 2
Let o(w) be the second derivative of w**5/120 - 13*w**3/36 + w**2 - 578*w. Factor o(b).
(b - 3)*(b - 1)*(b + 4)/6
Let z(d) be the first derivative of 3*d**5/80 + d**4/16 - 13*d + 10. Let w(o) be the first derivative of z(o). Determine 