 - 5. Factor -2*l**2 - 44*l - l**4 - 3*l**3 + 43*l - l**x.
-l*(l + 1)**3
Let j(h) = -45*h**4 + 183*h**3 - 148*h**2 - 168*h - 41. Let o(g) = 22*g**4 - 92*g**3 + 74*g**2 + 84*g + 20. Let s(l) = 4*j(l) + 9*o(l). Factor s(a).
2*(a - 4)*(a - 2)*(3*a + 1)**2
Let r(w) be the third derivative of 5/12*w**4 - 15/14*w**7 - 5/3*w**5 + 0 + 0*w + 5/6*w**3 - 11/4*w**6 - 50*w**2. Suppose r(m) = 0. Calculate m.
-1, -1/3, 1/5
Suppose u - 3*d = -5, 10*u - 12*u - 3*d + 17 = 0. Let g(f) be the third derivative of 0*f - 1/12*f**3 + 0 + 3/80*f**5 - f**2 - 7/96*f**u. Factor g(y).
(y - 1)*(9*y + 2)/4
Suppose -6*b = -9*b + 15. Find r, given that r**5 - 9*r**4 + 6*r**3 - 6*r**4 + 6*r**2 + 2*r**b + 6*r**4 + 3 - 9*r = 0.
-1, 1
Let v(l) be the third derivative of l**5/420 + l**4/84 - l**3/14 + 896*l**2. Factor v(q).
(q - 1)*(q + 3)/7
Find b, given that 165*b + 5*b**3 - 12 + 42 + 90*b**2 + 50 = 0.
-16, -1
Let u = 1/1898 + 5689/9490. Suppose 3/5*j**4 - u*j**2 + 0 + 3/5*j**3 - 3/5*j = 0. What is j?
-1, 0, 1
Let n(w) be the first derivative of w**3 + 3*w**2 - 552. Find x, given that n(x) = 0.
-2, 0
Let h(k) be the second derivative of 3*k**10/3920 + k**9/1470 + k**8/5880 - k**4/3 + 16*k. Let c(d) be the third derivative of h(d). Factor c(a).
2*a**3*(9*a + 2)**2/7
Suppose -56/9 - 8/9*w + 20/9*w**3 + 2/9*w**4 + 14/3*w**2 = 0. What is w?
-7, -2, 1
Let j(z) be the second derivative of 0*z**2 + 20*z - 5/12*z**3 + 0 - 3/16*z**5 + 35/48*z**4. Factor j(r).
-5*r*(r - 2)*(3*r - 1)/4
Solve 3/4*p**2 + 3/4*p**5 - 11/4*p**3 + 2*p - 1 + 1/4*p**4 = 0 for p.
-2, -1, 2/3, 1
Let g(o) be the second derivative of -2*o**7/231 - o**6/15 - 23*o**5/110 - 23*o**4/66 - o**3/3 - 2*o**2/11 + 112*o - 1. Find d such that g(d) = 0.
-2, -1, -1/2
Let a(s) be the second derivative of s**6/55 + 3*s**5/110 - 4*s**4/11 - 12*s**3/11 - 20*s - 1. Factor a(c).
6*c*(c - 3)*(c + 2)**2/11
Let i = -55 + 55. Let k be (-6)/3 - (-14)/2. Factor 2/3*n**k + 4/3*n**2 + 10/3*n**3 + i*n + 8/3*n**4 + 0.
2*n**2*(n + 1)**2*(n + 2)/3
Let q = -52 + 54. Suppose -58*t**q - 4 + 4 - 6*t + 55*t**2 = 0. What is t?
-2, 0
Let y = 4/5 - 2/5. Let l(z) be the first derivative of 4*z**2 + 2*z**4 + 6 - y*z**5 - 4*z**3 - 2*z. Factor l(v).
-2*(v - 1)**4
Factor 1/9*f + 0 - 5/9*f**2 + 4/9*f**3.
f*(f - 1)*(4*f - 1)/9
Factor -68 - 49*n + 118*n + 262*n**2 - 263*n**2.
-(n - 68)*(n - 1)
Let t(o) be the second derivative of o**6/30 + 3*o**5/20 - 3*o**4/4 - 23*o**3/6 - 6*o**2 - 118*o + 1. Factor t(u).
(u - 3)*(u + 1)**2*(u + 4)
Suppose -4*i - 18 + 21 = -3*p, 15 = i + 4*p. Suppose 0*g + 4/15*g**i + 0 + 2/15*g**4 + 2/15*g**2 = 0. Calculate g.
-1, 0
Suppose -4*w - w - 75 = 0. Let y = -12 - w. Let 8*t**y + 3*t + 0*t - t**5 - 6*t**3 - 4*t = 0. Calculate t.
-1, 0, 1
Let t be 1*((3 - 7) + 4). Suppose 0 = 2*y - 0*v - v - 2, 3*v + 6 = t. Factor -2/7*s + 2/7*s**4 + y + 2/7*s**3 - 2/7*s**2.
2*s*(s - 1)*(s + 1)**2/7
Solve 32*j**2 - 50*j + 15 + 17 - 6*j**3 + 10 - 18 = 0 for j.
1, 4/3, 3
Find v such that 17*v + v**3 - 23*v + 27*v + 18*v + 28 + 12*v**2 = 0.
-7, -4, -1
Let o = 14 + -9. Suppose 0 = o*c - 10 - 0. Solve z**4 + c*z**5 - 2*z**3 - 5*z**2 - 5*z**2 - 4*z**3 + z**4 - 4*z = 0.
-1, 0, 2
Let x(z) = -2*z**2 - 3*z - 1. Let v(h) = -3*h**2 - 3*h. Suppose 4*y - 5 = 7*y + 5*n, -4*y = -4*n - 36. Let s(f) = y*v(f) - 6*x(f). What is t in s(t) = 0?
-1, 2
Let y(n) = n**2 - 7*n - 11. Let a(u) = 24 - 9*u**2 + 2*u**2 + 2*u**2 + 41 + 43*u. Let r(q) = 6*a(q) + 34*y(q). Let r(v) = 0. Calculate v.
-4, -1
Let x(n) = -3*n**3 + n**2 - 1. Let a be x(-1). Let d = -356 - -361. Factor -1/4*l**4 + 0 + 1/8*l**a + 1/8*l**d + 0*l + 0*l**2.
l**3*(l - 1)**2/8
Let r(j) be the first derivative of -j**5/5 - 7*j**4/4 - 11*j**3/3 - 5*j**2/2 - 515. Determine m, given that r(m) = 0.
-5, -1, 0
Let 15*v - 7*v**3 + 3/2*v**4 + 9/2 + 2*v**2 = 0. Calculate v.
-1, -1/3, 3
Let c(x) be the second derivative of -x**5/35 - x**4/21 + 4*x**3/3 + 48*x**2/7 + 152*x + 2. Factor c(l).
-4*(l - 4)*(l + 2)*(l + 3)/7
Let t(d) = -6*d**4 + 4*d**3 + 3*d**2 - 9*d + 4. Let m(c) = -19*c**4 + 10*c**3 + 9*c**2 - 28*c + 13. Let p(u) = -2*m(u) + 7*t(u). Solve p(w) = 0.
-1, 1/2, 2
Let k(a) = -27*a**4 + a**3 + 16*a**2 - 6*a - 6. Let d(u) = -160*u**4 + 5*u**3 + 95*u**2 - 35*u - 35. Let f(o) = -6*d(o) + 35*k(o). What is r in f(r) = 0?
-1, 0, 2/3
Let s(d) be the second derivative of -d**4/18 - 8*d**3/9 - 4*d**2 - 101*d + 1. Factor s(w).
-2*(w + 2)*(w + 6)/3
Suppose -29*g + 27*g + 78 = 0. Factor 38*a - 119*a + a**2 + g*a - 2 + 41*a.
(a - 2)*(a + 1)
What is j in 97*j + 5*j**2 - 383 + 63*j + 1663 = 0?
-16
Let z(u) = -3*u - 5*u**4 + 156*u**3 - 152*u**3 + 3*u**4 - 5*u**5 + 2*u**2. Let v(g) = g**5 + g**4 - g**2. Let f(q) = 4*v(q) + z(q). Factor f(x).
-x*(x - 3)*(x - 1)*(x + 1)**2
Let p(g) = g**2 - 7*g - 50. Let n be p(12). Suppose q = -5*a + 3 - 8, 5*a + 2*q + n = 0. Factor 4/17*b**2 + a + 2/17*b + 2/17*b**3.
2*b*(b + 1)**2/17
Let k(a) be the first derivative of a**4/4 - 32. Let r(q) = -6*q**3 + 2*q**2. Let n(l) = 5*k(l) + r(l). Factor n(t).
-t**2*(t - 2)
Let m(x) be the second derivative of x**6/60 + x**5/20 - 5*x**4/24 - x**3/2 + 883*x. Find t, given that m(t) = 0.
-3, -1, 0, 2
Let c = -38 + 17. Let k = -11 - c. Factor -k*w**3 + 7*w + 4 - 4 + 5*w**5 - 2*w.
5*w*(w - 1)**2*(w + 1)**2
Let p be (-6 - -5)*-3 - 18. Let r be ((-2)/20)/(9/p). Factor r*w**3 + 0 + 0*w + 0*w**2 + 0*w**4 - 1/6*w**5.
-w**3*(w - 1)*(w + 1)/6
Solve 40*i**2 + 0*i**3 + 0*i - 500 - 4/5*i**4 = 0.
-5, 5
Suppose 6*f = 3*f + 39. Let j = -10 + f. Factor -3 - j*u**3 - 12*u + 3*u - 3*u**2 - 9*u**2 + 3*u**2.
-3*(u + 1)**3
Let f(l) be the third derivative of l**6/300 - l**5/150 - l**4/12 - l**3/5 - 17*l**2 + 1. Determine m so that f(m) = 0.
-1, 3
Let t = 2668/1287 + -190/99. Solve -18/13*z**2 + 48/13*z + t*z**3 - 32/13 = 0.
1, 4
Let g(f) be the third derivative of f**7/525 - 53*f**6/150 + 2701*f**5/150 + 477*f**4/5 + 972*f**3/5 - 481*f**2. Suppose g(j) = 0. Calculate j.
-1, 54
Let j(x) be the second derivative of x**4/24 - 31*x**3/6 + 27*x - 7. Determine u, given that j(u) = 0.
0, 62
Let q(y) = -7*y**4 - 4*y**2 + 4*y - 4. Let p(z) = -5*z**4 - 4*z**2 + 3*z - 3. Let s(w) = -4*p(w) + 3*q(w). Solve s(d) = 0.
-2, 0, 2
Suppose -2*u + 2*i = -34, -4*i = 5*u - 3*i - 85. Let v = 27 - u. Factor 4*h**4 - v*h**2 + 0*h**5 + 0*h**5 + 6*h**3 + 2*h**2 - 2*h**5 - 8*h.
-2*h*(h - 2)**2*(h + 1)**2
Let -6 - 13*u**2 - 2 - 10*u**2 + 5*u**2 - u**4 - 7*u**3 - 20*u = 0. What is u?
-2, -1
Let v(z) be the third derivative of z**7/42 - z**6/3 + 2*z**5 - 20*z**4/3 + 40*z**3/3 - 10*z**2 + 2. Suppose v(j) = 0. Calculate j.
2
Let v(k) be the third derivative of -k**8/131040 - k**7/4680 + k**5/30 - 2*k**3/3 + 5*k**2 - k. Let u(j) be the third derivative of v(j). Factor u(n).
-2*n*(n + 7)/13
Let r(z) be the first derivative of -z**5/600 + z**4/40 + 7*z**3/60 + 15*z**2/2 - 11. Let a(p) be the second derivative of r(p). Factor a(h).
-(h - 7)*(h + 1)/10
Suppose -4*x - j + 13 = 5, 2*j + 2 = x. Let t(f) be the first derivative of 4/15*f**3 + 1/30*f**6 - 3/25*f**5 + 0*f**x - 7 + 0*f + 0*f**4. Factor t(o).
o**2*(o - 2)**2*(o + 1)/5
Let n(v) be the first derivative of 4*v**5 - 39*v**4 + 112*v**3/3 + 676. Suppose n(c) = 0. What is c?
0, 4/5, 7
Let p(d) = d**3 + 6*d**2 - 18*d - 12. Let m be p(-8). Factor 24/13*o**2 + 2/13*o**m + 0 + 16/13*o + 12/13*o**3.
2*o*(o + 2)**3/13
Let o(w) = -w**4 - 4*w**2 + 5. Let m(r) = r**4 + 3*r**2 - 4. Let a = 4 + -9. Let p(f) = a*o(f) - 6*m(f). Factor p(q).
-(q - 1)**2*(q + 1)**2
Factor 24*d**3 - 300*d**2 + 17*d**3 - 282*d + 4*d**3 - 320 + 842*d.
5*(d - 4)*(3*d - 4)**2
Let f(h) be the third derivative of h**8/896 - h**7/140 - 11*h**6/160 + h**5/40 + 21*h**4/64 + 2*h**2 + 22*h. Suppose f(y) = 0. What is y?
-3, -1, 0, 1, 7
Let u(h) be the second derivative of -h**6/60 + h**5/30 - h**3/2 - 16*h. Let z(j) be the second derivative of u(j). Solve z(k) = 0.
0, 2/3
Factor 0 + 76/5*a + 2/5*a**2.
2*a*(a + 38)/5
Let c(j) be the second derivative of -j**7/63 + j**6/45 + 41*j**5/30 + 107*j**4/18 + 100*j**3/9 + 32*j**2/3 - 68*j + 3. Let c(r) = 0. Calculate r.
-4, -1, 8
Let -3/4*j**2 + 135/2*j + 273/4 = 0. What is j?
-1, 91
Let g(o) be the third derivative of -24*o**3 - 1/15*o**5 + 2*o**4 + 0*o - o**2 + 0. Factor g(b).
-4*(b - 6)**2
Let s(g) be the first derivative of 16 - 1/5*g**3 + 42/5*g**2 - 588/5*g. What is j