he second derivative of -i**7/231 - i**6/55 + 3*i**5/110 + i**4/6 + 2*i**3/11 - 97*i. Determine a, given that l(a) = 0.
-3, -1, 0, 2
Let l(s) be the second derivative of -s**4/12 + 2*s**3/3 - 3*s**2/2 - 3*s. Let d be l(3). Let 6*p**3 + 8*p**2 - 8*p**3 + 0 - 6*p + d = 0. Calculate p.
0, 1, 3
Let m(k) be the second derivative of -k**6/1800 - k**5/120 - k**4/20 - k**3 + 20*k. Let t(i) be the second derivative of m(i). Let t(f) = 0. Calculate f.
-3, -2
Factor -3*q**2 + 354*q - 860*q + 266*q - 4800.
-3*(q + 40)**2
Solve -15*i**2 + 9*i + 3*i**3 + 12*i + 85 - 94 = 0.
1, 3
Let b(g) be the first derivative of -g**4/10 + 26*g**3/15 - 12*g**2/5 + 73. Factor b(l).
-2*l*(l - 12)*(l - 1)/5
Suppose 5*f + 16 = 4*x + f, 2*x + f + 1 = 0. Let q be x/(((-5)/5)/(-3)). Find b, given that -b + 1/2*b**2 + b**q + 0 - 1/2*b**4 = 0.
-1, 0, 1, 2
Let x(d) be the third derivative of -d**6/96 + 23*d**5/240 - 5*d**4/48 - d**3/3 - 230*d**2 + d. Solve x(b) = 0 for b.
-2/5, 1, 4
Find g, given that 117*g**2 - 209*g**2 - 216*g + 104*g**2 + 54*g**3 - 3*g**4 = 0.
-2, 0, 2, 18
Let n = -2068 + 349488/169. Let t = n + 1372/845. Factor t*h - 6/5*h**2 - 2/5.
-2*(h - 1)*(3*h - 1)/5
Let w(u) be the third derivative of -u**8/168 + u**7/9 - 17*u**6/60 + u**5/10 + 5*u**4/18 - 82*u**2. Determine m, given that w(m) = 0.
-1/3, 0, 1, 10
Determine r so that -32*r**3 - 16*r + 19*r**4 + 80 - 12*r**4 + 4*r**4 - 140*r**2 + r**4 = 0.
-2, -1, 2/3, 5
Let r(l) be the third derivative of -l**7/2940 + l**5/140 + 13*l**4/12 - 13*l**2. Let u(f) be the second derivative of r(f). Determine h, given that u(h) = 0.
-1, 1
Let r(a) = -21*a - 3. Let z be r(-2). Suppose -b = 2*i - 13, i - 3*i - z = -3*b. Solve 3*x**3 - 3*x**2 - x**4 + b*x**2 + 17*x**3 + 6*x**4 - 15 - 20*x = 0 for x.
-3, -1, 1
Let w(b) be the third derivative of 0 + 2*b**2 - 25/4*b**3 + 5/8*b**4 - 1/40*b**5 + 0*b. Factor w(a).
-3*(a - 5)**2/2
Let q(j) be the second derivative of -j**4/24 - 396*j. Let q(p) = 0. What is p?
0
Let j(u) be the second derivative of -u**6/75 + 18*u**5/25 + 19*u**4/15 - 12*u**3/5 - 37*u**2/5 - 114*u. Suppose j(d) = 0. What is d?
-1, 1, 37
Suppose a + 0*a = 0. Suppose -2*s + a*s = -2, 4*p - 39 = 5*s. Factor -30*c**2 - 13*c + 1 + 5 + 21*c - p*c.
-3*(2*c + 1)*(5*c - 2)
Let t(n) be the third derivative of -n**9/60480 + n**8/3360 - n**7/560 + n**6/180 + 2*n**5/15 + 4*n**2. Let c(f) be the third derivative of t(f). Factor c(l).
-(l - 4)*(l - 1)**2
Let o(l) be the second derivative of l**6/345 + 4*l**5/115 + 11*l + 3. Factor o(q).
2*q**3*(q + 8)/23
Let g(f) be the third derivative of -f**5/210 + 13*f**4/84 - 4*f**3/7 - f**2 - 85*f. Factor g(o).
-2*(o - 12)*(o - 1)/7
Let w(g) be the first derivative of 2*g**6/15 - 52*g**5/25 + 19*g**4/5 + 116*g**3/3 + 352*g**2/5 + 256*g/5 + 82. Let w(t) = 0. What is t?
-1, 8
Solve -16 + 1/2*n**5 - n**4 + 8*n**2 + 8*n - 4*n**3 = 0 for n.
-2, 2
Let d be 2*(-4)/16 - (-2)/4. Solve 10*b - 9*b**3 + 15*b**4 - 18*b**2 - 5*b**5 + d*b**5 + 3*b**2 + 4*b**3 = 0 for b.
-1, 0, 1, 2
Let v = 4/47 + 66/329. Suppose 3*s = -0*s + 6. Solve -v*j**s + 0 + 0*j = 0 for j.
0
Let a(h) = 5*h + 10. Let u be a(-2). Suppose -x - 4*x - 4*d = -15, u = -2*d. Factor -2/11*q**4 + 8/11*q**x - 24/11*q + 4/11*q**2 - 18/11.
-2*(q - 3)**2*(q + 1)**2/11
Let f = 13870 - 13870. Suppose 0 + f*i - 3/4*i**2 = 0. Calculate i.
0
Let m be ((-22)/33)/(1/(3/(-1))). Suppose 2*n + m = 3*n + t, n = 3*t + 2. Factor 2/5*k**n + 2/5 + 4/5*k.
2*(k + 1)**2/5
Suppose -7*v + 95 - 97 = -8*v. Determine u so that -7/2 - 4*u - 1/2*u**v = 0.
-7, -1
Factor 26/5*n**2 - 9/5 + 56/5*n**3 - 24/5*n - 49/5*n**4.
-(n - 1)**2*(7*n + 3)**2/5
Let -8/9 - 6962/9*h**2 - 472/9*h = 0. What is h?
-2/59
Suppose 0 = 5*z - 5*o - 35, -2*z = o - 2 - 0. Let 4 - 4 - 6*b**3 + 3*b**4 + z*b**2 = 0. Calculate b.
0, 1
Let x be (-3 - (-35)/12)*(-207)/276. Let j(a) be the third derivative of -1/6*a**3 - x*a**4 - 1/120*a**5 + 0*a + 0 - 7*a**2. Factor j(r).
-(r + 1)*(r + 2)/2
Let m(h) be the second derivative of 5*h**7/42 + 5*h**6/6 - 3*h**5/2 - h + 196. Determine k so that m(k) = 0.
-6, 0, 1
Suppose 39*u - 175*u - 5 = -277. Factor 0*p**u - 512/11*p**3 + 2/11 + 24/11*p.
-2*(4*p - 1)*(8*p + 1)**2/11
Solve -102*s - s**2 - 157 - 2*s**2 - 51 - s**2 - 10*s = 0 for s.
-26, -2
Let d(z) be the first derivative of 1/20*z**5 - 5/16*z**4 + 1/2*z - 7/8*z**2 + 11 + 3/4*z**3. Solve d(i) = 0.
1, 2
Suppose -3/4*a**3 + 12 + 9/4*a**5 - 27*a**2 + 3*a + 21/2*a**4 = 0. Calculate a.
-4, -2, -2/3, 1
Let l(t) be the third derivative of -t**7/1260 - t**6/18 - 5*t**5/3 - 250*t**4/9 - 2500*t**3/9 + 93*t**2. Find q, given that l(q) = 0.
-10
Let b(o) be the second derivative of -o**3 - 3/8*o**4 - 3*o - 1/20*o**5 + 0 + 5*o**2. Let v(y) be the first derivative of b(y). Factor v(l).
-3*(l + 1)*(l + 2)
Suppose -1/2 + 1/4*z**2 + 1/4*z = 0. Calculate z.
-2, 1
Let r = -2/4323 - -8660/30261. Factor 2/7*m**4 + 0 + 0*m + r*m**3 + 0*m**2.
2*m**3*(m + 1)/7
Let k(w) be the third derivative of -w**5/600 + 7*w**4/120 - 2*w**3/5 + 48*w**2. Suppose k(n) = 0. Calculate n.
2, 12
Suppose q = i + 6*q - 22, 0 = i - q + 2. Determine m, given that 59 - i*m**2 - 55 + 0*m**2 + 6*m + 4*m**2 = 0.
-2, -1
Suppose -4*x + 35 = -2*b + 15, -5*b - 15 = -3*x. Let c(d) be the second derivative of -1/15*d**3 - 8*d + 1/30*d**4 + b + 1/50*d**5 - 1/5*d**2. Factor c(k).
2*(k - 1)*(k + 1)**2/5
Let f(m) be the third derivative of -1/42*m**7 - 14*m**2 + 0*m**6 + 7/12*m**5 + 0*m**3 + 0 + 5/4*m**4 + 0*m. Factor f(u).
-5*u*(u - 3)*(u + 1)*(u + 2)
Suppose 0 = -4*a + 4*h + 120, 4*h - 96 = -4*a - 0*h. Let v be (-126)/a*(-3)/11. Let v*c**4 - 24/11*c**2 - 8/11*c + 18/11*c**3 + 0 = 0. What is c?
-2, -2/7, 0, 1
Factor 0 + 0*r**4 + 3/7*r**3 - 3/7*r**5 + 0*r**2 + 0*r.
-3*r**3*(r - 1)*(r + 1)/7
Let a(f) be the second derivative of -2/165*f**6 + 21/110*f**5 + 0*f**2 - 2*f - 8/231*f**7 + 0 - 13/66*f**4 + 2/33*f**3. Let a(x) = 0. Calculate x.
-2, 0, 1/4, 1/2, 1
Let t = 792 - 792. Let v(x) be the third derivative of 0*x**3 + 0 + 1/108*x**4 + 7*x**2 - 1/540*x**6 + t*x**5 + 0*x. Solve v(j) = 0.
-1, 0, 1
Suppose 166 - 1200*p - p**2 + 2426*p - 1145*p = 0. What is p?
-2, 83
Let o(p) = p**2 - 6*p - 4. Let n be o(-4). Suppose -x = n - 38. Determine k, given that 108/5*k**4 - 27/5*k**3 + 0 - 12/5*k**x + 3/5*k = 0.
-1/3, 0, 1/4, 1/3
Let y(n) = -81 - 359 - 20*n + 59*n - 11*n**2 + 25*n. Let f(q) = -4*q**2 + 21*q - 147. Let s(z) = 8*f(z) - 3*y(z). Factor s(h).
(h - 12)**2
Let h = 41425 - 41425. Let b be 74/40 + (-4)/(-10). Factor b*j + h + 1/4*j**3 - 3/2*j**2.
j*(j - 3)**2/4
Let v be 0/2*1*(20 - 19). Find o such that -68/3*o**4 - 20/3*o**5 - 28*o**3 + v - 44/3*o**2 - 8/3*o = 0.
-1, -2/5, 0
Suppose -13 = 2*z - 5*z - 4*f, 4*z - 19 = -5*f. Suppose 4*i = z + 1. Let 0*u**5 - 3*u**5 + i*u**4 - 15*u**3 + 6*u**2 + 10*u**4 - u**4 = 0. Calculate u.
0, 1, 2
Let a(g) be the third derivative of g**7/2940 - g**6/630 + g**5/420 + 5*g**3/2 + 25*g**2. Let f(h) be the first derivative of a(h). Factor f(v).
2*v*(v - 1)**2/7
Let j = 194 - 300. Let w = -106 - j. Factor 0*c + w*c**2 + 0 + 2/13*c**3.
2*c**3/13
Suppose -3*f = 3*r - 5*r + 5, 0 = r - f - 3. Suppose -5 = -r*j + 3. Let -3 - 13 - 12*u**j - 2*u**3 - u - 20*u - 3*u = 0. Calculate u.
-2
Suppose a - 4*a + 6 = 0. Let f(q) = 0*q**2 + 3 - 2 - 2*q**a + 3*q**2. Let j(b) = b**3 + 6*b**2 + 5. Let r(o) = -10*f(o) + 2*j(o). Factor r(c).
2*c**2*(c + 1)
What is w in 0 - 5/2*w**2 + w**4 + 1/4*w**5 - 3/4*w**3 + 2*w = 0?
-4, -2, 0, 1
Suppose -5*a + 12 = -28. Suppose 2*o + a = 3*w, -4*w + 28 = 5*o + 2. Factor 2/3*i - 1/3*i**o - 1/3.
-(i - 1)**2/3
Let h(z) = 13*z**5 - 3*z**4 - 24*z**2 - 7. Let w(c) = 4*c**5 - 8*c**2 - 2. Let i(b) = -2*h(b) + 7*w(b). Factor i(a).
2*a**2*(a - 1)*(a + 2)**2
Let j(p) be the second derivative of 165*p**4 + 17/2*p**5 + 6655/2*p**2 + 0 - 43*p + 1/6*p**6 + 4235/3*p**3. Factor j(f).
5*(f + 1)*(f + 11)**3
Factor 2/5*u**2 - 12/5*u - 14/5.
2*(u - 7)*(u + 1)/5
Let u(r) = -6*r**4 + 9*r**3 - 73*r**2 - 61*r - 7. Let q(f) = -2*f**4 + 4*f**3 - 24*f**2 - 20*f - 2. Let m(l) = -17*q(l) + 6*u(l). Factor m(x).
-2*(x + 1)**3*(x + 4)
Let s(w) = w**2 - w - 1. Suppose -5*k + 3*c = 15, 0 = 2*k - 4*c + 2 + 4. Let g(h) = -2*h**2 - 3*h - 3. Let x(n) = k*g(n) - 3*s(n). Factor x(t).
3*(t + 2)**2
Let v(n) be the third derivative of -n**5/12 - 295*n**4/12 - 17405*n**3/6 - 98*n