alculate u.
-1, -2/3
Let l(b) be the second derivative of -b**6/30 - b**5/16 - b**4/48 + 10*b. Let l(g) = 0. What is g?
-1, -1/4, 0
Let r be (-5*1)/((-232)/(-24)). Let s = 221/203 + r. Find w such that 0 + 2/7*w**3 + 0*w + s*w**2 = 0.
-2, 0
Let j(q) = -3*q**3 + 17*q**2 + 3*q - 17. Let o(s) = -s**3 + 6*s**2 + s - 6. Let r(c) = 6*j(c) - 17*o(c). Find t such that r(t) = 0.
-1, 0, 1
Let p(c) = -2*c**2 + 28*c - 24. Let x be p(13). Factor 3/4*o**4 + 1/4 - o**x + 1/2*o - 1/2*o**3.
(o - 1)**2*(o + 1)*(3*o + 1)/4
Factor 4*c**3 - 2*c**3 + 2*c - 3*c**3 + c**2 - 2*c**2.
-c*(c - 1)*(c + 2)
Let n(d) be the second derivative of 4*d**6/15 - 13*d**5/10 + 5*d**4/2 - 7*d**3/3 + d**2 + 12*d. Factor n(x).
2*(x - 1)**3*(4*x - 1)
Let d(n) be the third derivative of n**7/1260 + n**6/360 - n**5/120 - n**4/18 - n**3/9 - 8*n**2. Factor d(c).
(c - 2)*(c + 1)**2*(c + 2)/6
Let i(n) = -n**2 - 17*n - 52. Let w be i(-13). Find d such that 2/7*d**2 - 16/7*d**5 + w*d - 2/7*d**3 - 20/7*d**4 + 0 = 0.
-1, -1/2, 0, 1/4
Solve 6*w**2 - 6*w**3 - 7 + 7 + 2*w**4 + w - 3*w = 0 for w.
0, 1
Let j(d) be the second derivative of 0 + 0*d**3 - 1/12*d**4 - 2*d + 1/40*d**5 + 0*d**2. Solve j(k) = 0.
0, 2
Let u(d) = -3*d + 6. Suppose -23 = -4*v + 5*f, -2*f + 14 = v - 6*f. Let i be u(v). Factor -2/9*l**4 - 4/9*l + 2/3*l**2 + 0 + i*l**3.
-2*l*(l - 1)**2*(l + 2)/9
Let x(g) = 2*g - 3. Let l be x(3). Factor 4 + 0 + s + l*s + s**2.
(s + 2)**2
Let f(x) be the second derivative of -5*x - 1/18*x**3 + 0*x**2 + 1/18*x**4 + 0 - 1/60*x**5. Factor f(i).
-i*(i - 1)**2/3
Let w be (8/32)/((-2)/((-32)/14)). Factor -6/7*x**2 + 6/7*x + w*x**3 - 2/7.
2*(x - 1)**3/7
Let f = -6 + 9. Let 7 - 21*x - 78*x**3 - 9*x - f + 76*x**2 + 28*x**4 = 0. Calculate x.
2/7, 1/2, 1
Let o(m) be the third derivative of 0*m**4 + 2*m**2 + 0*m - 1/60*m**5 - 1/336*m**8 + 0 - 1/40*m**6 + 0*m**3 - 1/70*m**7. Determine b, given that o(b) = 0.
-1, 0
Let k(q) be the second derivative of q**4/36 - 5*q**3/18 + q**2 + 34*q. Factor k(x).
(x - 3)*(x - 2)/3
Let v = 316/77 - 42/11. Factor -6/7*f**2 - v - 8/7*f.
-2*(f + 1)*(3*f + 1)/7
Suppose 3*t = -2*g + 10, -t + 2*g - 6 = -2*g. Let k be t + (-21)/15 + 0. Factor -k*z - 3/5*z**2 - 1/5*z**3 - 1/5.
-(z + 1)**3/5
Suppose 4*n = -3*d + 3, 2*n = -5*d - 0*d - 9. Let z(m) be the third derivative of 0 - 2*m**2 - 1/18*m**5 + 0*m + 1/90*m**6 - 1/9*m**n + 1/9*m**4. Factor z(o).
2*(o - 1)**2*(2*o - 1)/3
Let t be 1 - 57*(-3)/(-9). Let s be t/(-63)*7/5. Factor s*o - 2/5*o**2 + 4/5.
-2*(o - 2)*(o + 1)/5
Let s be (0 + (-3)/(-9))*0. Solve o**4 + o + o**5 - o**4 + s*o - 2*o**3 = 0 for o.
-1, 0, 1
Let l(j) = -j**2 + 1. Let b(k) = k**2 + 4*k - 6. Let x = 0 - -6. Let d(i) = x*l(i) + 3*b(i). Solve d(f) = 0.
2
Factor 2*f**3 + 3*f**3 - 5*f + 68*f**2 - 73*f**2 + 5*f**4.
5*f*(f - 1)*(f + 1)**2
Let b(c) be the third derivative of 1/12*c**3 - 1/240*c**6 + 2*c**2 + 0 - 1/120*c**5 + 1/48*c**4 + 0*c. Solve b(s) = 0.
-1, 1
Let i = -3139 + 59617/19. Let h = i + 282/133. Factor -2/7*r**3 + 6/7*r**2 + 2/7 - h*r.
-2*(r - 1)**3/7
Let a = 95 + -93. Find r, given that -8/3*r - 46/3*r**3 - 2*r**5 + 0 + 28/3*r**4 + 32/3*r**a = 0.
0, 2/3, 1, 2
Let b(k) be the second derivative of -k**6/180 - k**5/30 - 5*k**4/72 - k**3/18 - 16*k. Factor b(m).
-m*(m + 1)**2*(m + 2)/6
Let r(b) be the first derivative of b**5/30 - b**4/9 + b**3/9 + 3*b**2/2 + 3. Let a(j) be the second derivative of r(j). Solve a(s) = 0.
1/3, 1
Let z(o) be the first derivative of -4/5*o**5 - 4 + 1/8*o**2 + 3/2*o**4 - 3/4*o**3 + 0*o. Factor z(i).
-i*(i - 1)*(4*i - 1)**2/4
Let i(o) = 11*o**2 + 7*o + 6. Let g(c) = -17*c**2 - 10*c - 9. Suppose 19 = -5*r - 3*m - 15, 5*r - 2*m = -19. Let q(a) = r*g(a) - 8*i(a). Factor q(h).
-3*(h + 1)**2
Let t(s) be the second derivative of -s**6/180 - s**5/60 + s**3/18 + s**2/12 - 6*s. Let t(h) = 0. Calculate h.
-1, 1
Let h be 0*((-2 - 1) + 2). Suppose h = 2*f + 3*f. Let f*u + 2*u**2 - u - u**2 = 0. Calculate u.
0, 1
Let d(i) be the second derivative of -i**4/3 - 10*i**3/3 + 12*i**2 + 45*i. Factor d(z).
-4*(z - 1)*(z + 6)
Let l(h) be the first derivative of -h**4/14 + 4*h**3/21 + h**2/7 - 4*h/7 - 9. Factor l(v).
-2*(v - 2)*(v - 1)*(v + 1)/7
Let t(g) be the third derivative of g**10/151200 + g**9/30240 - g**7/2520 - g**6/720 - g**5/60 - 3*g**2. Let y(b) be the third derivative of t(b). Factor y(q).
(q - 1)*(q + 1)**3
Let b(c) be the third derivative of -c**7/630 - c**6/45 - c**5/12 + c**4/9 + 8*c**3/9 + 17*c**2. Factor b(q).
-(q - 1)*(q + 1)*(q + 4)**2/3
Let o(h) be the second derivative of 5*h**4/6 + 2*h**3/21 - 47*h. Determine f, given that o(f) = 0.
-2/35, 0
Let k be (8/(-4))/(1/(-2)). Let d be (-16)/(-18)*1/k. Determine c so that 0*c**2 + 0 + d*c - 2/9*c**3 = 0.
-1, 0, 1
Let a be 3/((-9)/3) - -1. Let u = a - -6. Factor 4*z**2 + 0*z - u*z**2 + 4*z.
-2*z*(z - 2)
Let m(w) = -4*w**4 - 28*w**3 + 52*w**2 - 27*w. Let b(l) = -3*l**4 - 19*l**3 + 35*l**2 - 18*l. Let g(i) = 7*b(i) - 5*m(i). Factor g(v).
-v*(v - 3)**2*(v - 1)
Let c be (-2)/8 - (-9)/4. Let -6*k + 48 + 3*k**3 + 4*k**c + 2*k**5 - 6*k**4 + k**3 - 46 = 0. Calculate k.
-1, 1
Let k = 8 + -6. Let g(l) be the second derivative of 0 + 4/3*l**3 + l + 4*l**k + 1/6*l**4. Factor g(o).
2*(o + 2)**2
Suppose -5 = 4*f - 5*f. Factor 4/9*v**2 - 2/9*v**3 - 8/9*v**4 + 2/3*v**f + 0 + 0*v.
2*v**2*(v - 1)**2*(3*v + 2)/9
Suppose 2*d + 5 = -5, 3*h + 4*d + 11 = 0. Factor -2 - 5*n + n - n**4 + 3*n**4 + 4*n**h.
2*(n - 1)*(n + 1)**3
Let r = 336836 + -30651016/91. Let s = 404/13 - r. Factor 98*c**5 + 112*c**4 + s*c - 268/7*c**2 - 46*c**3 - 16/7.
2*(c + 1)**2*(7*c - 2)**3/7
Let s(u) be the second derivative of 1/4*u**2 - 2*u + 9/40*u**5 + 31/48*u**4 + 0 + 5/8*u**3. Factor s(y).
(y + 1)*(2*y + 1)*(9*y + 2)/4
Let r(s) = s**2 + 7*s - 4. Let x be r(-8). Let k(f) be the second derivative of 0*f**5 - f + 1/126*f**7 + 0*f**2 + 0*f**3 + 0*f**6 + 0 + 0*f**x. Factor k(m).
m**5/3
Let c(n) = n + 6. Let o be c(-4). Suppose -4*y = -16, 2*p - 6 - 2 = -o*y. Suppose 4/3*w - 2*w**2 + p = 0. What is w?
0, 2/3
Suppose s - d + 4 = -0*s, -28 = 5*s + 3*d. Let m = s - -7. What is p in -3 - 3*p + 3*p**3 + p**2 + 6*p**2 - 4*p**m = 0?
-1, 1
Let c be -5 - 2*21/(-6). Let z(r) be the third derivative of 0 + 0*r - 1/27*r**3 + 1/270*r**5 + 1/540*r**6 + 4*r**c - 1/108*r**4. Factor z(v).
2*(v - 1)*(v + 1)**2/9
Determine b so that 3/2 + 3/4*b - 3/4*b**2 = 0.
-1, 2
Let t be (8/24)/(1/4 + 0). Factor -4/3 - t*z + z**2.
(z - 2)*(3*z + 2)/3
Let h be 3/16*((-12)/2)/(-3). Let t(m) be the first derivative of 0*m**5 + h*m**4 - 1/12*m**6 - 2 + 0*m**2 + 0*m + 1/3*m**3. Factor t(y).
-y**2*(y - 2)*(y + 1)**2/2
Let i = 53/60 + 13/15. Factor 0 + 1/4*j**2 + 9/4*j**5 + 0*j + i*j**3 + 15/4*j**4.
j**2*(j + 1)*(3*j + 1)**2/4
Let a = 95 + -90. Let d(b) be the second derivative of 1/10*b**4 + 0 + 0*b**2 + 1/10*b**3 + 3*b + 3/100*b**a. Determine h, given that d(h) = 0.
-1, 0
Let w(q) = 5*q**2 - 4*q. Let v(j) = -11*j**2 + 9*j. Let i(o) = 6*v(o) + 13*w(o). Factor i(r).
-r*(r - 2)
Let x = 31 - 61/2. Let h(m) be the second derivative of 0 - 1/12*m**4 - 2*m + 1/12*m**3 + x*m**2 - 1/40*m**5. Factor h(p).
-(p - 1)*(p + 1)*(p + 2)/2
Factor -2*j**3 + 0 + 24/7*j**2 + 8/7*j.
-2*j*(j - 2)*(7*j + 2)/7
Let l(q) be the third derivative of q**7/280 - 3*q**5/40 - q**4/4 - q**3/3 - 4*q**2. Let z(b) be the first derivative of l(b). Let z(n) = 0. Calculate n.
-1, 2
Factor -1/3*k**3 + 0 - 12*k - 4*k**2.
-k*(k + 6)**2/3
Let r be (-571)/42 + (-9)/(-21). Let c = 27/2 + r. Factor 0 - 1/3*b**3 + 0*b**2 + c*b.
-b*(b - 1)*(b + 1)/3
Let o = 1/3 + 1/15. Solve o*k**2 - 2/5 - 2/5*k**3 + 2/5*k = 0.
-1, 1
Let z(t) = 2*t**4 + 9*t**3 - 7*t**2 - 9*t + 5. Let n(j) = 6*j**4 + 26*j**3 - 20*j**2 - 26*j + 14. Let w(p) = 5*n(p) - 14*z(p). Factor w(l).
2*l*(l - 1)*(l + 1)*(l + 2)
Let x(g) be the second derivative of 3*g + 0 + 0*g**3 + 1/60*g**5 + 1/180*g**6 + 1/72*g**4 + 0*g**2. Suppose x(a) = 0. Calculate a.
-1, 0
Let r be (-2)/6*(-12)/8. Suppose 10 = -u + 12. Factor r*m**u + 1/2 - m.
(m - 1)**2/2
Let c(n) = 4*n**2 - 37*n + 69. Let t(x) = 10*x**2 - 92*x + 172. Let r(w) = 12*c(w) - 5*t(w). Factor r(q).
-2*(q - 4)**2
Let q(m) be the first derivative of 0*m**3 + 0*m**2 - 1/12*m**4 + 1 + 0*m. Factor q(o).
-o**3/3
Suppose 0 = 2*i - 5*u - 4 + 26, -2*u = i - 7. Let q be ((-8)/1)/(-1 + i). Factor -3*w**4 + 2*w**3 - 3*w**4 - q*w**3.
-2