lculate q.
-1
Let m(n) = 4*n**2 + 11*n - 24. Let c(p) = 5*p**2 + 7*p - 24. Let t(j) = -3*c(j) + 4*m(j). Factor t(s).
(s - 1)*(s + 24)
Let w(x) be the third derivative of -4*x**7/105 + 7*x**6/12 - x**5/2 - 35*x**4/6 - 16*x**3/3 + 460*x**2. Let w(u) = 0. Calculate u.
-1, -1/4, 2, 8
Let u(d) be the third derivative of d**8/672 - d**7/420 - d**6/240 + d**5/120 + 282*d**2. Find o, given that u(o) = 0.
-1, 0, 1
Let v(p) be the first derivative of 2/3*p**3 + 52 + 1/12*p**4 + 4/3*p + 3/2*p**2. Factor v(b).
(b + 1)**2*(b + 4)/3
Factor 0*y**2 + 6/5*y**4 + 0*y**3 - 3/5*y**5 + 0 + 0*y.
-3*y**4*(y - 2)/5
Let q(o) be the first derivative of 1/4*o**3 - 3/4*o + 3/8*o**2 + 4 - 3/16*o**4. Determine k, given that q(k) = 0.
-1, 1
Let n(d) = -26*d**2 + 40*d - 40. Let c(l) be the second derivative of -5*l**4/12 + 4*l**3/3 - 4*l**2 - 17*l. Let w(y) = -16*c(y) + 3*n(y). Factor w(t).
2*(t - 2)**2
Let h be (2 - -3 - 40/12)/(20/8). Let c = -1 + 1. Factor 0 - h*v**3 + 0*v**2 + c*v.
-2*v**3/3
Let t(k) = k + 4. Let m be t(-3). Let n be (1/2)/(m/6). Factor n*c - 2*c - 2*c - 2*c - 3*c**2.
-3*c*(c + 1)
Let j(w) be the third derivative of -3/10*w**6 + 0*w + 2*w**2 - 5/6*w**4 + 4/3*w**3 - 38 - 16/15*w**5. Factor j(x).
-4*(x + 1)**2*(9*x - 2)
Suppose -275*v + 214 + 295 = -41. Factor 2/13*q**v - 2/13*q + 0.
2*q*(q - 1)/13
Let c(u) = -16*u**3 + 151*u**2 + 161*u + 62. Let g(w) = -6*w**3 + 51*w**2 + 54*w + 21. Let k(q) = -6*c(q) + 17*g(q). Suppose k(s) = 0. Calculate s.
-5, -1, -1/2
Let t(s) be the second derivative of -s**4/66 - 12*s**3/11 - 324*s**2/11 - 68*s. Factor t(n).
-2*(n + 18)**2/11
Let p be (-24)/45*6/(-56). Let y(t) be the first derivative of 8/7*t + 26/21*t**3 + 5 + p*t**5 + 3/7*t**4 + 12/7*t**2. Factor y(s).
2*(s + 1)**2*(s + 2)**2/7
Let t = 228 + -228. Let y(p) be the third derivative of t*p**3 + 0*p**4 - 1/315*p**7 + 1/90*p**5 - 2*p**2 + 0*p + 0*p**6 + 0. Factor y(r).
-2*r**2*(r - 1)*(r + 1)/3
Let b(f) be the first derivative of f**6/2340 - 3*f**5/260 - 16*f**3/3 - 6. Let i(x) be the third derivative of b(x). Let i(v) = 0. What is v?
0, 9
Let m(v) be the third derivative of -3/7*v**5 + 23*v**2 + 0*v + 0 - 16/7*v**3 - 1/140*v**6 + 13/7*v**4 + 1/98*v**7. Solve m(d) = 0 for d.
-4, 2/5, 2
Suppose -5*l - 2*p + 54 = 0, -42 = -4*l - 0*l - 2*p. Let c be (-2)/l + (-19)/(-6). Factor q**3 + 2*q**c - 3*q**2 - 6*q**2 + 6*q.
3*q*(q - 2)*(q - 1)
Let b(l) = 2*l**5 - 28*l**4 - 132*l**3 + 4*l**2 - 4*l. Let m(h) = -h**5 - h**4 + h**3 - h**2 + h. Let x(f) = b(f) + 4*m(f). Factor x(y).
-2*y**3*(y + 8)**2
Let y(c) = 7 - 4 + c**2 - 3 + c. Let t(p) = -2*p**2 - 21*p + 81. Let m(a) = 4*t(a) + 12*y(a). Suppose m(r) = 0. What is r?
9
Let a = 87 + -85. Let g be 1/((104/20 - 1) + -4). Solve -2/7*s**a + 2/7 + 8/7*s**g + 0*s**4 + 6/7*s - 2*s**3 = 0 for s.
-1, -1/2, 1
Suppose -3*t - 221 = 2*q, t + 4*q = -29 - 28. Let i = 77 + t. Solve i - 3/5*c**3 + 0*c - 3/5*c**2 + 3/5*c**5 + 3/5*c**4 = 0.
-1, 0, 1
Let x(r) = 88*r + 24 + 12*r**2 + 20 + 32. Let g(b) = -b**2 - 8*b - 7. Let a = -324 + 327. Let q(w) = a*x(w) + 32*g(w). Factor q(p).
4*(p + 1)**2
Suppose 2*h - 3*o = -o + 146, -5*o - 209 = -3*h. Let r be 1 + 5/(-2) - (-273)/h. Factor 2/5*i**r - 2/5*i + 0.
2*i*(i - 1)/5
Suppose 36*h = -5*h + 82. Factor -2/5*t - 1/5*t**h + 3/5.
-(t - 1)*(t + 3)/5
Suppose -12 = -4*w, r = -0*r - 2*w + 10. Let 20*h**3 - r*h**2 + 10 - 15*h - 5*h**2 - 5*h**5 - h**2 = 0. What is h?
-2, -1, 1
Let t(s) = -4*s**2 - 15*s - 81. Let o(q) = -5*q**2 - 14*q - 81. Let a(g) = 3*o(g) - 4*t(g). Factor a(l).
(l + 9)**2
Let s(j) be the second derivative of 1/195*j**6 - 2/39*j**3 + 0 + 7*j + 0*j**2 - 5/78*j**4 + 1/273*j**7 - 3/130*j**5. Let s(l) = 0. Calculate l.
-1, 0, 2
Let a(t) be the third derivative of 3*t**6/10 - 83*t**5/15 + 15*t**4 - 32*t**3/3 + 3*t**2 + 11. Factor a(g).
4*(g - 8)*(g - 1)*(9*g - 2)
Let u(f) be the third derivative of 0*f + 0 + 5/12*f**4 - 1/12*f**5 - 1/24*f**6 + 0*f**3 + 7*f**2. What is r in u(r) = 0?
-2, 0, 1
Let g(h) be the third derivative of -h**9/30240 + h**8/2240 - h**7/420 + h**6/180 - h**4/3 - 26*h**2. Let x(a) be the second derivative of g(a). Factor x(j).
-j*(j - 2)**3/2
Let t(l) be the second derivative of -1/14*l**5 + 3/14*l**4 - 1/3*l**3 - 7*l + 1/105*l**6 + 2/7*l**2 + 0. Let t(z) = 0. What is z?
1, 2
Let f be (2 + -4 - 1)*-13. Let p = f + -6. Factor -p*r - 14*r**3 - 4*r**4 - 8 - 33*r**2 - 6*r**3 + 5*r - 3*r**2.
-4*(r + 1)**3*(r + 2)
Let a(u) be the third derivative of u**7/315 + 23*u**6/180 + 43*u**5/90 + 7*u**4/12 + 97*u**2. Factor a(j).
2*j*(j + 1)**2*(j + 21)/3
Suppose 0 = -2*r - 4*f, -r = r - f. Suppose 0 = -2*i + 4 - r. Factor 4*d - d - i*d**3 - 3*d - 4*d**2 + 2*d + 4*d**4.
2*d*(d - 1)*(d + 1)*(2*d - 1)
Let r(b) = -8*b**2 - 38*b - 128. Let i(q) = -q**2 - q. Suppose 5*t = -15, 2*g - 4*t + 7*t = -21. Let m(n) = g*i(n) + r(n). Factor m(w).
-2*(w + 8)**2
Let a(r) = 3*r**3 - 5*r + 4. Let d be a(1). Find t such that -4/3*t**3 + 4/3*t + 0 - 2*t**4 + d*t**2 = 0.
-1, -2/3, 0, 1
Let b(n) be the second derivative of -n**7/42 - n**6/6 - n**5/5 + 4*n**4/3 + 16*n**3/3 + 8*n**2 + 232*n. Let b(x) = 0. Calculate x.
-2, -1, 2
Let s(q) be the second derivative of 2/51*q**3 + 0 + 1/102*q**4 - 1/170*q**5 - 6*q + 0*q**2. Determine d so that s(d) = 0.
-1, 0, 2
Let r(b) = b**3 + 37*b**2 + 33*b - 101. Let j be r(-36). Let z(p) be the first derivative of -j + 3/4*p**2 + 1/3*p**3 - p - 3/8*p**4. Factor z(u).
-(u - 1)*(u + 1)*(3*u - 2)/2
Let t(k) be the second derivative of 3/10*k**5 + 28*k + 0 - 3/10*k**6 - 3/2*k**3 + 1/14*k**7 + 1/2*k**4 + 3/2*k**2. Determine y, given that t(y) = 0.
-1, 1
Let c(q) be the third derivative of 0*q + 1/1008*q**8 + 2*q**2 + 0 - 1/360*q**6 + 1/315*q**7 - 1/90*q**5 + 0*q**3 + 0*q**4. Suppose c(h) = 0. Calculate h.
-2, -1, 0, 1
Let r(p) be the third derivative of p**5/40 + 3*p**4/16 + p**3/2 - 13*p**2 + 2*p. Factor r(g).
3*(g + 1)*(g + 2)/2
Let l(n) be the first derivative of 0*n + 10/3*n**3 + 2*n**2 + 2/5*n**5 + 2*n**4 - 11. Let l(k) = 0. Calculate k.
-2, -1, 0
Let j(d) be the first derivative of d + 9/2*d**2 + 3 + d**3 + 1/12*d**4. Let w(r) be the first derivative of j(r). Factor w(q).
(q + 3)**2
Let q = -34642 - -381074/11. Find j such that -8/11 + 18/11*j - q*j**2 + 2/11*j**3 = 0.
1, 4
Let j(a) = 30 - 34 - 6*a + 2*a + 2*a**2. Let i(x) = -x**3 + 3*x**2 - 3*x - 4. Let m(p) = 4*i(p) - 6*j(p). Factor m(b).
-4*(b - 2)*(b + 1)**2
Let y(p) be the third derivative of p**6/40 + 67*p**5/20 + 131*p**4/8 + 65*p**3/2 + 600*p**2. Factor y(f).
3*(f + 1)**2*(f + 65)
Let n(r) = r**2 - 2*r - 193. Let p be n(-13). Determine t so that -19/5*t**4 + 28/5*t**p + 0 + 4/5*t + 47/5*t**3 - 12*t**5 = 0.
-2/3, -2/5, -1/4, 0, 1
Let b = -6017201/133 + 45241. Let c = 4/133 - b. Factor 12/7*z**3 + 0 + 0*z + c*z**2.
4*z**2*(3*z + 2)/7
Let u = 129/4 - 79/4. What is s in u - 115/4*s - 25/4*s**2 = 0?
-5, 2/5
Let u be (-1)/3 - 40/(-48). Let q be 3*(6/56 - 4/(-28)). Determine i so that q*i + u + 1/4*i**2 = 0.
-2, -1
Determine m, given that 0*m + 1/3*m**4 + 4/3*m**5 + 0 - 4/3*m**3 - 1/3*m**2 = 0.
-1, -1/4, 0, 1
Let -4/3*u**2 - 16 + 2/3*u**3 - 40/3*u = 0. Calculate u.
-2, 6
Let q(b) be the first derivative of b**5/60 + b**4/72 - 2*b**3/9 - b**2/3 + 5*b + 28. Let w(t) be the first derivative of q(t). Factor w(g).
(g - 2)*(g + 2)*(2*g + 1)/6
Let u(c) be the second derivative of -c**4/24 - 23*c**3/12 - 11*c**2/2 - 10*c. Factor u(n).
-(n + 1)*(n + 22)/2
Let i(x) be the third derivative of x**7/105 - x**5/10 - x**4/6 - 127*x**2. What is t in i(t) = 0?
-1, 0, 2
Suppose -32 = 18*k + 21*k - 47*k. Determine w, given that -3/2*w**k - 3/2*w**2 + 0*w + 0 + 3*w**3 = 0.
0, 1
Let d be (8/(-7))/(6/(-21)). Let t(i) be the first derivative of 5 + 0*i + 0*i**2 - 1/30*i**5 + 1/12*i**d - 1/18*i**3. Factor t(u).
-u**2*(u - 1)**2/6
Suppose 0*d = -4*d - 12. Let p be 210/(-12)*d/5. Factor -p*f**3 - 9/2*f - 18*f**2 + 3.
-3*(f + 1)**2*(7*f - 2)/2
Suppose 0 - 3/8*v**3 + 3/8*v**4 - 15/8*v**2 - 9/8*v = 0. What is v?
-1, 0, 3
Let q(o) be the first derivative of -4*o**3/9 - 112*o**2/3 - 3136*o/3 + 3. Factor q(z).
-4*(z + 28)**2/3
Let x(g) = -19*g**2 + 2549*g - 204811. Let m(i) = 5*i**2 - 637*i + 51203. Let w(a) = -11*m(a) - 3*x(a). Let w(k) = 0. Calculate k.
160
Let t(d) be the third derivative of d**10/37800 - d**9/9450 + d**8/8400 - 5*d**4/24 + 8*d**2. Let x(w) b