 + 1/2*r**2 + 0 + 1/12*r**3. Determine k so that b(k) = 0.
-1, 2
Let x(g) be the first derivative of g**4 + 1468*g**3/3 - 3097. Factor x(l).
4*l**2*(l + 367)
Let p(g) = 4*g**3 + 113*g**2 + 404*g + 315. Let i(a) = 6*a**3 + 172*a**2 + 606*a + 472. Let q(m) = -5*i(m) + 8*p(m). What is d in q(d) = 0?
-16, -5, -1
Suppose 4*k + 2*r = -10 + 14, 2*k - 6 = r. Suppose k*u = -5*p - 1, -38*u = -33*u - 4*p - 14. Factor -1/2*b**4 - u + 3*b**3 - 13/2*b**2 + 6*b.
-(b - 2)**2*(b - 1)**2/2
Let 166*w**3 - 2169*w**3 + 3737*w**4 - 4313*w**4 + 73*w - 2573*w - 973*w**3 - 4900*w**2 = 0. Calculate w.
-25/12, -1, 0
Suppose -153*b + 55*b + 983 - 199 = 0. Let t(x) be the third derivative of b*x**2 + 0 + 0*x**3 + 1/480*x**6 + 1/60*x**5 + 0*x + 0*x**4. Factor t(k).
k**2*(k + 4)/4
Suppose 4752 = 272*y - 274*y + 4*o, -o - 11825 = 5*y. Let q = y + 21304/9. Let -q*w**2 - 2/9*w**4 - 4/9*w - 8/9*w**3 + 0 = 0. Calculate w.
-2, -1, 0
Let l(k) be the first derivative of -k**6/4 - 93*k**5/10 - 639*k**4/8 - 337*k**3/2 - 231*k**2/2 - 3993. Solve l(m) = 0 for m.
-22, -7, -1, 0
Factor 4068*y + 5*y**2 - 819*y - 5480 + 2226*y.
5*(y - 1)*(y + 1096)
Let m(p) be the first derivative of p**5/230 - 4*p**3/69 - 9*p + 48. Let o(a) be the first derivative of m(a). Factor o(r).
2*r*(r - 2)*(r + 2)/23
Let c be 25/825*1430/195. Solve c*o**3 + 218/9*o**2 + 648 + 672*o = 0.
-54, -1
Let r = -2688 - -2692. Let t(c) be the first derivative of 15 - 44/3*c**3 + 0*c - 3*c**r - 12*c**2. Factor t(d).
-4*d*(d + 3)*(3*d + 2)
Let y(x) be the second derivative of -3*x**4/4 + 32*x**3 + 345*x**2/2 + 952*x + 1. Factor y(j).
-3*(j - 23)*(3*j + 5)
Let v(f) be the first derivative of -1/36*f**5 + 7/2*f**2 + 0*f - 5/9*f**3 + 26 - 5/24*f**4. Let w(k) be the second derivative of v(k). Factor w(p).
-5*(p + 1)*(p + 2)/3
Let b(z) be the third derivative of -z**6/30 + 4*z**5/15 + 22*z**4/3 - 64*z**3 - 259*z**2 + 2*z. Factor b(u).
-4*(u - 8)*(u - 2)*(u + 6)
Let q(m) be the second derivative of -m**6/150 - 13*m**5/100 + m**4/15 + 26*m**3/15 + 309*m. Find a, given that q(a) = 0.
-13, -2, 0, 2
Let n(k) be the first derivative of 33 - k**5 - 20*k**3 - 15*k + 25*k**2 + 15/2*k**4. Factor n(z).
-5*(z - 3)*(z - 1)**3
Find t, given that -502/5 + 100*t + 2/5*t**2 = 0.
-251, 1
Let w(l) be the third derivative of -l**5/240 - 3*l**4/16 + 273*l**3/8 + 4*l**2 + 23*l - 1. Factor w(b).
-(b - 21)*(b + 39)/4
Let q(r) be the first derivative of -148 - 10092*r - 37 - 95*r**2 - r**3 + 2*r**2 - 81*r**2. Factor q(x).
-3*(x + 58)**2
Let j(b) be the second derivative of 0*b**3 - 1/105*b**7 + 2/25*b**6 + 0*b**2 + 2/15*b**4 + 0 - 82*b - 9/50*b**5. Find d such that j(d) = 0.
0, 1, 4
Let d(j) be the third derivative of 2/195*j**5 + 7/780*j**6 + 0*j**3 + 0*j + 1/1365*j**7 + 102*j**2 - 1/13*j**4 + 0. Factor d(q).
2*q*(q - 1)*(q + 2)*(q + 6)/13
Let c = 30820 + -4622977/150. Let q(f) be the third derivative of 43*f**2 + 0*f + 0 - 3/5*f**3 + c*f**5 + 1/75*f**6 + 1/2*f**4. Factor q(w).
2*(w + 3)**2*(4*w - 1)/5
Factor 1/4*u**4 + 10951206*u**2 + 13325434761604 - 2702*u**3 - 19726772408*u.
(u - 2702)**4/4
Let t(m) be the first derivative of m**6/2 - 153*m**5/5 + 2019*m**4/4 - 525*m**3 - 1875*m**2 - 2940. Let t(s) = 0. Calculate s.
-1, 0, 2, 25
Let a(o) = -5*o + 83. Let v be a(16). Let r(x) = -7*x**2 - 40*x + 159. Let k(w) = -76*w**2 - 440*w + 1748. Let p(u) = v*k(u) - 32*r(u). Factor p(y).
-4*(y - 3)*(y + 13)
Let n(w) be the third derivative of w**5/12 - 47*w**4/24 - 44*w**3/3 - w**2 + 61*w. Let z(p) = p**2 - 16*p - 29. Let y(h) = 2*n(h) - 7*z(h). Factor y(t).
3*(t + 3)**2
Suppose 4*y - 223 = 6*u + 265, 0 = -u + 3*y - 72. Let l be u/10 - (-1332)/148. Find o, given that l*o**3 + 11/5*o - 2*o**2 - 4/5 = 0.
1, 4/3
Let a(w) be the third derivative of 37*w**5/180 - 151*w**4/72 + 2*w**3/3 - 312*w**2 - 5*w. Factor a(f).
(f - 4)*(37*f - 3)/3
Let p(s) = -3*s**4 + 11*s**3 + 10*s**2 + 12*s + 8. Let q(i) = i**4 - i**3 + i**2 - i - 2. Let y(w) = 5*p(w) + 20*q(w). Factor y(t).
5*t*(t + 1)*(t + 2)*(t + 4)
Let o(d) be the second derivative of -35*d**4/12 + 670*d**3/3 - 190*d**2 + 51*d - 8. Suppose o(z) = 0. Calculate z.
2/7, 38
Let v(j) = j**3 + 6*j**2 - 29*j - 150. Let k be v(-6). Let 7 - 21 - k*q + 2*q**2 - 58 + 83*q - 41*q = 0. What is q?
-12, 3
Let x = 2965 - 2960. Let v(h) be the first derivative of -1/22*h**4 + 0*h**2 - 2/55*h**x + 8 + 1/33*h**6 + 2/33*h**3 + 0*h. Suppose v(r) = 0. What is r?
-1, 0, 1
Let j(u) be the second derivative of 10/3*u**3 - 1/10*u**5 - 1/30*u**6 + 6*u**2 + 0 + 43*u + 7/12*u**4. Factor j(b).
-(b - 3)*(b + 1)*(b + 2)**2
Let c(x) be the third derivative of x**5/270 + 26*x**4/27 - 16*x**3 + 11*x**2 - 45*x. Let c(h) = 0. What is h?
-108, 4
Let z be (-1617)/(-84) + 13/52. Factor -z*r**2 - 29/2*r + 28*r**3 - 2 + 8*r**4.
(r - 1)*(r + 4)*(4*r + 1)**2/2
Let z(l) be the first derivative of -l**6/2 + 24*l**5/5 - 27*l**4/2 + 4*l**3 + 57*l**2/2 - 36*l - 2956. Solve z(r) = 0 for r.
-1, 1, 3, 4
Suppose 0 = 2*i - 31*s + 32*s - 8803, 8821 = 2*i - 5*s. Let z = -13084/3 + i. Factor 100*y - 230/3*y**2 - 5/3*y**4 + 20*y**3 - z.
-5*(y - 5)**2*(y - 1)**2/3
Let r(o) be the second derivative of -11*o**5/4 + 745*o**4/6 - 2935*o**3/6 + 750*o**2 + 5*o - 102. Find d such that r(d) = 0.
1, 12/11, 25
Suppose -3*j = -m - 47, j + 7767*m + 10 = 7765*m. Solve -j - 16/3*y + 1/3*y**2 = 0.
-2, 18
Let x(j) be the second derivative of j**4/72 - 179*j**3/36 + 59*j**2/2 + 741*j. Factor x(t).
(t - 177)*(t - 2)/6
Let -2/11*z**2 + 16*z - 174/11 = 0. Calculate z.
1, 87
Let z(s) be the third derivative of -s**6/90 - 7*s**5/15 - 49*s**4/6 - 29*s**3/3 - 16*s**2 - 2*s. Let r(h) be the first derivative of z(h). Factor r(v).
-4*(v + 7)**2
Let p = 3880 + -3878. Let q(u) be the first derivative of 0*u**p - 30 + 1/5*u**4 - 1/25*u**5 + 0*u - 1/5*u**3. Factor q(s).
-s**2*(s - 3)*(s - 1)/5
Let q = -466 + 476. Find p, given that 4*p**4 + 2*p**3 - q*p**3 + 4*p**3 - p**5 + 5*p - 2*p**2 + 2 - 6 + 2 = 0.
-1, 1, 2
Let q(f) be the third derivative of -3*f**6/160 + 277*f**5/80 - 45*f**4/16 - 23*f**3 + 1606*f**2. Let q(o) = 0. Calculate o.
-2/3, 1, 92
Let i(v) be the second derivative of v**5/100 - 3*v**4/40 - v**3 + 34*v**2 - 47*v. Let k(r) be the first derivative of i(r). Factor k(u).
3*(u - 5)*(u + 2)/5
Let d(w) be the first derivative of -2*w**6/21 - 48*w**5/35 + 23*w**4/7 + 184*w**3/7 + 208*w**2/7 + 2177. Solve d(q) = 0 for q.
-13, -2, -1, 0, 4
Suppose 0 = 5*a - 60 + 10. Let u be -4 + (3 - (7 - a)). Let 0*y**u + 0*y + 0*y**3 + 0 + 1/2*y**5 + 1/2*y**4 = 0. What is y?
-1, 0
Suppose 0 = -3*r - 7*o + 147, 120 = 3*r - 67*o + 71*o. Factor -2/3*f**4 - 32/3*f**3 - r*f**2 - 26/3 - 80/3*f.
-2*(f + 1)**3*(f + 13)/3
Let q = -4409 - -4409. Let o(j) be the third derivative of 0 + 1/84*j**4 - 1/420*j**6 + 3*j**2 + 0*j**5 + 0*j**3 + q*j. Factor o(s).
-2*s*(s - 1)*(s + 1)/7
Let -3/5*f**3 - 117/5 - 27/5*f**2 + 147/5*f = 0. Calculate f.
-13, 1, 3
Let c(v) be the second derivative of -33*v + 0*v**2 - 5/36*v**4 + 5*v**3 + 1. Suppose c(g) = 0. Calculate g.
0, 18
Let h(m) = -252*m - 730. Let z be h(-3). Let o(t) be the first derivative of -5*t + 3*t**2 - 1/3*t**3 - z. Factor o(f).
-(f - 5)*(f - 1)
Let j = 3262 - 29326/9. Let q = 1555/738 - 27/82. Suppose j - q*c + 2/9*c**2 = 0. Calculate c.
4
Factor 3/2*n**3 + 0 + 3*n - 99/8*n**2.
3*n*(n - 8)*(4*n - 1)/8
Suppose -3*q - 9 = -21. Suppose 2*l = b - 7 + 3, 4*b + q*l = 28. Determine g so that b*g + 5*g - 10*g - 2*g**2 + 3*g**2 = 0.
-1, 0
Factor 372/11*k + 106/11*k**2 - 2/11*k**3 - 2016/11.
-2*(k - 56)*(k - 3)*(k + 6)/11
Let d(m) = -m**2 - 20*m + 25. Let w(t) = -19*t + 25. Let h(b) = -b**2. Let j(u) = h(u) + w(u). Let x(q) = -5*d(q) + 4*j(q). Factor x(z).
(z - 1)*(z + 25)
Let k(c) be the third derivative of 3*c**5/10 - 37*c**4/60 - 8*c**3/15 - 487*c**2 - 3*c - 1. Let k(g) = 0. Calculate g.
-8/45, 1
Let c(l) be the first derivative of -15/2*l**2 - 43 - l - 49/4*l**4 - 21*l**3. Solve c(t) = 0.
-1, -1/7
Factor -49/5*f + 1/5*f**2 + 72.
(f - 40)*(f - 9)/5
Let g(u) be the second derivative of -u**7/21 - 38*u**6/3 + 96*u**5/5 + 95*u**4/3 - 191*u**3/3 - 1507*u. Determine l so that g(l) = 0.
-191, -1, 0, 1
Let o(n) = 46*n - 416. Let s be o(10). Let y be (-3)/9 - 7/((-168)/s). Factor 30*k + 150 + y*k**2.
3*(k + 10)**2/2
Factor 8*w**2 + 16*w + 1104 - 6*w**2 - 1522.
2*(w - 11)*(w + 19)
Factor -60