first derivative of 5*w**4/4 + 55*w**3/6 + 15*w**2 - 10*w - 29. Let k(i) be the first derivative of t(i). Factor k(m).
5*(m + 3)*(3*m + 2)
Let n(o) = 15*o**2 - 370*o - 20. Let m(z) = -13*z**2 + 371*z + 16. Let a(x) = 5*m(x) + 4*n(x). Determine b, given that a(b) = 0.
0, 75
Let q(k) be the first derivative of -49*k**5/120 - 7*k**4/8 - 5*k**3/12 - k**2/12 + 22*k + 10. Let s(z) be the first derivative of q(z). Solve s(o) = 0.
-1, -1/7
Let c(q) be the third derivative of -1/52*q**4 - 1/130*q**5 - 1/780*q**6 - 1/39*q**3 - 10*q**2 + 0*q + 0. Factor c(d).
-2*(d + 1)**3/13
Factor -1/2*s + 0 + 1/2*s**3 + 3/4*s**2.
s*(s + 2)*(2*s - 1)/4
Suppose 0*a - 22 = -2*a. Suppose -2*n = -5*q + a, -2*q + 5*q - 4*n = 1. Factor -3*l + q*l**2 - 197 + 197.
3*l*(l - 1)
Let t(j) be the third derivative of 32*j**8/63 - 32*j**7/35 - 37*j**6/45 + 61*j**5/20 - 3*j**4 + 3*j**3/2 - j**2 - 42*j. Determine r so that t(r) = 0.
-1, 3/8, 1
Let t(h) be the third derivative of 1/80*h**5 + h**2 + 1/160*h**6 + 0 - 1/32*h**4 + 0*h - 1/8*h**3. Solve t(a) = 0 for a.
-1, 1
What is m in 0*m**5 - 102*m**2 + 6*m**5 - 3*m**5 + 12*m**4 - 135*m - 21*m - 72 - 9*m**3 + 0*m**5 = 0?
-2, -1, 3
Let i(g) be the third derivative of 0 + 0*g**3 + 1/84*g**4 - 1/420*g**6 - 8*g**2 + 1/735*g**7 - 1/210*g**5 + 0*g. Factor i(l).
2*l*(l - 1)**2*(l + 1)/7
Let y(v) = 57*v**2 + 102*v - 87. Let r(i) = -16*i**2 - 29*i + 25. Let z(u) = 18*r(u) + 5*y(u). Determine s, given that z(s) = 0.
-5, 1
Let r = -434 + 437. Factor 0*p**2 + 0 + 0*p + 2/3*p**4 + 1/3*p**r.
p**3*(2*p + 1)/3
Suppose 20 = 5*r, 5*r - 23 = -2*u + 1. Factor -149*o**u - o**4 + 0*o**4 + 150*o**2.
-o**2*(o - 1)*(o + 1)
Let m(p) be the first derivative of 3*p**4/7 + 12*p**3 + 243*p**2/14 + 60*p/7 - 196. Factor m(w).
3*(w + 20)*(2*w + 1)**2/7
Let r(s) be the second derivative of -s**7/42 + s**6/15 - s**4/6 + s**3/6 + 14*s + 8. Factor r(w).
-w*(w - 1)**3*(w + 1)
Let y(j) be the first derivative of -5*j**6/72 - 13*j**5/24 + 5*j**4/4 + 2*j**3 - 32. Let a(d) be the third derivative of y(d). Suppose a(m) = 0. Calculate m.
-3, 2/5
Let q = 376 + -22559/60. Let d(f) be the third derivative of 0*f**4 - f**2 + 1/210*f**7 + 0*f + 1/336*f**8 + 0 - 1/120*f**6 - q*f**5 + 0*f**3. Factor d(l).
l**2*(l - 1)*(l + 1)**2
Let o(t) be the third derivative of 2*t**7/105 + t**6/15 - 4*t**5/15 - t**4/3 + 2*t**3 + 4*t**2 + 1. Factor o(j).
4*(j - 1)**2*(j + 1)*(j + 3)
Let p be 18/(-8)*(-22)/429. Let j = p + 11/130. Solve -4/5*i**2 - 6/5*i**3 - 1/5*i**5 + 0 - j*i - 4/5*i**4 = 0.
-1, 0
Let u(t) be the second derivative of -3/20*t**5 - 10*t - 1/2*t**4 - 1/2*t**3 + 0 + 0*t**2. Factor u(m).
-3*m*(m + 1)**2
Let f = -6010 - -12021/2. Factor 1/4*p**3 + 0 + f*p + 3/4*p**2.
p*(p + 1)*(p + 2)/4
Let k be (125 - -5) + -3*(-2)/(-3). Factor 80 - 27*w - 13*w + 133*w**2 - k*w**2.
5*(w - 4)**2
Let f be 8*((-603)/(-54) - 11). Factor f - 1/3*n**2 + n.
-(n - 4)*(n + 1)/3
Let g be 3072/336 + 1*-9. What is h in -g*h**2 - 8/7*h - 16/7 = 0?
-4
Suppose 7*i - 215 = -201. Determine h, given that 0 - 2/5*h**i - 8/5*h = 0.
-4, 0
Let u(o) be the second derivative of -o**6/70 - 3*o**5/140 - 4*o - 14. Factor u(a).
-3*a**3*(a + 1)/7
Let g = 1681 - 21845/13. Solve 0 + 8/13*x + 2/13*x**3 - g*x**2 = 0 for x.
0, 2
Let j(m) be the third derivative of -m**5/12 - 95*m**4/24 - 15*m**3 + 169*m**2. Find z, given that j(z) = 0.
-18, -1
Let c(x) = 36*x**2 - 804*x + 312. Let h(f) = -11*f**2 + 268*f - 104. Let t(b) = -3*c(b) - 8*h(b). Find v, given that t(v) = 0.
2/5, 13
Let a(y) = 622*y - 48060. Let m(q) = q**2 + 623*q - 48065. Let g(o) = -6*a(o) + 4*m(o). Solve g(x) = 0.
155
Factor 69/5*r + 72/5 - 3/5*r**2.
-3*(r - 24)*(r + 1)/5
Let m(c) be the third derivative of c**6/140 - 29*c**5/70 + c**4 - 288*c**2. Factor m(z).
6*z*(z - 28)*(z - 1)/7
Let h(j) be the second derivative of -1/3*j**4 - 2*j**3 - 18*j + 0 - 2/15*j**6 + 4*j**2 + 3/5*j**5. Factor h(d).
-4*(d - 2)*(d - 1)**2*(d + 1)
Suppose 0 = -f - 0*f + 2. Suppose 0*t = f*t - 16. Factor -19*a**2 + 15*a - 7 + t - 7 + 7*a**2 + 3*a**3.
3*(a - 2)*(a - 1)**2
Let g(o) be the first derivative of o**5/15 - o**4/12 - 13*o**3/9 + 25*o**2/6 - 4*o - 120. Find u such that g(u) = 0.
-4, 1, 3
Find t such that -44*t + 33*t + 5*t**2 - 36 + 63 + 93 - 44*t = 0.
3, 8
Suppose 6*n = -48 + 138. Suppose 12 - 5*b - 2*b**2 + 0*b**2 + n*b = 0. Calculate b.
-1, 6
Factor -1/4 + 1/8*k**2 + 1/8*k**4 - 3/8*k**3 + 3/8*k.
(k - 2)*(k - 1)**2*(k + 1)/8
Let w be 0*((-44)/110)/(4/5). Let m(v) be the third derivative of -v**2 + 1/30*v**5 + 0*v**3 + 0 + w*v**4 + 0*v. Factor m(o).
2*o**2
Let n(t) be the first derivative of 2*t**3/3 - 2*t**2 - 6*t - 44. Factor n(y).
2*(y - 3)*(y + 1)
Let t(a) be the first derivative of -4*a**5/25 - a**4 - 28*a**3/15 - 6*a**2/5 + 111. Factor t(p).
-4*p*(p + 1)**2*(p + 3)/5
Let j(d) be the second derivative of -d**4/18 - 4*d**3 - 108*d**2 + 88*d. Let j(o) = 0. Calculate o.
-18
Suppose -j = -k - 3, -5*j - 2 = k - 23. Let g(d) be the second derivative of 1/20*d**5 + 0 + d**2 + 1/3*d**j + d + 5/6*d**3. Factor g(x).
(x + 1)**2*(x + 2)
Let w = -107 - -109. Let q(l) be the second derivative of -1/105*l**6 + 0 - 2*l + 1/35*l**5 + 0*l**w - 1/42*l**4 + 0*l**3. Factor q(z).
-2*z**2*(z - 1)**2/7
Let i(k) be the second derivative of -k**5/20 + k**4 - 11*k**3/6 + 3*k**2/2 - 37*k. Let a be i(11). Factor 1/3*c**a + 0*c**2 - 1/3*c + 0.
c*(c - 1)*(c + 1)/3
Factor 3/7*x**3 + 18/7*x**2 + 18/7 + 33/7*x.
3*(x + 1)*(x + 2)*(x + 3)/7
Factor 57/7 + 174/7*x + 9/7*x**2.
3*(x + 19)*(3*x + 1)/7
Let g be (312/234 - 5/5)*12/10. Find u, given that g*u**2 + 0 - 2/15*u**3 + 8/15*u = 0.
-1, 0, 4
Let s(y) be the third derivative of y**7/7 + 5*y**6/24 - 7*y**5/12 - 25*y**4/24 + 5*y**3/6 - y**2 - 5. Let s(k) = 0. Calculate k.
-1, 1/6, 1
Let v be 3/(36/(-78))*(0 + -2). Factor 17*x - 1 - x**2 - 2*x**2 - 26*x + v.
-3*(x - 1)*(x + 4)
Let f = 3 + -1. Let m = f - -4. Find w, given that 7*w**4 - 9*w**3 + 3*w**5 + w**2 + 4*w**3 - m*w**5 = 0.
0, 1/3, 1
Let -2*g**2 + 2/5*g**3 - 44/5*g - 32/5 = 0. What is g?
-2, -1, 8
Factor 0*y**2 - 8/21*y**4 + 0 + 2/21*y**5 + 8/21*y**3 + 0*y.
2*y**3*(y - 2)**2/21
Let y(b) be the second derivative of 1/21*b**3 + 0 + 3/70*b**5 - 5/42*b**4 + 0*b**2 - 11*b + 3/35*b**6. Factor y(r).
2*r*(r + 1)*(3*r - 1)**2/7
Suppose 0 = 3*r + r - 4*i - 20, -4*i - 12 = -2*r. Suppose 5*q = 10, -2*q + 5 = r*b + 1. Find t such that b*t - 8/11 - 2/11*t**3 + 6/11*t**2 = 0.
-1, 2
Let c(p) be the third derivative of p**7/70 - p**6/20 - p**5/4 + 3*p**4/4 - 69*p**2. Factor c(l).
3*l*(l - 3)*(l - 1)*(l + 2)
Let v(f) = -f**3 + 6*f**2 - 17*f - 3. Let z(q) = 2*q**3 + q + 3. Let a(j) = -2*v(j) - 2*z(j). Factor a(g).
-2*g*(g - 2)*(g + 8)
Let z be ((-16)/(-14))/(38/133). Suppose -2*h + z = -0*h. Factor -f**h - f - f**2 - f - 4*f.
-2*f*(f + 3)
Let k(l) be the third derivative of -l**7/1995 + 67*l**6/1140 + l**2 - 123*l. Factor k(j).
-2*j**3*(j - 67)/19
Let b(o) be the second derivative of -o**4/60 - 13*o**3/15 - 21*o**2/2 - 171*o. Factor b(i).
-(i + 5)*(i + 21)/5
Let v(f) be the third derivative of 22445*f**8/336 + 4355*f**7/21 + 1319*f**6/8 - 65*f**5/3 + 5*f**4/6 + 143*f**2. Suppose v(w) = 0. Calculate w.
-1, 0, 2/67
Suppose s = -4*j + 17 - 3, 5*j = -2*s + 31. Suppose s = 5*u - 4*l, u + 0*u + 8 = -5*l. Factor -16/7*o**u - 2*o - 6/7*o**3 - 4/7.
-2*(o + 1)**2*(3*o + 2)/7
Let g be -9 + -184*(-14)/280. Solve 3/5 + g*r**3 + 7/5*r + r**2 = 0 for r.
-3, -1
Let d(n) = 5*n**2 - n. Let z(x) = -44*x**2 - 76*x - 18. Let u(o) = -28*d(o) - 4*z(o). Factor u(r).
4*(r + 9)*(9*r + 2)
Determine z so that 631*z - 652*z - 5 - 3*z**3 - 12*z**2 - 5 + 2*z**3 = 0.
-10, -1
Suppose 31*o - 5*o**2 + 62 + 34*o - 128 - 114 = 0. Calculate o.
4, 9
Let u(m) be the first derivative of -7*m**4/16 - 11*m**3/4 + 27*m**2/2 - 7*m + 396. Factor u(r).
-(r - 2)*(r + 7)*(7*r - 2)/4
Let m(s) be the third derivative of s**6/30 - s**5 + 8*s**4 - 88*s**3/3 + 26*s**2 - 5. Factor m(k).
4*(k - 11)*(k - 2)**2
Let p(d) be the second derivative of 1/4*d**5 + 5/2*d**4 + 10*d**2 + 0 + 31*d + 15/2*d**3. Suppose p(c) = 0. What is c?
-4, -1
Let j(i) be the second derivative of i**5/10 + 3*i**4/2 + 20*i**3/3 + 12*i**2 + 5*i - 27. Factor j(p).
2*(p + 1)*(p + 2)*(p + 6)
Let p be (12/(-18))/(6/(-27)). Let l(k) be the third derivative of 4*k**2 - 7/15*k**7 - 2/15*k**5 + 0*k**p + 0 + 0*k**4 - 7/15*k*