second derivative of -32*o - 1/2*o**3 + 0*o**2 + 1/36*o**4 + d. Factor s(x).
x*(x - 9)/3
Let w(v) be the second derivative of v**6/30 - 57*v**5/10 + 3469*v**4/12 - 2090*v**3 + 6050*v**2 - 2879*v. Factor w(t).
(t - 55)**2*(t - 2)**2
Factor n**2 + 29/4*n + 6 - 1/4*n**3.
-(n - 8)*(n + 1)*(n + 3)/4
Let c(x) be the first derivative of x**7/210 + 11*x**6/90 - 8*x**3 + 74. Let l(s) be the third derivative of c(s). Find k, given that l(k) = 0.
-11, 0
Let s(v) be the second derivative of v**6/120 + v**5/12 + v**4/12 - 4*v**3/3 - 3*v**2 - 2*v + 7. Let b(q) be the first derivative of s(q). Factor b(m).
(m - 1)*(m + 2)*(m + 4)
Suppose 5*j - 135 = -8*h + 3*h, -5*j = 3*h - 83. What is u in -514*u**3 + h*u**4 - u**5 + 7*u**3 + 3375*u**2 + 19*u**4 - 168*u**3 = 0?
0, 15
Suppose -11 = j - 6. Let g(i) = -6*i - 10. Let x be g(j). Factor 4*y**3 - 8*y - 12*y**3 - x*y**2 - 4*y**4 - 8*y**3.
-4*y*(y + 1)**2*(y + 2)
Let r(t) be the second derivative of 5/12*t**2 + 1/6*t**3 + 4 - 5*t - 1/180*t**6 - 1/20*t**5 - 1/18*t**4. Factor r(j).
-(j - 1)*(j + 1)**2*(j + 5)/6
Factor -36/5*o**2 - 3/5*o**3 + 36/5 + 3/5*o.
-3*(o - 1)*(o + 1)*(o + 12)/5
Let x(i) = i**2 + i - 9. Let g be x(-4). Find b such that -282*b + 43*b**3 + 490*b**4 - 58*b - 220*b**g - 870*b**2 - 278*b**3 - 40 = 0.
-1/2, -2/7, 2
Suppose -17*g + 24 = -15*g. Factor 21*y**2 - g - 5*y - 22*y - 3*y**3 - y + y - 39*y**2.
-3*(y + 1)**2*(y + 4)
Let n = -2/201771 - -174330166/2219481. Find i, given that 2/11*i**3 - 42/11*i**2 + n + 144/11*i = 0.
-3, 12
Let d(t) = t**2 - t - 1. Let g(a) be the third derivative of 0*a - 2/5*a**5 + 0 + 2/3*a**4 + 18*a**2 + 10/3*a**3. Let p(k) = 20*d(k) + g(k). Factor p(n).
-4*n*(n + 1)
Let z(l) = l**3 - 22*l**2 + 36*l + 83. Let p be z(20). Find g, given that -p*g**2 - 50 + 345*g - 773*g + 351*g = 0.
-25, -2/3
Suppose 18*n + 80*n = 16*n + 328. Let u(q) be the second derivative of -1/12*q**3 - 1/2*q**2 + 1/24*q**n + 9*q + 0. Suppose u(i) = 0. What is i?
-1, 2
Factor 1408*o**3 + 122500 - 42*o**4 + 46*o**4 + 31979*o**2 - 72665*o + 319065*o + 93325*o**2.
4*(o + 1)**2*(o + 175)**2
Let f(b) be the third derivative of 4/9*b**3 + 2*b**2 + 0*b - 1/10*b**5 - 4/9*b**4 + 0. Determine k so that f(k) = 0.
-2, 2/9
Let j = -394 + 399. Factor j*z**5 - 4*z**4 - 12*z**3 - 2*z**5 + 9*z**4 + 4*z**4.
3*z**3*(z - 1)*(z + 4)
Suppose 5*r + 2*v - 121 = 0, 2*r - 5*v - 44 = -8*v. Factor w + r*w + 3721 + 4*w + 92*w + w**2.
(w + 61)**2
Let v = 17 + 28. Suppose 14*q - 5*q - v = 0. Solve 11*r**3 - 12*r**2 + 9*r**3 - 4*r**q - 4*r**4 + 0*r**2 = 0.
-3, 0, 1
Let 129*m**2 - 18383*m**5 - 258*m**3 + 18380*m**5 - 99*m**4 + 231*m**2 = 0. What is m?
-30, -4, 0, 1
Let a(f) = f - 28. Let k be a(32). Factor -5*d**k + 129*d**3 + 168*d**2 - 136*d**3 - d**5 - 171*d**2.
-d**2*(d + 1)**2*(d + 3)
Suppose -97 + 13 = -21*k. Factor -k*v**2 - 91*v**3 + 25*v**2 + 94*v**3.
3*v**2*(v + 7)
Solve 1/3*t**3 + 1/3*t**2 + 0 + 0*t - 1/3*t**4 - 1/3*t**5 = 0 for t.
-1, 0, 1
Let w(i) = 4*i**2 + 253*i + 1008. Let f be w(-59). Let 12/5*h**4 + 32/5 + 4*h**f + 292/5*h**2 - 188/5*h**3 - 168/5*h = 0. What is h?
-4, 2/5, 1
Let z(a) = 72*a**2 + 13*a + 31. Let r be z(-3). Factor -318 + 190 + 160*k**3 + 20*k**4 + 473 + 1280*k + 679 + k**5 + r*k**2.
(k + 4)**5
Let q(s) = 2*s**5 - 2*s**4 + 2*s**3 + s + 1. Let l(n) = 45*n**5 + 205*n**4 - 3320*n**3 - 9800*n**2 + 276025*n + 560025. Let y(f) = l(f) - 25*q(f). Factor y(t).
-5*(t - 20)**3*(t + 2)*(t + 7)
Let o(q) = -2*q**2 + 858*q + 3. Let m be o(0). Factor 169 + 351*f + 781/4*f**2 + 27/2*f**m + 1/4*f**4.
(f + 1)**2*(f + 26)**2/4
Let s(k) be the third derivative of -k**5/30 + 21*k**4/2 - 248*k**3/3 + 98*k**2 + 2*k - 10. Factor s(x).
-2*(x - 124)*(x - 2)
Let i = 161029 + -161027. Let 1 + 1/4*d**i - d = 0. What is d?
2
Let f(t) be the third derivative of 2*t**7/105 + 13*t**6/5 + 20*t**5 + 148*t**4/3 - 65*t**2 - 1. Factor f(s).
4*s*(s + 2)**2*(s + 74)
Let v = -31 + 34. Solve -d**4 - 3*d**2 - 15 + 10*d**v - 6*d**2 - 4*d**2 - 21 - 60*d = 0 for d.
-1, 6
Let s(t) = 25*t - 859. Let j be s(35). Let l be 1 + 39 + (-2 - -4). Suppose -47*b**4 - 6*b**2 - 5*b**3 + l*b**4 + j*b**2 = 0. What is b?
-2, 0, 1
Solve 350*n**3 + 3 - 113/2*n + 230*n**2 = 0.
-6/7, 1/10
Let j(p) be the first derivative of -2*p**4/15 + 3*p**3/5 - 2*p**2/5 + 59*p - 6. Let n(w) be the first derivative of j(w). Suppose n(l) = 0. What is l?
1/4, 2
Factor -w**3 + 169 - 280*w**2 + 1900*w + w**4 - 129 - 40.
w*(w - 10)**2*(w + 19)
Let x(h) be the first derivative of -2*h**3/21 + 2*h**2/7 + 6916. Factor x(j).
-2*j*(j - 2)/7
Let r(o) be the second derivative of 7/15*o**3 + 0*o**2 - 1/5*o**4 - 1/50*o**5 - 1 + 15*o. Suppose r(m) = 0. What is m?
-7, 0, 1
Let n be -3 - 3/(12/(-32)). Suppose 0 = -r + 5*r - n*q - 18, -3*q = -r + 1. Factor -r*j**2 + 0*j**2 + 5*j + 2*j**2 - 13 + 23.
-5*(j - 2)*(j + 1)
Let m(p) be the third derivative of -p**5/90 - 11*p**4/18 - 19*p**3/3 - 752*p**2 - 4*p. Factor m(h).
-2*(h + 3)*(h + 19)/3
Find f, given that -8*f**2 + 5*f**2 - 272*f - 9*f**2 + 8*f**2 + 153 + 123 = 0.
-69, 1
Factor 5*p**3 + 240/7*p - 1/7*p**4 - 274/7*p**2 + 0.
-p*(p - 24)*(p - 10)*(p - 1)/7
Factor -543*x - x**3 - 23*x**2 - 138 - x**3 - 15*x**2 + 721*x.
-2*(x - 3)*(x - 1)*(x + 23)
Let c(v) = -24*v + 27. Let u be c(1). Factor -735*h**4 - u*h**5 + 368*h**4 + 370*h**4 + 6*h**3.
-3*h**3*(h - 2)*(h + 1)
Let r(v) = 2*v**2 - 6*v + 2. Let u be r(3). Find k such that 29*k + 5*k**2 - 2*k**2 - 35*k - 2*k**u = 0.
0, 6
Determine z so that -5259 - 218*z - 1221 - 466*z + 0*z**2 + 4*z**2 = 0.
-9, 180
Let j = 111924 - 111922. Factor 43/4*w**j + 17/4*w**4 - 7/2*w - 1/4*w**5 - 45/4*w**3 + 0.
-w*(w - 14)*(w - 1)**3/4
Let z = 566 + -430. Let d be (2210/z)/((-5)/(-6)). Let -57/2*x**3 + 18*x + 6 - d*x**2 + 21/2*x**5 + 27/2*x**4 = 0. What is x?
-2, -1, -2/7, 1
Suppose -27*b**4 + 102*b**4 + 1980*b**2 + 175*b**3 - 1052*b**3 + 40*b**4 - 5*b**5 + 37*b**3 = 0. What is b?
0, 6, 11
Let q(x) be the first derivative of -125 + 17/12*x**3 - x + 4*x**2. Suppose q(l) = 0. Calculate l.
-2, 2/17
Suppose -3*x = -j - 64, 7*j + 25 = x + 3*j. Suppose x*p + 20 = 26*p, 0 = -2*g + 5*p - 20. Find h such that 0*h**2 + 0*h + 3/7*h**4 + g + 3/7*h**3 = 0.
-1, 0
Let f(a) = 465*a**2 - 31*a + 30. Let v be f(1). Let j = 937/2 - v. Factor -3/2*g + 1/8*g**2 + j.
(g - 6)**2/8
Let r = 78091 - 390447/5. Factor 2/5*j**3 + 8/5 - 2/5*j**2 - r*j.
2*(j - 2)*(j - 1)*(j + 2)/5
Let m(t) be the second derivative of -t**7/63 + t**6/45 + 91*t**5/30 + 431*t**4/18 + 78*t**3 + 120*t**2 - 1986*t. Determine w so that m(w) = 0.
-5, -3, -2, -1, 12
Suppose 814 = -f + 820. Suppose 0 = -3*n + f - 0. Factor 3/7*l**n + 72/7*l + 432/7.
3*(l + 12)**2/7
Let v(d) = -d**4 - 1. Suppose 10*h - 47*h = -111. Let f(y) = 9*y**4 + 34*y**3 - 289*y**2 + 10. Let o(w) = h*f(w) + 30*v(w). Factor o(q).
-3*q**2*(q - 17)**2
Let o(j) be the first derivative of -j**7/10 - 37*j**6/40 - j**5/2 + 15*j**2/2 + 2*j - 91. Let b(w) be the second derivative of o(w). What is h in b(h) = 0?
-5, -2/7, 0
Let w(r) be the first derivative of 0*r**3 + 0*r**2 + 2/5*r**5 - 34 + 1/3*r**4 + 0*r + 1/9*r**6. Factor w(g).
2*g**3*(g + 1)*(g + 2)/3
Factor 41*k**5 - 7*k**2 + 15*k + 8*k**4 - 40*k**5 + 6*k**3 - k**2 - 22*k.
k*(k - 1)*(k + 1)**2*(k + 7)
Suppose 709 = 37*r + 154. Let p(z) be the first derivative of 2/75*z**5 + 0*z + 0*z**3 + 1/15*z**4 + 0*z**2 - r. Find m such that p(m) = 0.
-2, 0
Let v(o) be the first derivative of -3*o**6/25 - o**5/25 - o**4/180 + 55*o**3/3 + 51. Let j(q) be the third derivative of v(q). Determine r so that j(r) = 0.
-1/18
Let z = 37384 + -37380. Factor -1/6 + 5/3*w + 11/3*w**3 - 7/6*w**z - 4*w**2.
-(w - 1)**3*(7*w - 1)/6
Let f(j) be the first derivative of 5/2*j**3 - 12 + 6*j + 3/20*j**5 - 3*j**2 - j**4. Let a(n) be the first derivative of f(n). Suppose a(l) = 0. Calculate l.
1, 2
Factor -87*i**2 - 92*i**2 + 38*i + 269*i**2 + 261 - 89*i**2.
(i + 9)*(i + 29)
Let b(u) be the first derivative of 144/5*u**2 - 2/15*u**3 - 10368/5*u + 254. Factor b(r).
-2*(r - 72)**2/5
Let x be ((-64)/48)/(-1 - 5/(-9)). Suppose 0 = -x*j + 3 + 21. Factor -13*y + j*y**2 + y**2 + 19*y + 3*y**3.
3*y*(y + 1)*(y + 2)
Let d(s) be the third derivative of -11*s**7/140 + s**6/8 + 91*s**5/10 + 363*s**4/8 + 63*s**3/4 + 2*s**2 - 709. Solve d(a) = 0.
-3, -1/11, 7
Let p = 1117 - 778. Factor 22*i + 2*i - p*i**2 + 342*i**