4. Factor b*r + 972 + 3*r**2 + 21*r - 198*r.
3*(r - 18)**2
Let n = 78 - 78. Factor -9*p**2 + 20 + n*p**2 - 5*p + 4*p**2 + 10.
-5*(p - 2)*(p + 3)
Let s = -680304/83 + 8196. Let q = s + 523/249. Factor -1/3*v**2 + 0 + q*v.
-v*(v - 5)/3
Let j = 403 + -401. Let n = 1/9060 + 163073/63420. Factor n + 2/7*h**j - 12/7*h.
2*(h - 3)**2/7
Let o(n) be the second derivative of n**4/6 - 440*n**3/3 + 876*n**2 - 5184*n. Solve o(z) = 0 for z.
2, 438
Let t(z) = -6*z**3 + 9*z**2 + 681*z. Let v(y) = -11*y**3 + 15*y**2 + 1360*y. Let j(b) = 5*t(b) - 3*v(b). Factor j(h).
3*h*(h - 15)*(h + 15)
Let v(i) be the second derivative of -2*i**6/21 + 39*i**5/70 - 6*i**4/7 - 4*i**3/21 - 1630*i. What is k in v(k) = 0?
-1/10, 0, 2
Let a(k) = -7*k**3 + 2350*k**2 + 2483*k - 4718. Let j(n) = 6*n**3 - 2352*n**2 - 2454*n + 4719. Let c(p) = 3*a(p) + 4*j(p). Suppose c(h) = 0. Calculate h.
-2, 1, 787
Let 55*b**4 + 8537*b**2 + 13680 - 4351*b - 8817*b**2 - 5489*b - 5*b**5 + 800*b**3 = 0. Calculate b.
-6, 2, 19
Let r be -1*(20 + -22 - (1983 + 0)). Let r*o**2 + 9*o**4 - 210*o**3 + 4620*o - o**4 - 2*o**4 + 2420 + 0*o**4 - o**4 = 0. Calculate o.
-1, 22
Let f(u) be the first derivative of 3/5*u**4 + 34 + 6*u + 87/10*u**2 - 43/5*u**3. Factor f(o).
3*(o - 10)*(o - 1)*(4*o + 1)/5
Let q(b) be the second derivative of 5/9*b**2 - 5*b + 1/54*b**4 - 2/9*b**3 - 1. Determine h, given that q(h) = 0.
1, 5
Let a(t) be the second derivative of 0*t**2 + 1/10*t**6 + 3/5*t**5 + 0 + 0*t**3 - 28*t + t**4. Suppose a(j) = 0. What is j?
-2, 0
Find y, given that -y**2 + 4*y**2 - 18 - 3*y**2 - 15*y + 3*y**2 + 0*y**2 = 0.
-1, 6
Factor -1488*a**3 - 553536*a**2 - 5674113024 - 91517952*a - 3/2*a**4.
-3*(a + 248)**4/2
Suppose -7*t + 7 + 105 = 0. Factor -28*q - 47*q**2 - 92*q**3 - 13 + t*q**4 + 167*q**2 - 3 + 0.
4*(q - 4)*(q - 1)**2*(4*q + 1)
Factor 41*n + 1681 + 1/4*n**2.
(n + 82)**2/4
Let v = 202 - 198. Factor 47*u**3 + 5*u**5 + 19*u**4 + 20 + 16*u**v + 80*u + 48*u**3 + 125*u**2.
5*(u + 1)**3*(u + 2)**2
Let r(f) be the third derivative of -f**8/336 + 11*f**7/210 + f**6/15 - 49*f**5/15 - 56*f**4/3 - 128*f**3/3 + 27*f**2 + 2*f - 81. Factor r(u).
-(u - 8)**2*(u + 1)*(u + 2)**2
Let a = 1338401/409200 - -1/17050. Let f = a + 33/16. Factor -4/3*u**2 - f - 16/3*u.
-4*(u + 2)**2/3
Solve 150*a**2 - 9/2*a**3 + 0 - 144*a - 3/2*a**4 = 0 for a.
-12, 0, 1, 8
Let h(z) = 1. Let j(p) = -15*p + 13. Let w be j(1). Let u(x) = -3*x**3 - 23*x**2 - 32*x - 13. Let b(c) = w*u(c) - 2*h(c). Let b(t) = 0. Calculate t.
-6, -1, -2/3
Let d(m) be the first derivative of 1 + 1/84*m**4 + 1/210*m**5 + 0*m**2 + 0*m + 4*m**3 + 1/1260*m**6. Let i(k) be the third derivative of d(k). Factor i(q).
2*(q + 1)**2/7
Let w(y) be the first derivative of y**8/112 - 3*y**7/70 - y**6/10 + 22*y**2 + 2*y - 25. Let h(p) be the second derivative of w(p). Factor h(s).
3*s**3*(s - 4)*(s + 1)
Suppose 96/17*z - 416/17 + 2/17*z**2 = 0. Calculate z.
-52, 4
Let t(b) = -6*b**2 + b - b**3 + b**4 - 7*b**2 + 14*b**2. Let h(j) = -3*j**4 - 2*j**3 + 2*j**2 + 14*j. Let p(d) = -3*h(d) - 6*t(d). Solve p(c) = 0 for c.
-4, -2, 0, 2
Solve 32*s**5 + 12*s**3 + 8*s**4 - 7*s**3 - 4*s**4 + 11*s**3 - 34*s**5 = 0 for s.
-2, 0, 4
Let z(f) be the first derivative of f**6/480 + 29*f**5/120 + 28*f**4/3 + 196*f**3/3 + 145*f**2/2 + 148. Let y(d) be the second derivative of z(d). Factor y(j).
(j + 2)*(j + 28)**2/4
Let j(l) = -l**3 + 47*l**2 - 51*l + 5. Let x(h) = h**2 - 1. Let q(b) = -j(b) - 5*x(b). Factor q(g).
g*(g - 51)*(g - 1)
Let g(f) be the third derivative of -f**8/21 - 118*f**7/105 - 137*f**6/30 - 58*f**5/15 + 4*f**4 - 198*f**2 + 2. Let g(i) = 0. Calculate i.
-12, -2, -1, 0, 1/4
Factor 1/2*d**3 - 113/2*d + 0 + 56*d**2.
d*(d - 1)*(d + 113)/2
Let v = 55713841/2561556 + 1/1280778. What is w in v*w**3 + 0*w + 9/2*w**2 + 45/2*w**4 + 0 + 21/4*w**5 = 0?
-3, -1, -2/7, 0
Let z(t) be the second derivative of t**6/6 + 9*t**5/4 - 5*t**4/4 - 125*t**3/6 + 45*t**2 - 244*t. What is b in z(b) = 0?
-9, -2, 1
Find i such that 0*i**2 + 0*i - 2/7*i**4 + 0 + 10/7*i**3 = 0.
0, 5
Let x(o) be the third derivative of -5/12*o**4 + 0 - 9*o + 0*o**3 - 2/15*o**5 + 11*o**2 + 1/60*o**6. Solve x(q) = 0 for q.
-1, 0, 5
Let z(h) = 3*h**3 + h**2 - h - 1. Let y be z(1). Determine p so that 15*p + p**3 + 5*p**2 + 6*p**2 + 6*p**2 - p**y = 0.
-15, -1, 0
Let w be (-2)/(-585)*(-6 - -3 - 89). Let y = 10/117 - w. Let -y*t**3 - 2 - 14/5*t**2 - 22/5*t = 0. Calculate t.
-5, -1
Let a be 3/(6/(-4)) - (-342)/57. Determine t, given that 144*t**3 + 4*t**5 - 79*t**2 - 49*t**2 - 71*t**a + 23*t**4 = 0.
0, 2, 8
Let u(d) be the second derivative of 13*d**3 - 14 - 21/4*d**6 + 3*d + 6*d**2 - 111/40*d**5 + 41/4*d**4. Find j, given that u(j) = 0.
-2/3, -2/5, -2/7, 1
Suppose 113*x + 783 = -73*x + 5433. Let h(o) be the first derivative of -1/36*o**3 - 1/4*o**2 - 3/4*o - x. Factor h(a).
-(a + 3)**2/12
Let y(r) be the second derivative of r**4/42 + 6*r**3/7 + 32*r**2/7 - 603*r. Factor y(k).
2*(k + 2)*(k + 16)/7
Find q such that -2768*q**3 + 24408 + 256*q**5 - 135*q - 704*q**4 - 24368 - 596*q**2 + 307*q = 0.
-2, -1/4, 1/4, 5
Let o(i) be the third derivative of -i**7/1260 - i**6/30 + 13*i**5/60 + 73*i**4/24 - 2*i**2 - 13. Let f(c) be the second derivative of o(c). Factor f(g).
-2*(g - 1)*(g + 13)
Let a = 203241 + -203238. Factor 0*m**2 + 0 + 2/13*m**a - 8/13*m.
2*m*(m - 2)*(m + 2)/13
Find a, given that -17/7*a**2 - 12/7*a**3 - 1/7*a**4 + 0 + 30/7*a = 0.
-10, -3, 0, 1
Find w, given that -60 + 415/6*w**2 - 5/6*w**5 - 55/6*w**4 + 25/3*w - 15/2*w**3 = 0.
-9, -4, -1, 1, 2
Suppose 8*i - 10 - 35 = -13. Let n = 115 - 801/7. Factor 0*d**2 - n*d**i + 0*d + 0*d**3 + 0 - 2/7*d**5.
-2*d**4*(d + 2)/7
Factor -2/19*h**2 - 178/19*h + 940/19.
-2*(h - 5)*(h + 94)/19
Factor 11000 - 21726 + 10880 + b**2 - 29*b.
(b - 22)*(b - 7)
Suppose 2 = 6*v - 16. Determine m, given that 18*m**2 - v - 21*m**2 + m + 5*m - 12*m = 0.
-1
Suppose -z + 21 = 6, h - 2*h = 4*z - 62. Factor 1/2*n**4 + 44 - 27/2*n**3 + 59*n**h - 90*n.
(n - 22)*(n - 2)**2*(n - 1)/2
Let q(n) be the second derivative of -n**5/20 - 7*n**4/6 + 12*n**3 - 4*n - 143. Factor q(z).
-z*(z - 4)*(z + 18)
Let m(y) = -2*y**2 + y - 3. Let x(a) = 5*a**2 + 1709*a - 732727. Let o(r) = -3*m(r) - x(r). Factor o(f).
(f - 856)**2
Let i(s) be the third derivative of s**7/630 - 227*s**6/360 - 919*s**5/180 - 1153*s**4/72 - 77*s**3/3 + 3228*s**2. Solve i(r) = 0.
-2, -1, 231
Let l = -452779/4 - -114005. Let p = l - 810. Find g such that 0 - 1/4*g - p*g**2 + 1/2*g**3 = 0.
-1/2, 0, 1
Let a(z) = -7*z**4 - 330*z**3 - 317*z**2 + 3*z + 3. Let d(o) = -48*o**4 - 2308*o**3 - 2220*o**2 + 20*o + 20. Let j(w) = -20*a(w) + 3*d(w). Solve j(t) = 0.
-80, -1, 0
Suppose 16 = 26*s - 30*s + 2*u, -2*s - u = 16. Let b be (-2)/(-6) - (s + 5)/(-21). Suppose b*g**3 + 0 - 2/7*g + 2/7*g**2 - 2/7*g**4 = 0. Calculate g.
-1, 0, 1
Let z(c) be the third derivative of 5*c**8/2016 - 47*c**7/1260 - 107*c**6/720 + 43*c**5/72 - 11*c**4/24 - 14134*c**2. Let z(p) = 0. Calculate p.
-3, 0, 2/5, 1, 11
Let o be 39 + -51 + 770/64. Let q(m) be the third derivative of 0 + 0*m - o*m**4 - 17*m**2 + 1/16*m**3 + 1/160*m**5. Factor q(r).
3*(r - 1)**2/8
Factor 1/6*n**3 + 32 - 31/3*n**2 - 131/6*n.
(n - 64)*(n - 1)*(n + 3)/6
Let o(z) be the third derivative of -z**7/420 + 187*z**6/240 - 183*z**5/20 + 545*z**4/12 - 362*z**3/3 - 35*z**2 + 5*z. Factor o(n).
-(n - 181)*(n - 2)**3/2
Factor -14279*i**2 + 28302*i**2 + 152*i - 374*i**3 - 14255*i**2 + 1 + 10*i**4 - 1.
2*i*(i - 38)*(i + 1)*(5*i - 2)
Let l be -2*208/64 - -7. Let y(c) be the first derivative of 4/3*c**2 - 2/15*c**5 + 0*c + 0*c**3 - 5 - l*c**4. Factor y(z).
-2*z*(z - 1)*(z + 2)**2/3
What is y in 5*y**5 - 116*y**4 + 232*y**2 + 56*y + 0*y**5 + 220*y**4 + 5*y**5 + 270*y**3 = 0?
-7, -2, -1, -2/5, 0
Factor -12923 + 24792 - 12376 + g**2 + 26*g.
(g - 13)*(g + 39)
Suppose -4 = -3*s + 4*t, 1 = 7*s - 9*s - t. Let 0*k**2 + 2/3*k**5 + 0 + 32/3*k**3 + s*k + 16/3*k**4 = 0. What is k?
-4, 0
Factor 0*r - 1/4*r**3 + 0*r**2 + 0.
-r**3/4
Suppose -3*i = 3, 0 = -8*g + 6*g - 3*i + 1413. Let o = g + -705. Solve 8/5*u**2 - 4/5*u**4 - 4/5*u**o + 2/5*u + 2/5*u**5 - 4/5 = 0.
-1, 1, 2
Let s(m) be the second derivative of m**4/12 + 22*m**3/3 - 45*m**2 + 2*m - 131. Let d be s(-46). Solve -1/2*w - 1/4 - 1/4*w**d = 0 for w.
-1
Let j be (-6 + 3952/650)/((9/(-30))/(-1)). Factor -2/