85. Factor 4440*s**3 + j*s + 173*s**4 + 331*s**4 + 216*s**4 - 9 + 7205*s**2 + 54.
5*(s + 3)**2*(12*s + 1)**2
Suppose -3*t - 80 = -86. Determine r, given that 21*r**2 - 40 + 28*r**2 - 73*r**t - 45*r + 19*r**2 = 0.
-8, -1
Factor -298112*f + 8034*f**3 - 480940 + 2188*f**2 - 8038*f**3 + 180636.
-4*(f - 274)**2*(f + 1)
Let h(f) be the second derivative of -f**5/12 - 5*f**4/24 + 10*f**3 - 62*f**2 + 7*f - 9. Let s(p) be the first derivative of h(p). Factor s(w).
-5*(w - 3)*(w + 4)
Let f be (-32)/(-15) + 3 + -5. Suppose -41*i + 108 = 13*i. Find v such that 2/15*v**i - f + 0*v = 0.
-1, 1
Let q(b) be the first derivative of 5*b**4/4 + 200*b**3 + 17385*b**2/2 - 37210*b + 3419. Factor q(x).
5*(x - 2)*(x + 61)**2
Let b(w) be the second derivative of -1/35*w**5 + 0 + 1/3*w**4 + 47*w - 16/21*w**3 - 32/7*w**2. Factor b(z).
-4*(z - 4)**2*(z + 1)/7
Let a = 1956/133 + -3513/266. Determine d, given that -3/2 + 1/2*d - 1/2*d**3 + a*d**2 = 0.
-1, 1, 3
Let t(m) be the first derivative of -2*m**3/39 + 30*m**2/13 + 198*m/13 + 2953. Suppose t(v) = 0. Calculate v.
-3, 33
Suppose d + 16 = 18. Suppose -6 = -2*t + 2*o, 10 - 1 = d*t + o. Find c, given that -23*c**4 + 13*c**t + 4*c + 9*c**4 - 3*c**3 = 0.
-2, 0, 1
Let k(v) be the second derivative of -v**8/2520 - v**7/420 - v**6/180 - v**5/180 - v**3/3 - v + 3. Let c(a) be the second derivative of k(a). Factor c(m).
-2*m*(m + 1)**3/3
Let q = 739960 - 739960. Determine n so that -4/5*n**3 + 0 + q*n**2 + 0*n = 0.
0
Suppose 4*y + 5*k = 25, 25 = 3*y + k - 2. Factor y*n**2 - 11 - 2*n**3 - 17*n + 1 - 13*n + 32*n.
-2*(n - 5)*(n - 1)*(n + 1)
Let a(j) be the first derivative of -57 - 1/2*j**6 + 3/5*j**5 + 0*j**2 + 0*j + 3*j**4 - 4*j**3. Suppose a(l) = 0. What is l?
-2, 0, 1, 2
Let n = 727/252 + -37/84. Let w(r) be the first derivative of n*r**3 - 2/3*r**4 + 1/15*r**5 + 3*r - 4*r**2 - 1. Factor w(k).
(k - 3)**2*(k - 1)**2/3
Let r(p) be the second derivative of p**6/30 - 59*p**5/20 + 41*p**4/3 + 112*p**3/3 + 10699*p. Let r(z) = 0. What is z?
-1, 0, 4, 56
Let c be -948 - -960 - (9 + 0). Let c*j + 3/2 + 3/2*j**2 = 0. Calculate j.
-1
Let r(p) = 6*p**4 - 22*p**3 + 22*p**2 + 5*p. Let d(a) = -5*a**4 + 20*a**3 - 23*a**2 - 4*a. Let x(l) = -5*d(l) - 4*r(l). Find y, given that x(y) = 0.
0, 3, 9
Let s(g) = 32*g**2 + 17331*g + 7499560. Let z(b) = 17*b**2 + 8666*b + 3749780. Let p(a) = 6*s(a) - 11*z(a). Factor p(c).
5*(c + 866)**2
Let b be 26/6 - (-5)/15*2. Suppose -b*p = -0*p - 160. Factor -p + 23*i - 33*i**2 - 7*i + 31*i**2.
-2*(i - 4)**2
Let j(m) = -15*m**2 + 5. Let r = 209 + -204. Let a(f) = 7*f**2 - 3. Let z(u) = r*a(u) + 2*j(u). What is v in z(v) = 0?
-1, 1
Let k(t) = -44*t - 229. Let q(h) = 144*h + 688. Let y(j) = -16*k(j) - 5*q(j). Let b be y(14). Factor -4/7*v**2 - 6/7*v**3 + b*v - 2/7*v**4 + 0.
-2*v**2*(v + 1)*(v + 2)/7
Factor -3*o**3 + 837*o - 56*o**2 - 1033*o - o**3.
-4*o*(o + 7)**2
Let y be -5*(4 + (-3 - 2)) + 627/(-133). Determine u so that y*u**2 + 4/7*u + 0 = 0.
-2, 0
Let v(s) be the third derivative of -s**5/48 + 3325*s**4/48 - 2211125*s**3/24 + 4*s**2 - 2*s + 288. Factor v(b).
-5*(b - 665)**2/4
Let g be -3*8/(-288)*39 + 11/(-44). Suppose -9/5*k**g - 24/5*k**2 - 16/5*k + 0 - 1/5*k**4 = 0. Calculate k.
-4, -1, 0
Suppose -6*c + c + 15 = 0. Factor 102*s**c + 5*s**4 - 3*s**5 - 2*s**5 - 92*s**3.
-5*s**3*(s - 2)*(s + 1)
Let l(h) be the second derivative of h**6/120 - h**5/12 + h**4/3 - 2*h**3/3 + 51*h**2 - 152*h. Let r(x) be the first derivative of l(x). Factor r(m).
(m - 2)**2*(m - 1)
Let w be (-9)/6*(136/24 + -7). Let c = -1 + 3. Factor -1 + 1 + 6*q + 1 + 3*q**w + c.
3*(q + 1)**2
Let j(u) be the second derivative of -79*u**5/120 - 53*u**4/24 - u**3/18 + 2611*u. Solve j(k) = 0.
-2, -1/79, 0
Let r(t) be the first derivative of 77 + 0*t**2 + 8/21*t**3 - 4/35*t**5 + 1/7*t**4 + 0*t. Factor r(p).
-4*p**2*(p - 2)*(p + 1)/7
Let 26/11*z + 82/11*z**2 - 26/11*z**3 + 2/11*z**4 - 84/11 = 0. What is z?
-1, 1, 6, 7
Let h(b) = -10*b - 2620*b**2 + 131*b**3 + 2410*b**2 + 164*b**3. Let f(w) = w**3 + w**2 + w. Let x(c) = 30*f(c) + h(c). Factor x(t).
5*t*(5*t - 2)*(13*t - 2)
Let l(f) be the third derivative of 0*f**4 + 87*f**2 + 0*f**3 + 1/120*f**5 + 1/240*f**6 + 0 + 0*f. Factor l(g).
g**2*(g + 1)/2
Let z(y) be the third derivative of y**6/75 + 14639*y**5/150 + 223199*y**4 - 223260*y**3 + 3*y**2 - 3*y - 1. Factor z(p).
2*(p + 1830)**2*(4*p - 1)/5
Let h(s) be the first derivative of -12*s**5/5 - 87*s**4/8 - 6*s**3 + 27*s**2/4 + 998. Determine c, given that h(c) = 0.
-3, -1, 0, 3/8
Let t(k) be the first derivative of -18*k + 5/24*k**3 + 1/12*k**4 - 18 + 1/4*k**2 + 1/80*k**5. Let q(m) be the first derivative of t(m). Factor q(j).
(j + 1)**2*(j + 2)/4
Let l = -1262965 - -1262969. Factor 2/5*o**3 + 0*o**2 + 0*o - 3/5*o**l + 0 - 2/5*o**5.
-o**3*(o + 2)*(2*o - 1)/5
Let q(d) = -6*d**3 - 129*d**2 - 284*d - 40. Let a(u) = -17*u**3 - 388*u**2 - 848*u - 112. Let z(k) = 5*a(k) - 14*q(k). Solve z(i) = 0.
-132, -2, 0
Let a be ((-70)/56)/((-15)/8). Let q = -57 + 59. Factor -2*z**2 + a*z**3 + q*z - 2/3.
2*(z - 1)**3/3
Let j(f) be the second derivative of -1/27*f**4 - 10*f + 2/45*f**5 + 4/135*f**6 - 2/9*f**2 + 0 - 5/27*f**3 + 1/189*f**7. Factor j(i).
2*(i - 1)*(i + 1)**3*(i + 2)/9
Let p = 5420043/836 + 93/209. Determine h, given that -p*h**2 + 737/4*h**3 - 42875/2 + 307475/4*h - 7/4*h**4 = 0.
2/7, 35
Let u(w) be the first derivative of w**6/3 - 14*w**5/5 - w**4/2 + 14*w**3/3 - 828. Factor u(y).
2*y**2*(y - 7)*(y - 1)*(y + 1)
Let h(y) = -y**2 - y. Let i be 10 - ((3 - 1) + -2). Let t(r) = 4 - 174*r + 186*r - 2 + i*r**2. Let g(x) = -12*h(x) - t(x). What is o in g(o) = 0?
-1, 1
Let b(u) be the second derivative of 0*u**2 - 1/12*u**4 - 87*u + 5/6*u**3 + 0. Find r, given that b(r) = 0.
0, 5
Let n(o) be the first derivative of -20 - 20*o**4 + 40*o**2 + 10/3*o**3 + 15*o - 6*o**5. Let g(u) = u**4 - u**2 - 1. Let z(x) = -5*g(x) + n(x). Solve z(t) = 0.
-2, -1, -2/7, 1
Let u(w) = -5*w**4 + 2*w**3 - 3*w**2 + 22*w - 4. Let s(x) = 11*x**4 - 4*x**3 + 6*x**2 - 49*x + 8. Let h(g) = 6*s(g) + 13*u(g). Factor h(i).
(i - 2)*(i + 1)**2*(i + 2)
Let p = -892 - -897. Let a(f) be the second derivative of -1/8*f**2 + 0*f**4 + 1/12*f**3 + 6*f + 0 - 1/40*f**p + 1/120*f**6. Suppose a(h) = 0. Calculate h.
-1, 1
Let x(d) = d**2 - 221*d + 8050. Let l be x(46). Let j be (-2)/(-5) + 21/(-90). Solve 0*k + l - j*k**2 + 1/6*k**3 = 0 for k.
0, 1
Let m(y) be the third derivative of y**5/120 - 21*y**4/8 - 129*y**3/4 + 2*y**2 - 2*y + 235. Factor m(c).
(c - 129)*(c + 3)/2
Suppose 103*f = 99*f - 16, 0 = -b + 5*f + 24. Let u(p) be the second derivative of 0 - 46*p - 1/20*p**b + 33/10*p**2 + p**3. Let u(l) = 0. Calculate l.
-1, 11
Factor -4/5*p**2 + 192/5*p - 368/5.
-4*(p - 46)*(p - 2)/5
Let q(x) be the third derivative of x**5/30 + 77*x**4/2 + 461*x**3/3 - 2*x**2 + 4*x - 26. Let q(t) = 0. What is t?
-461, -1
Let z(k) = k**3 - 5*k**2 + 3*k - 12. Let g be z(5). Let f(i) = 10*i**2 - 20*i + 9. Let t(q) = 9*q**2 - 19*q + 8. Let o(l) = g*t(l) - 2*f(l). Factor o(r).
(r - 2)*(7*r - 3)
Let b(d) be the first derivative of 1/15*d**3 + 0*d + 22 + 0*d**2 + 3/10*d**6 + 7/20*d**4 + 3/5*d**5. Solve b(g) = 0 for g.
-1, -1/3, 0
Let r(y) be the second derivative of -y**4/48 - 7*y**3/8 + 11*y**2/4 + 165*y. Factor r(p).
-(p - 1)*(p + 22)/4
Let q = -51 - -54. Let j(o) = -5*o**2 - 6*o - 6. Let p(h) = h**2 + 2. Let l(f) = q*p(f) + j(f). Factor l(k).
-2*k*(k + 3)
Suppose -3*r + 7*x = -4167 + 4130, -5*r = 2*x - 7. Suppose -10 - 5/3*a**4 - 5/3*a**r + 5/3*a + 35/3*a**2 = 0. Calculate a.
-3, -1, 1, 2
Determine n, given that -7/6*n + 5/6 - 2*n**2 = 0.
-1, 5/12
Let o(j) = 2*j**2 - 20*j - 12. Let u be o(11). Suppose -66 = 4*w - 5*n - 56, -5*n = -u. Factor -4/3*f**3 + 0*f + w + 8/3*f**2.
-4*f**2*(f - 2)/3
Let d be ((-30)/310)/((-18)/102). Let i = d - -8/155. Determine c so that i*c**5 + 0 - 9/5*c**3 - 3/5*c**4 + 3/5*c**2 + 6/5*c = 0.
-1, 0, 1, 2
Let l(u) = -96*u**2 + 609*u - 303. Let f(t) = 10*t**2 + 2*t - 1. Let a(h) = -9*f(h) - l(h). Factor a(m).
3*(m - 104)*(2*m - 1)
Let r(j) be the first derivative of -10*j**6/3 - 48*j**5/5 + 11*j**4 + 104*j**3/3 - 24*j**2 - 32*j + 896. Solve r(c) = 0.
-2, -2/5, 1
Let u(h) be the third derivative of h**5/540 + h**4/18 - 85*h**3/54 - 500*h**2. Factor u(s).
(s - 5)*(s + 17)/9
Let a = 97 + 70. Factor -578 - 138*f