8. Determine p, given that -1/6*p + 2/3*p**g + 0 + 2/3*p**2 - 1/2*p**3 - 2/3*p**4 = 0.
-1, 0, 1/2, 1
Factor 4752/5*r + 3/5*r**4 - 39/5*r**3 - 72*r**2 + 0.
3*r*(r - 12)**2*(r + 11)/5
Let i = 53449/51 + -1048. Let x(p) be the first derivative of 0*p**4 + 0*p + 37 + i*p**6 - 1/17*p**2 + 4/51*p**3 - 4/85*p**5. Let x(w) = 0. What is w?
-1, 0, 1
Find q, given that -4431*q**2 + 9655*q**2 - 960*q + 958*q**3 + 2*q**5 - 484*q**4 - 4740*q**2 = 0.
-1, 0, 1, 2, 240
Let j(k) be the second derivative of -2*k**4 - 3/5*k**5 + 0*k**3 + 1/14*k**7 + 0 + 10*k + 1/5*k**6 + 0*k**2. Factor j(g).
3*g**2*(g - 2)*(g + 2)**2
Factor 536/7*f + 1/7*f**2 + 0.
f*(f + 536)/7
Let m(n) be the first derivative of -1/18*n**4 + 1/45*n**5 - 4/9*n - 1/9*n**3 + 22 + 4/9*n**2. Factor m(l).
(l - 2)*(l - 1)**2*(l + 2)/9
Let a(x) be the first derivative of -x**7/420 + x**6/90 - x**5/60 - 26*x**3 + 51. Let n(t) be the third derivative of a(t). Suppose n(q) = 0. What is q?
0, 1
Solve 95935*z**3 + 33*z**4 - 33*z**2 + 30*z - 191917*z**3 + 95955*z**3 - 3*z**5 = 0 for z.
-1, 0, 1, 10
Factor 3017*h + 21*h**3 + 699*h - 2366 + 6945*h**2 - 175 + 561 + 1228*h.
3*(h + 1)*(h + 330)*(7*h - 2)
Factor 119/2 - 445/4*r + 29/4*r**3 + 1/4*r**4 + 177/4*r**2.
(r - 1)**2*(r + 14)*(r + 17)/4
Let z(b) = 9*b**2 + 37*b + 69. Let q be (-1)/(3*5/(-30)). Let p(l) = -2*l**2 + 35 + 9*l + 13*l + 7*l**q - 3*l. Let a(i) = -5*p(i) + 3*z(i). Factor a(v).
2*(v + 4)**2
Let i be (-9180)/13600 - (18/15 - 2). Factor 13/8*x - i*x**2 + 0.
-x*(x - 13)/8
Let m be 2/4*(-7 - -5)*-3. Suppose 0 = m*r - 2 - 10. Suppose -175*t**3 + 1203*t - 120*t**r + 120 - 823*t + 65*t**5 - 20*t**5 + 250*t**2 = 0. Calculate t.
-1, -2/3, 2, 3
Let p(c) be the second derivative of 1/9*c**4 - 56/9*c**3 + 392/3*c**2 - 6*c + 5. Suppose p(y) = 0. Calculate y.
14
Let p = 963/224 + -835/224. What is s in 48/7 + 20/7*s**3 + 12/7*s**4 - 60/7*s**2 - p*s**5 - 16/7*s = 0?
-2, -1, 1, 2, 3
Let z = 18320 + -18304. Let t(f) be the first derivative of -13 - z*f**3 - 4*f**4 - 32*f - 32*f**2 - 2/5*f**5. Factor t(d).
-2*(d + 2)**4
Factor 27047*y**3 - 2*y**4 - 206*y - 13274*y**3 + 2*y**2 - 13567*y**3.
-2*y*(y - 103)*(y - 1)*(y + 1)
Let t(v) be the first derivative of -3*v**5/5 - 11*v**4 - 61*v**3/3 + 28*v**2 + 52*v + 1128. Find m, given that t(m) = 0.
-13, -2, -2/3, 1
Let f = -2602 - -7820/3. Suppose -2*r - 3*i = -0*r + 6, 20 = 4*r - 2*i. Factor -38/3*a**r - 50/3*a**2 - 32/3*a - 8/3 - f*a**4 - 2/3*a**5.
-2*(a + 1)**3*(a + 2)**2/3
Factor 0 + 148/3*z**2 - 20*z + 5/3*z**3.
z*(z + 30)*(5*z - 2)/3
Suppose 5*u - 3*x = -38, -156*u + 111*u = -3*x - 42. Factor 15/4 - 15/4*o**u - 3/4*o**3 + 3/4*o.
-3*(o - 1)*(o + 1)*(o + 5)/4
What is t in 640 + 72*t + 4/5*t**2 = 0?
-80, -10
Let o(j) be the second derivative of 0*j**2 + 30 - 41/32*j**4 - 1/80*j**6 - 33/80*j**5 + j - 5/4*j**3. Factor o(z).
-3*z*(z + 1)**2*(z + 20)/8
Let b(p) be the third derivative of -p**6/40 + 13*p**5/20 - 3*p**4/2 + 152*p**2 - 1. Determine r so that b(r) = 0.
0, 1, 12
Let b(p) be the third derivative of -p**5/180 - 3*p**4/8 - 25*p**3/9 + 8120*p**2. Suppose b(h) = 0. Calculate h.
-25, -2
Suppose 0 = 4*p - 28 + 8. Suppose -4*j + 4 = 3*t - 11, p*j = -t + 16. Factor -6*o**2 - 6*o - 20*o - o + 27*o**j + 6.
3*(o - 1)*(o + 1)*(9*o - 2)
Let 2*r**3 - 88*r + 2*r**3 - 60*r**2 - 80*r + 135*r**2 + r**2 = 0. What is r?
-21, 0, 2
Suppose 5*g + 4*k + 683 = 7721, -2*g = -3*k - 2829. Suppose -g = -o - 5*o. What is l in 235*l - o*l + 4*l**2 - 1 - 3*l**2 = 0?
-1, 1
Let g be 6/10*671/366. Let z = 14485/2 - 7242. Factor -1/5*v**2 + g*v - z.
-(v - 5)*(2*v - 1)/10
Let p be (0 + 2)*(-19)/76*-92. Suppose -p*q + 10 = -41*q. Suppose -1/4*v - 1/8*v**4 + 1/8*v**q + 0 + 1/4*v**3 = 0. Calculate v.
-1, 0, 1, 2
Let r(x) be the first derivative of -x**6/33 - 46*x**5/55 - 41*x**4/11 - 236*x**3/33 - 7*x**2 - 38*x/11 + 352. Factor r(h).
-2*(h + 1)**4*(h + 19)/11
Let q = -2/22445 - -22461/179560. Factor 1/8 + q*s**2 - 1/4*s.
(s - 1)**2/8
Find p such that -416344 + 2*p**2 + 297*p - 3503*p - 122*p + 1800792 = 0.
832
Let v be 1/(-3 + ((-8)/(-48))/((-3)/(-63))). Let b(d) be the first derivative of 16*d - 9 + 1/3*d**3 + 4*d**v. Factor b(h).
(h + 4)**2
Let x(g) = 159*g**2 - 845*g + 254. Let h be x(5). Factor 7/3*s + h + 1/6*s**2.
(s + 2)*(s + 12)/6
Factor h + 1/11*h**2 - 102/11.
(h - 6)*(h + 17)/11
Suppose 0 = 5*s + 441 + 289. Let h = 599/4 + s. Find g such that -h*g - 9/4*g**2 + 3/2 = 0.
-2, 1/3
Let c(t) be the first derivative of t**5/15 + 286*t**4 + 490776*t**3 + 421085808*t**2 + 180645811632*t - 1359. Factor c(p).
(p + 858)**4/3
Factor -1476225 + 3/5*u**5 - 43578*u**2 - 297/5*u**4 + 404595*u + 11502/5*u**3.
3*(u - 27)**2*(u - 15)**3/5
Let -72*s**3 - 68*s**3 - 27376*s - 27848 - 80*s**2 + 204*s**3 - 66*s**3 + 550*s**2 = 0. What is s?
-1, 118
Let v = -180 + 225. Factor 2*b**2 - 13*b**2 + 52 + 5*b + 9*b**2 + v*b.
-2*(b - 26)*(b + 1)
Let f(j) be the second derivative of 5*j**4/24 + 80*j**3/3 - 325*j**2/4 - 38*j - 6. Factor f(q).
5*(q - 1)*(q + 65)/2
Let z(s) be the third derivative of s**8/84 + 28*s**7/15 + 461*s**6/5 + 6036*s**5/5 + 14715*s**4/2 + 24300*s**3 - 1055*s**2 - 2. Suppose z(v) = 0. What is v?
-45, -3, -2
Let j(a) be the second derivative of -107/32*a**4 + 1 + 3*a - 34/3*a**3 - 1/240*a**6 - 17/80*a**5 - 16*a**2. What is m in j(m) = 0?
-16, -1
Let j be (-4)/(-2) + 5 - -163. Let i = 1532/9 - j. Find s such that 8/9*s - 4/3*s**2 + 8/9*s**3 - i*s**4 - 2/9 = 0.
1
Suppose -21 + 7 = h. Let l = 18 + h. Factor 5*n**5 - 4*n**2 + 0*n**2 + 3*n**l - 6*n**5.
-n**2*(n - 2)**2*(n + 1)
Let g(q) = -210513*q**3 + 1005675*q**2 + 235746*q + 13500. Let t(h) = 50523*h**3 - 241362*h**2 - 56579*h - 3240. Let r(i) = -13*g(i) - 54*t(i). Factor r(v).
3*(v - 5)*(53*v + 6)**2
Let y(g) be the third derivative of 99/320*g**6 - g**2 - 3/80*g**7 - 11*g + 0*g**3 + 0*g**4 + 121/160*g**5 + 0 + 1/896*g**8. Factor y(l).
3*l**2*(l - 11)**2*(l + 1)/8
Let c = 183 + -176. Let q be (c - (-178)/(-24))*(-6)/20. Let -1/4*s**2 + 0 + 0*s - q*s**3 = 0. What is s?
-2, 0
Let -140 - 2/3*v**3 - 514/3*v - 32*v**2 = 0. Calculate v.
-42, -5, -1
Let m(h) = h**3 - 27*h**2 + 24*h + 108. Let l be m(26). Suppose -l + 68 = 6*o. What is c in 28/5*c**4 + 64/5*c**3 - 24/5*c - 68/5*c**o + 0 = 0?
-3, -2/7, 0, 1
Let i(d) be the second derivative of -d**4/6 + 17*d**3/3 - 60*d**2 - 122*d + 3. Determine h, given that i(h) = 0.
5, 12
Let g = -20 + 24. Factor -g*i + 560*i**3 - 3*i + 6 - 559*i**3.
(i - 2)*(i - 1)*(i + 3)
Let x(d) be the second derivative of 8*d + 5/12*d**4 + 1/6*d**3 - 3 + 0*d**2 + 7/20*d**5 + 1/10*d**6. What is k in x(k) = 0?
-1, -1/3, 0
Let j(c) = -64332*c - 64306. Let a be j(-1). What is s in -131/4*s - 3/2*s**3 + a*s**2 + 1/4*s**5 + 12 - 4*s**4 = 0?
-3, 1, 16
Let l(w) be the first derivative of 5*w**7/336 + w**6/48 - 3*w**5/80 + w**4/48 + w**3/3 - 18. Let y(c) be the third derivative of l(c). Factor y(j).
(j + 1)*(5*j - 1)**2/2
Let g(b) = b**2 - 4*b + 10. Let m be g(10). Factor -18*w**3 - 200 + 3*w**3 + m*w**2 - 86*w + 146*w - 5*w**4.
-5*(w - 2)**2*(w + 2)*(w + 5)
Let x = 205 + -211. Let j be 4 + x - 16/(-4). Suppose -8/3*w**j - 2/3*w**3 - 10/3*w - 4/3 = 0. What is w?
-2, -1
Factor -11/2*f**2 - f + 0 + 13/2*f**3.
f*(f - 1)*(13*f + 2)/2
Factor 623*c**2 + 635*c**2 + 82*c + 709*c**2 - 2103*c**2 + 14*c**3 + 4*c + 36.
2*(c - 9)*(c - 1)*(7*c + 2)
Let o(m) be the second derivative of m**7/28 + m**6/4 + 3*m**5/5 + m**4/2 + 192*m - 4. Factor o(j).
3*j**2*(j + 1)*(j + 2)**2/2
Let g(u) be the first derivative of -3/14*u**4 + 4/7*u**2 + 0*u + 7 - 4*u**5 + 40/21*u**3 + 7/3*u**6. Determine j so that g(j) = 0.
-2/7, 0, 1
Let v(q) be the first derivative of 41*q**6/120 + q**5/20 - 58*q**3/3 - 119. Let d(w) be the third derivative of v(w). Factor d(f).
3*f*(41*f + 2)
Let w = -9140/141 - -3078/47. Determine i so that -14/3*i**3 - 16/3*i + 28/3*i**2 + w*i**4 + 0 = 0.
0, 1, 2, 4
Let n(s) be the third derivative of -s**8/504 - s**7/35 - 5*s**6/36 - 3*s**5/10 - 5*s**4/18 - 1922*s**2 + 1. Find u such that n(u) = 0.
-5, -2, -1, 0
Let j(g) be the second derivative of -17/21*g**3 + 0*g**2 - 1/105*g**6 + 0 - 19/70*g**5 - 153*g - 5/6*g**4. Factor j(y).
-2*y*(y + 1)**2*(y + 17)/7
Let b be (4/10)/(372/15 - -4). Let r(p) be the third derivative of 0*p**3 + 0*p - b*p**4 + 1/360*p**5 - 14*p**2 + 1/720*p**6 + 0. Factor r(u).
u*(u - 1)*