4*a. Factor -m**3 + 7*m**d + 7*m**3 + 72 + 7*m**2 + 0*m**3 - 120*m.
2*(m - 3)*(m + 6)*(3*m - 2)
Let a(p) be the first derivative of 3*p**5 - 815*p**4/4 + 615*p**3 - 1305*p**2/2 + 260*p - 391. Solve a(j) = 0.
1/3, 1, 52
Let r(i) be the third derivative of -i**6/40 + 71*i**5/10 - 1345*i**4/8 + 1650*i**3 - 147*i**2 + 7. Suppose r(g) = 0. Calculate g.
5, 132
Let s(p) be the third derivative of p**5/450 + 356*p**4/45 + 506944*p**3/45 + 4133*p**2. What is y in s(y) = 0?
-712
Factor -44 - 51*b**2 + 29/2*b**3 + 78*b - 3/2*b**4.
-(b - 2)**3*(3*b - 11)/2
Let v = 78 - 18. Suppose 4*u = v - 4. What is q in 35*q - 26*q**2 + 10*q**3 + 13*q**4 - u*q**2 - 5*q**5 - 10 + 2*q**4 - 5*q**4 = 0?
-2, 1
Let o(c) = -11*c**3 + 192*c**2 + 407*c - 6. Let f(i) = 74*i**3 - 1346*i**2 - 2848*i + 40. Let x(t) = -3*f(t) - 20*o(t). Solve x(p) = 0.
-2, 0, 101
Let n(v) = -61*v - 56. Let m be n(-19). Let f = m - 1101. Factor -1/6*r**f + 0 - 1/6*r.
-r*(r + 1)/6
Let g be 29/6 + -1 - 5/(-30). Suppose -g*k - 32 = -12*k. Find h, given that -5*h**2 - 20*h + 21*h + k*h**2 = 0.
0, 1
Let s(z) be the third derivative of -z**5/90 + 311*z**4/36 + 104*z**3/3 + 488*z**2. Let s(o) = 0. Calculate o.
-1, 312
Let m = 1402249/5 - 280449. Factor 32/5 + 84/5*p**2 - 4*p**3 - 92/5*p - m*p**4.
-4*(p - 1)**3*(p + 8)/5
Let y(u) = -u**2 + 346*u - 29925. Let p be y(174). Factor -1/4*c**4 + 1/4*c**5 - 7/4*c**p + 0 - 3/2*c + 13/4*c**2.
c*(c - 2)*(c - 1)**2*(c + 3)/4
Let a(m) = -2*m + 9. Let r be (-155)/(-55) - ((-4)/22 - 0). Let c be a(r). Let -20*o**4 + 35*o**c + 30*o**2 + 8 + 17*o - 18 - 52*o = 0. Calculate o.
-1, -1/4, 1, 2
Let r = -467 - -477. Let s be (r + -9)/(-2)*24/(-14). Let -3/7*z + 3/7*z**3 + 6/7*z**2 - s = 0. What is z?
-2, -1, 1
Let 7/3*d - 7/3*d**3 - 1/3*d**4 - 5/3*d**2 + 2 = 0. Calculate d.
-6, -1, 1
Let q(z) be the second derivative of -z**4/12 - 25*z**3/6 + 27*z**2 + 760*z + 2. Determine t, given that q(t) = 0.
-27, 2
Let r(c) = 20*c - 2*c**2 + c**2 - 53 + 18. Let j be r(9). Let 44*i**2 - 4*i**3 - 69*i**2 - 20*i**5 - 5*i**4 - 10*i + j*i**3 = 0. What is i?
-2, -1/4, 0, 1
Suppose 12*r + 151 = -49*r + 2*r + 446. Factor 0*v + 0 + 10/11*v**4 + 8/11*v**2 - 16/11*v**3 - 2/11*v**r.
-2*v**2*(v - 2)**2*(v - 1)/11
Let r(g) be the first derivative of -13/15*g**2 + 2/75*g**5 + 2/3*g**3 - 7/30*g**4 - 132 + 8/15*g. Factor r(b).
2*(b - 4)*(b - 1)**3/15
Let q(w) = 5*w**2 - 3*w**2 - 22*w - 7*w**2 - 10*w**2. Let y(m) = -7*m**2 - 11*m. Let u(d) = 6*q(d) - 13*y(d). Factor u(n).
n*(n + 11)
Let m = 1100/19 + -10793/171. Let f = 50/9 + m. Factor 2/3*l**3 + 2/3*l**4 - f*l**5 - 8/3*l**2 + 7/3*l - 2/3.
-(l - 1)**4*(l + 2)/3
Let y = 104 - 101. Suppose -o - 8 = y*a - 19, -2*a - 4*o = -24. Solve 0 + 2/11*w - 14/11*w**a = 0.
0, 1/7
Let a(s) = -8*s**2 + 56*s - 150. Let z be (-6 - (-5 - -10)) + 6. Let t(u) = 3*u**2 - 19*u + 51. Let k(i) = z*a(i) - 14*t(i). Factor k(n).
-2*(n - 2)*(n + 9)
Factor 1/8*f**2 + 0*f - 729/8.
(f - 27)*(f + 27)/8
Find f such that 168*f + 90*f - 236 - 26*f + 4*f**2 = 0.
-59, 1
Let r(t) = -t**2 - 9*t + 40. Let n be r(-12). Factor 0*c**4 + c**4 + 0*c**4 - n*c**3 - 3*c**4.
-2*c**3*(c + 2)
Suppose 667*u - 663*u = 1004. Find d, given that 156*d**2 - 500 - 61*d**2 - 5*d**3 - 149*d - u*d = 0.
-1, 10
Let -1/2*s**2 + 135/2 + 67*s = 0. Calculate s.
-1, 135
Let z(w) = -175*w**3 + 175*w**2 + 300*w. Let m(h) = 69*h**3 - 87*h**2 - 150*h. Let q(u) = -5*m(u) - 2*z(u). Factor q(r).
5*r*(r + 2)*(r + 15)
Suppose 185 + 51 = 59*v. What is i in -40 - 24*i + v*i - 140 + 4*i**2 - 11*i - 17*i = 0?
-3, 15
Let z(n) be the first derivative of n**5/5 + 4*n**4 + 21*n**3 + 46*n**2 + 44*n - 593. Find a such that z(a) = 0.
-11, -2, -1
Let q(l) = -l**2 - 4*l + 115. Let g be q(-12). Find v such that -16*v**3 - 48*v + 9*v**3 - 45*v**2 + 12*v**4 - 12 + g*v**3 = 0.
-2, -1/2, 2
Solve 0*u - 4356/5*u**3 + 2371842/5*u**2 + 0 + 2/5*u**4 = 0.
0, 1089
Let n(c) be the second derivative of 1/30*c**5 - 1/9*c**4 + 0 - 71*c - 8*c**2 - 20/9*c**3. What is j in n(j) = 0?
-2, 6
Let k = -59 + 74. Let h = -10 + k. Factor -4*l**2 - h + 13*l**2 - 7*l + l - 10*l**2.
-(l + 1)*(l + 5)
Let u = -126781236213/2086 + 60777200. Let x = u - 1/298. Factor -26/7*b**2 + 0 + x*b**3 - 12/7*b.
2*b*(b - 3)*(5*b + 2)/7
Let p(g) be the second derivative of -g**4/36 - 385*g**3/9 - 148225*g**2/6 - 1022*g - 1. What is w in p(w) = 0?
-385
Solve 387/5*h - 1188/5 + 3/5*h**2 = 0.
-132, 3
Let l(p) = -14*p - 34. Let v = -77 + 73. Let i be l(v). Determine d, given that -18*d**2 + 52*d**2 - 14*d**2 - i*d**2 = 0.
0
Suppose 4*b - 42 = 5*v, v - 187 = 2*b - 211. Factor 0 - 8/5*k**v - 4/5*k - k**3 - 1/5*k**4.
-k*(k + 1)*(k + 2)**2/5
Suppose -6*a**3 - 2*a**3 + 22*a**2 - 18*a**2 + 6*a**3 = 0. What is a?
0, 2
Suppose 4*t - 5*j - 15 = 6*t, -15 = -t + 2*j. Let v(f) be the first derivative of -1/7*f**3 + 0*f - 7 + 1/35*f**t + 0*f**4 + 1/7*f**2. Factor v(n).
n*(n - 1)**2*(n + 2)/7
Let v(g) be the third derivative of 841*g**5/20 - 319*g**4/4 + 121*g**3/2 - 4*g**2 + 29. Factor v(y).
3*(29*y - 11)**2
Let s(m) be the third derivative of -19*m**8/224 + 33*m**7/35 - 29*m**6/16 - 39*m**5/5 - m**4 + 1387*m**2. Find q, given that s(q) = 0.
-1, -1/19, 0, 4
Let k(m) be the second derivative of -9*m**4/4 + 242*m**3/9 + 2*m**2 - 87*m + 1. Find b such that k(b) = 0.
-2/81, 6
Let v be (36/42)/(17/14 + -1). Factor 6*w**4 + 0 + 2*w**5 + 100*w**2 + 0 + 10*w**3 - 104*w**2 - 14*w**v.
2*w**2*(w - 2)*(w - 1)**2
Let f = 7751/30 + -3868/15. Factor -f*m**2 + 5/2*m + 3.
-(m - 6)*(m + 1)/2
Let z(d) be the second derivative of d**6/15 + 13*d**5/10 - 13*d**4/6 - 157*d**3/3 + 156*d**2 + 8*d - 125. Suppose z(r) = 0. Calculate r.
-13, -4, 1, 3
What is z in 3830*z - 31*z**2 + 30*z**2 + 449691 - 4116916 = 0?
1915
Let f(h) be the second derivative of 3*h**5/20 - 69*h**4/2 - h**3/2 + 207*h**2 - 2*h + 244. Let f(t) = 0. Calculate t.
-1, 1, 138
Let z(o) be the third derivative of -21/80*o**6 - 194481/16*o**3 - 1323/80*o**5 - 3 - 9261/16*o**4 - 2*o**2 + 0*o - 1/560*o**7. Factor z(k).
-3*(k + 21)**4/8
Suppose 42*l - 43*l = -51. Determine t so that 61*t**2 - 5*t**4 + 107*t - 7*t + l + 29*t**2 + 20*t**3 - 16 = 0.
-1, 7
Let s be ((-142)/852)/(552/80 + -7). Solve -10*n**4 + 55/3*n - s*n**5 - 50/3*n**3 + 0*n**2 + 10 = 0.
-3, -2, -1, 1
Let u = -33 - -17. Let i be (u - -21) + -3 + 0/(-2). Factor -3 - 6 + 12 - 4*a**i + 9*a - 5.
-(a - 2)*(4*a - 1)
Let w be (-68538)/39780 - (13/2)/(-13). Let t = 2/255 - w. Factor -t*l**2 + 2/13*l**5 + 0*l + 0 - 12/13*l**4 + 24/13*l**3.
2*l**2*(l - 2)**3/13
Let x be ((-70837)/14014 + 5)*(-72)/2. Let z = -52/49 + x. Factor 8/11*n - z + 2/11*n**2.
2*(n - 1)*(n + 5)/11
Let r(t) = 2*t**2 + 120*t + 235. Let c be r(-2). Let -18/11*l**c + 0*l - 16/11*l**2 - 2/11*l**4 + 0 = 0. What is l?
-8, -1, 0
Let d be -3 - -7 - (-6)/(-3). Let l be 3/(18/24) - (-2)/d. Determine b so that -10*b + 20 + l*b**2 - 4*b - 10*b - b = 0.
1, 4
Suppose 7*p = 25*p + 38*p. Let j(a) be the first derivative of -10 + 0*a**4 + 5/18*a**6 + 0*a + p*a**2 + 0*a**3 - 1/3*a**5. Factor j(x).
5*x**4*(x - 1)/3
Let y be 34044/(-621)*3*301/(-56) + 85/(-510). Suppose -21296/23*v - 6468/23*v**3 + y*v**2 + 686/23*v**4 + 0 = 0. What is v?
0, 22/7
Suppose -4*r + 30 = -5*y, -3*r + 2 + 11 = y. Determine i so that 3466 + 12*i - r*i**2 + 8*i - 3486 = 0.
2
Let t(q) = -17*q + 8. Let h be t(-1). Suppose 0*d = -5*d + h, -o = 2*d - 10. Factor -1/3*r + o + 1/3*r**2.
r*(r - 1)/3
Let f(h) be the second derivative of -131*h + 0 - 7/10*h**5 - 7/3*h**4 - 8/3*h**3 - 1/15*h**6 + 0*h**2. Solve f(p) = 0.
-4, -2, -1, 0
Let y(k) be the first derivative of -56 - 2/3*k**3 - 1352*k + 52*k**2. Find n such that y(n) = 0.
26
Let x(y) = y**3 + 11*y**2 + y + 14. Let o be x(-11). Solve -4*i**2 - 2*i**5 - 32*i**o + 24*i + 3*i**4 + 10*i**3 + 16 - 15*i**4 + 0*i**2 = 0.
-2, -1, 1
Let i be ((-7)/1)/(-21)*(59 + -2). Suppose i*h - 8*h = 66. Factor h*q - 11*q**3 + 6*q**2 + 9*q**3 + 2*q.
-2*q*(q - 4)*(q + 1)
Let q(b) = 116*b**2 + 8684*b - 128. Let y(z) = 18*z**2 + 1336*z - 20. Let n(x) = -5*q(x) + 32*y(x). Factor n(p).
-4*p*(p + 167)
Let p(z) be the first derivative of z**4/14 + 52*z**3/21 + 176*z**2/7 + 512*z/7 - 497. Find r, given that p(r) = 0.
-16, -8, -2
Let u be ((-10)/(-13))/(-5) - (-19 + (-12903)/(-715)). Factor 4/5*k**3 - u*k - 2/5 + 0*k**2 + 2/5*k**4.
2*(k - 1)*(k + 1)**3/5
Factor 25 - 10/3*j