m. Let a = -44 + m. Factor -9*w + a*w - 2*w - 12*w**2.
-4*w*(3*w - 2)
Let p = 298/115 - 706/805. Factor p*c**2 - 2/7*c**3 + 0 + 2*c.
-2*c*(c - 7)*(c + 1)/7
Let n be (12/(-96) - 3/8)*(-3 + 3). Let g(w) be the second derivative of -10*w**3 + 11/4*w**5 - w**6 + 5/42*w**7 - 5/6*w**4 + n + 4*w + 20*w**2. Factor g(z).
5*(z - 2)**3*(z - 1)*(z + 1)
What is y in 1/2*y**2 - 219/2 + 109*y = 0?
-219, 1
Let j(h) = h**3 - 17*h**2 + h - 15. Let q be j(17). What is l in -1 - 22*l + 4 + 5 + q*l**2 - 32 = 0?
-1, 12
Let s(z) be the first derivative of 3*z**5/80 - 11*z**4/16 + 3*z**3 + 27*z**2/2 + 13*z - 65. Let u(q) be the first derivative of s(q). Factor u(p).
3*(p - 6)**2*(p + 1)/4
Let p = -8 - 8. Let i be (-40)/(-19) + p/152. Determine n, given that 0*n**i + 0*n**3 - 5*n**5 + 4*n**2 + n**2 - 5*n**4 + 5*n**3 = 0.
-1, 0, 1
Let a be (-36501)/(-2645) + 1/5. Factor -1/2*b**2 + a*b - 98.
-(b - 14)**2/2
Let v(k) be the third derivative of k**5/180 + 47*k**4/8 + 4*k**2 - 435. Find l such that v(l) = 0.
-423, 0
Let z(o) be the third derivative of o**5/135 - 3104*o**4/27 + 19269632*o**3/27 - o**2 - 7*o + 1. Factor z(d).
4*(d - 3104)**2/9
Let r(s) be the second derivative of s**5/20 + 3*s**4/2 + 59*s**3/6 - 99*s**2 - 8547*s. Factor r(h).
(h - 2)*(h + 9)*(h + 11)
Let k(n) be the first derivative of n**4/32 + 1013*n**3/24 + 256035*n**2/16 - 257049*n/8 - 5336. What is f in k(f) = 0?
-507, 1
Let l = 168 + -174. Let m(c) = -3*c**2 + 31*c + 13*c**2 + 5*c**2. Let i(h) = -16*h**2 - 32*h - 1. Let s(r) = l*i(r) - 7*m(r). Factor s(b).
-(b + 3)*(9*b - 2)
Solve 121 + 978*u**2 + 2214 + 25*u**3 - 4665*u - 20*u**3 + 1347*u**2 = 0 for u.
-467, 1
Let y(c) be the first derivative of -4*c**5/55 + 75*c**4/22 - 730*c**3/33 + 420*c**2/11 - 256*c/11 - 1529. Let y(x) = 0. What is x?
1/2, 1, 4, 32
Let i be (-3 + 4*-10)/(-2 - -1). Let j = i - 38. Factor 1 - j*m**2 - 4*m + 4*m**2 + 3*m**2 - 7.
2*(m - 3)*(m + 1)
Let i(r) be the first derivative of -r**5/40 + 7*r**3/12 + 3*r**2/2 - 68*r + 79. Let m(w) be the first derivative of i(w). Factor m(f).
-(f - 3)*(f + 1)*(f + 2)/2
Let b(c) be the third derivative of c**5/40 + 51*c**4/16 + 315*c**3/2 + 2*c**2 - 22*c - 28. Factor b(z).
3*(z + 21)*(z + 30)/2
Find x, given that -1/5*x**3 - 11236/5 - 213/5*x**2 - 11448/5*x = 0.
-106, -1
Let m(o) be the first derivative of o**3/3 - 23*o**2/2 + 3*o + 120. Let i(f) = -2*f**2 + 66*f - 8. Let j(p) = -3*i(p) - 8*m(p). Factor j(b).
-2*b*(b + 7)
Let r(s) be the third derivative of -s**5/120 + 188*s**4/3 - 565504*s**3/3 + 5863*s**2. Suppose r(i) = 0. Calculate i.
1504
Let x be ((-54)/1782*0)/(-2 + 4). Factor 0*f**3 + 0 + 1/2*f**5 + 0*f**2 - 5*f**4 + x*f.
f**4*(f - 10)/2
Let s(i) be the third derivative of i**5/360 + 119*i**4/8 + 127449*i**3/4 + 265*i**2 - 2*i. Suppose s(a) = 0. What is a?
-1071
Let d(p) be the first derivative of 27/8*p**4 + 9/4*p + 219/16*p**2 + 55 + 57/2*p**3. Factor d(m).
3*(m + 6)*(6*m + 1)**2/8
Suppose 177 = -7*r + 23. Let h(y) = y + 25. Let k be h(r). Factor -8*m + 90*m**2 + 24*m**k - 66*m**2 - 10*m**3.
2*m*(m + 2)*(7*m - 2)
Suppose -59*c + 51 = -42*c. Let i(l) be the first derivative of 8/5*l + 4/15*l**c + 7/5*l**2 - 1/10*l**4 - 15. Factor i(b).
-2*(b - 4)*(b + 1)**2/5
Let p(y) be the third derivative of -y**8/2240 + y**7/420 + 7*y**4/6 - 36*y**2. Let z(s) be the second derivative of p(s). Factor z(x).
-3*x**2*(x - 2)
What is z in -56*z**3 - 76*z**2 - 148*z**2 - 82*z - 119*z + 7*z - 62*z - 4*z**4 = 0?
-8, -4, -2, 0
Let d(c) = -c**2 - 4*c + 12. Let h = 84 + -91. Let b(f) = f**2 + 5*f - 12. Let k(t) = h*b(t) - 6*d(t). Factor k(r).
-(r - 1)*(r + 12)
Let g(t) be the first derivative of t**6/180 + 29*t**5/270 + 53*t**4/108 - 7*t**3/9 - 161*t**2/2 - 171. Let x(k) be the second derivative of g(k). Factor x(v).
2*(v + 3)*(v + 7)*(3*v - 1)/9
Let k be 2 - (7 - (7 + 1)). Factor -610*g**2 + 26*g - 45*g - 9*g**k - g**4 - 6 + 589*g**2.
-(g + 1)**3*(g + 6)
Let m be ((-7)/(-105))/((-56)/(-24)). Let x(i) be the second derivative of m*i**5 + 0*i**2 + 0 + 15*i + 4/21*i**3 + 1/7*i**4. Suppose x(r) = 0. Calculate r.
-2, -1, 0
Let n(l) be the second derivative of -l**4/18 - 110*l**3/9 - 72*l**2 + 35*l + 21. Determine z so that n(z) = 0.
-108, -2
Let o(z) be the second derivative of 1/2*z**3 + 23*z + 0 + 0*z**2 + 3/20*z**5 + 1/2*z**4. Factor o(b).
3*b*(b + 1)**2
Let z(c) be the second derivative of -1/16*c**4 + 3*c**2 + 0 + 1/6*c**3 + 14*c - 1/60*c**5. Let h(r) be the first derivative of z(r). Factor h(j).
-(j + 2)*(2*j - 1)/2
Let k(a) = -13*a**2 - 1388*a - 4079. Let c(h) = -12*h**2 - 1387*h - 4081. Let u(z) = 8*c(z) - 7*k(z). Suppose u(w) = 0. What is w?
-273, -3
Let h(r) = -145*r - 130. Let b(n) = -13*n - 41. Let y be b(-3). Let k(q) = -q**2 - 72*q - 65. Let t(d) = y*h(d) + 5*k(d). Let t(m) = 0. What is m?
-13, -1
Let o(c) be the third derivative of -c**7/210 + c**6/24 + c**5/60 - 17*c**4/24 - 2*c**3 + 14*c**2 + 29. Determine g, given that o(g) = 0.
-1, 3, 4
Let i(b) be the third derivative of 5*b**9/3024 + b**8/84 - b**7/56 - b**6/4 - 8*b**3 - 10*b**2. Let h(q) be the first derivative of i(q). Factor h(m).
5*m**2*(m - 2)*(m + 3)**2
What is g in 15/2*g**2 - 4505 - 13505/2*g = 0?
-2/3, 901
Let w = 167052 + -334101/2. Factor 60*h**2 - w - 9/2*h.
3*(5*h - 1)*(8*h + 1)/2
Let b(v) be the first derivative of v**3 + 5/2*v**2 - 5/4*v**4 - 249 - 4*v + 1/5*v**5. Factor b(y).
(y - 4)*(y - 1)**2*(y + 1)
Let u be (-1 - 1) + (-112)/(140/10). Let i(l) = -3*l**2 - 11*l + 32. Let m(q) = q**2 + 6*q - 16. Let y(t) = u*m(t) - 4*i(t). Determine r so that y(r) = 0.
4
Let o(l) be the third derivative of -l**6/360 - 29*l**5/90 - 505*l**4/72 - 200*l**3/3 - 1140*l**2. Factor o(j).
-(j + 5)**2*(j + 48)/3
Let m be (-39508)/560 + 74 - 6/5. Factor 5/2*w + 1/4*w**2 + m.
(w + 1)*(w + 9)/4
Factor -267 + 714*j**2 - 3*j**4 - 2139*j**2 - 711*j + 267 - 717*j**3.
-3*j*(j + 1)**2*(j + 237)
Let o(m) be the second derivative of -m**5/4 + 235*m**4/12 - 430*m**3/3 - 2*m - 123. Factor o(t).
-5*t*(t - 43)*(t - 4)
Let v(h) = 2*h**4 - 3*h**3 - 3*h**2. Let c(y) = 246*y**4 + 300*y**3 + 34*y**2. Let p(m) = 2*c(m) + 20*v(m). Factor p(s).
4*s**2*(s + 1)*(133*s + 2)
Suppose 0 = 10*t - 530 + 500. Let r(p) be the first derivative of -1/4*p**4 - t*p - 7/2*p**2 - 2 - 5/3*p**3. Factor r(z).
-(z + 1)**2*(z + 3)
Suppose 3*n + 585 = 4*k, 4*n = 5*k - 552 - 178. Find f such that 66*f**2 + 41472 + 6*f**3 - 3*f**3 + k*f**2 + 584*f + 4600*f = 0.
-24
Factor 358 - 21502*b**2 + 43000*b**2 - 21499*b**2 - 177*b.
-(b - 2)*(b + 179)
Let p be (-1 + 2)/(3*2/12). Determine c, given that 12*c**3 - 5 - 2*c**p - 111*c**5 + 108*c**5 - 1 - 9*c + 8*c**2 = 0.
-1, 1, 2
Let o(i) be the first derivative of 5*i**3/3 - 2455*i**2/2 - 2460*i + 106. Suppose o(r) = 0. What is r?
-1, 492
Let m(d) be the second derivative of -d**5/24 - 25*d**4/48 - 5*d**3/3 + 68*d**2 + 38*d. Let h(b) be the first derivative of m(b). Find s such that h(s) = 0.
-4, -1
Let m(h) be the third derivative of -3*h**8/112 + 43*h**7/70 - 21*h**6/5 + 32*h**5/5 + 18*h**2 - 3*h. Determine j, given that m(j) = 0.
0, 1, 16/3, 8
Let a(y) be the first derivative of 2*y**3/33 + 14*y**2/11 + 98*y/11 + 3198. Find q, given that a(q) = 0.
-7
Let v be (1202831/5544)/(-31) + 10 + -3. Let o = v + 6323/10296. Factor -8/13 - o*u - 2/13*u**2.
-2*(u + 2)**2/13
Solve 57/4*j**2 + 189/4 - 495/8*j + 3/8*j**3 = 0.
-42, 1, 3
Let q(w) be the second derivative of -w**5/20 - w**4/6 + 74*w**3/3 - 140*w**2 - 10226*w. Determine k so that q(k) = 0.
-14, 2, 10
Let w(p) be the first derivative of p**4/5 - 76*p**3/15 + 22*p**2 + 1452*p/5 - 1203. Factor w(v).
4*(v - 11)**2*(v + 3)/5
Let y be ((-1)/(24/(-16)))/(2/3207). Factor -3*l**3 - l**4 - 2 - y*l**2 + 1072*l**2 + l + 2*l**3.
-(l - 1)**2*(l + 1)*(l + 2)
Suppose k + w - 21 + 15 = 0, 2*w + 2 = 5*k. Determine r so that 0 - 200/11*r - 2/11*r**3 - 40/11*r**k = 0.
-10, 0
Let x be (36/(-126) - 22/(-28)) + 84/56. Let s(j) be the first derivative of -4/5*j**5 + 0*j - x*j**3 - 9/4*j**4 - 1/2*j**2 + 11. Factor s(y).
-y*(y + 1)**2*(4*y + 1)
Let x(q) = -q**3 + 28*q**2 + 31*q - 55. Let p be x(29). Let b be (-6)/p*27/(-6). Factor 0*j**4 - 6*j**4 + j**4 + b*j**4 - 4*j**2.
4*j**2*(j - 1)*(j + 1)
Let m(i) be the second derivative of -i**5/60 - 53*i**4/12 - 2809*i**3/6 - 103*i**2/2 - i - 11. Let q(n) be the first derivative of m(n).