, given that g(r) = 0.
-2, 11
Let z = -377 + 408. Factor 4*y**3 - 9*y - 55*y**2 + 6*y**4 - 11*y**4 - 21*y - z*y**3 - 3*y**3.
-5*y*(y + 1)*(y + 2)*(y + 3)
Let k(a) be the second derivative of a**7/840 - a**6/160 - a**5/240 + a**4/32 - 43*a**2/2 + 14*a. Let z(f) be the first derivative of k(f). Factor z(v).
v*(v - 3)*(v - 1)*(v + 1)/4
Let x(u) = u**3 + 9*u**2 + 14*u + 8. Let p be x(-7). Let h be 264/60 + p/(-20). Factor 0 - 2/13*q + 2/13*q**3 - 2/13*q**2 + 2/13*q**h.
2*q*(q - 1)*(q + 1)**2/13
Let f(c) be the second derivative of -8/15*c**3 - 1/30*c**4 - 150*c + 0*c**2 + 0. Factor f(a).
-2*a*(a + 8)/5
Let b = 208739 + -1878631/9. Determine j, given that b*j + 4/9*j**2 + 16/9 = 0.
-4, -1
Suppose 347/2*z + 259*z**2 + 87/2 - 1/2*z**5 + 83/2*z**4 + 171*z**3 = 0. What is z?
-1, 87
Factor 3/2*a**2 + 225/2*a - 114.
3*(a - 1)*(a + 76)/2
Let f(b) be the third derivative of b**6/120 + b**5/30 - 17*b**4/6 + 20*b**3 + 5*b**2 - 67*b. Factor f(q).
(q - 6)*(q - 2)*(q + 10)
Let a be ((-24 + 24)/3)/(-1). Let i(m) be the second derivative of -1/8*m**4 + 0*m**2 - 1/80*m**5 + a*m**3 + 0 + 48*m. Solve i(h) = 0 for h.
-6, 0
Let h be 30731/6320 + -7 + 444/64. Solve h + 28/5*k + 4/5*k**2 = 0 for k.
-6, -1
Let t(g) = -3*g**3 - 55*g**2 - 7*g + 1017. Let h(m) = m**3 + 27*m**2 + 3*m - 509. Let w(o) = 14*h(o) + 6*t(o). Suppose w(p) = 0. What is p?
-4, 8
Let y(b) = -b**3 - 27*b**2 + 57*b - 26. Let p be y(-29). Let g(a) be the first derivative of 30 + 3/2*a - 1/6*a**p + 1/2*a**2. Suppose g(j) = 0. Calculate j.
-1, 3
Let j(y) = 26*y**2 + 91*y + 138. Let c(q) = -27*q**2 - 90*q - 162. Let w(l) = -4*c(l) - 5*j(l). Factor w(v).
-(2*v + 1)*(11*v + 42)
Let g(u) be the third derivative of 7/2*u**3 + 0 + 0*u + 0*u**4 - 1/1080*u**6 + 1/360*u**5 - 11*u**2. Let d(s) be the first derivative of g(s). Factor d(t).
-t*(t - 1)/3
Let o = 167 - 164. Factor -g**3 + 9*g**2 + 10*g + 7*g**2 + 8*g**o - g**3.
2*g*(g + 1)*(3*g + 5)
Suppose 126*i - 496 = -133*i + 11*i. Suppose -20/11*y + 0 + 2/11*y**i = 0. Calculate y.
0, 10
Suppose 4*y = 5*g + 2, 0*g - 3*g - 3 = -3*y. Factor 5 + 3*k**2 + y*k + 12 - 35.
3*(k - 2)*(k + 3)
Let 2*o**2 - o - 29 - o**3 - 35 + 64 = 0. Calculate o.
0, 1
Let i(u) = -13*u**2 + 4*u + 3. Let l be i(-1). Let b = 16 + l. Factor 0 - 3*a**b + 4*a**2 - 9*a + 6 + 2*a**2.
3*(a - 2)*(a - 1)
Let z be 3/(195/(-80) + 3) - (-711)/(-158). Suppose 5*h + 0 - z*h**3 + 25/6*h**2 = 0. What is h?
-1, 0, 6
Let 528/5 - 1/5*h**3 - 349/5*h - 178/5*h**2 = 0. Calculate h.
-176, -3, 1
Suppose t - 21 = -3*k, 5*t = 22*k - 20*k + 122. Let y = t - 22. Factor -2/3*o**4 - 236/3*o**y - 120*o - 40/3*o**3 - 54.
-2*(o + 1)**2*(o + 9)**2/3
Let i(s) = s**2 + 5915*s - 12054. Let c(l) = 5*l**2 + 35490*l - 72375. Let v(n) = 4*c(n) - 25*i(n). What is f in v(f) = 0?
-1185, 2
Let q be ((-8)/(-10))/((-6)/(-10)). Suppose -733289*v - 768 = -733385*v. Let 8/3*z**2 - 20/3*z - v + q*z**3 = 0. Calculate z.
-3, -1, 2
Let z(j) = -3*j**3 + j**2 + j. Let h(r) = 10*r**2 + 41*r + 2. Let p be h(-4). Let w(n) = -4*n**3 + 2*n**2. Let l(x) = p*w(x) + 4*z(x). Factor l(m).
-4*m*(m - 1)*(m + 1)
Suppose 75 = 30*m - 75. Let x be m - ((-518)/63)/(-2). Determine d so that 0*d + 0 - x*d**2 + 4/9*d**4 - 4/9*d**3 = 0.
-1, 0, 2
Factor -3/4*w**2 + 4 + 1/8*w**3 + 0*w.
(w - 4)**2*(w + 2)/8
Factor 2962/5*x - 2963/5 + 1/5*x**2.
(x - 1)*(x + 2963)/5
Factor 1816*w**2 + 337095715 + 2484735*w + 3707*w**2 + 5*w**3 + 582*w**2.
5*(w + 407)**3
Let w = 12 - 12. Suppose 4*l + t - 4 = 2*l, 3*t + 12 = w. Factor -5*q**4 + 12*q**3 + q - 2*q**4 + l*q**4 - 49*q + 48.
-3*(q - 2)**3*(q + 2)
Suppose -2*i + 3*o + 22 = 0, 34*i - 29 = 29*i + o. Let p(k) be the first derivative of 0*k**2 - 1/36*k**3 - 1/24*k**4 - 1/60*k**i - 1 + 0*k. Factor p(v).
-v**2*(v + 1)**2/12
Suppose 15*u**2 - 24*u + 3/2*u**3 - 240 = 0. What is u?
-10, -4, 4
Let z(c) be the third derivative of 3/200*c**6 + 0 - 36*c**2 + 7/100*c**5 + 19/120*c**4 + 1/5*c**3 + 0*c + 1/1050*c**7. Determine p, given that z(p) = 0.
-6, -1
Let v(i) = 2*i**2 - 22*i + 40. Suppose -3*y = 4*o - 51, -37 + 32 = -y. Let m be v(o). Let -2*q**2 + 0*q**3 - 4/3*q + 2/3*q**m + 0 = 0. What is q?
-1, 0, 2
Suppose -u = -3*w + 4, 4 = 2*w + 8. Let s be (-22)/u - 1/5. Factor 14*o**3 + 44*o**s + o + o - 7*o**3 - 53*o**2.
o*(o - 1)*(7*o - 2)
Suppose -4*c**4 + 44*c**2 + c**3 + 80*c**2 - 14*c**3 - 174*c - 70*c + 17*c**3 + 120 = 0. What is c?
-6, 1, 5
Let v(r) be the first derivative of 90 + 8/3*r**3 - 8*r + r**4 - 2*r**2. Solve v(l) = 0 for l.
-2, -1, 1
Let t be (-74 + 82)*(-2)/(-4). Let o = -7 + 12. What is j in -15*j**o + 2*j**t - 5*j + 16*j**5 - 2*j**2 + 0*j**4 + 4*j = 0?
-1, 0, 1
Find z such that -4*z + 238*z - 3*z**2 + 606 + 63*z = 0.
-2, 101
Let f(g) be the third derivative of g**7/420 - 37*g**6/240 + 117*g**5/40 - 105*g**4/16 - 8418*g**2. Factor f(y).
y*(y - 21)*(y - 15)*(y - 1)/2
Let o = 113 - 111. Factor -8*h + 4*h + 15*h**2 - 5*h**2 - 10 + 4*h**o.
2*(h - 1)*(7*h + 5)
Let j(i) be the first derivative of 0*i**2 - 1/78*i**4 - 1/39*i**3 - 10*i - 15. Let x(l) be the first derivative of j(l). Suppose x(r) = 0. What is r?
-1, 0
Let o(i) be the second derivative of 5/24*i**6 - 45*i - 1/4*i**5 + 0 + 5/6*i**3 - 7/16*i**4 - 1/2*i**2. Find k such that o(k) = 0.
-1, 2/5, 1
Let t(i) be the third derivative of i**6/40 - 143*i**5/20 - 73*i**4/4 + 144*i**3 + 3111*i**2 - i + 2. Let t(n) = 0. What is n?
-2, 1, 144
Let b(f) be the first derivative of 39 - 8*f + 8/3*f**3 - 2*f**2 + f**4. Factor b(r).
4*(r - 1)*(r + 1)*(r + 2)
Let c(l) be the third derivative of l**5/270 - 5*l**4/36 + l**2 + 31*l. Factor c(q).
2*q*(q - 15)/9
Let i be (-4688)/42 + (-48)/(-168). Let x = i + 112. Factor -1/3*o**2 - x - o.
-(o + 1)*(o + 2)/3
Let x(y) be the third derivative of -y**7/350 - 3*y**6/50 - 29*y**5/100 - 9*y**4/20 - 2111*y**2. Factor x(b).
-3*b*(b + 1)*(b + 2)*(b + 9)/5
Let m be ((-7)/28)/(81/(-144)). Suppose -39 = 6*j - 57. What is b in -m*b + 1/9*b**2 + 1/9*b**j - 4/9 = 0?
-2, -1, 2
Let z(l) = -l**3 - 4*l**2 - l - 1. Let v be z(-4). Suppose 0 = 2*n - 4*j - v + 11, -2*j - 12 = -5*n. What is o in 3*o**n + 0*o**4 + 244*o**3 - 244*o**3 = 0?
0
Suppose 16*d - 3616 - 1232 = 0. Factor -6*g**2 - 237*g**3 + 3*g**5 + 0*g + d*g**3 - 33 + 39*g**4 - 69*g.
3*(g - 1)*(g + 1)**3*(g + 11)
Factor -1710 + 167*m**2 + 1325*m**2 - 522*m**2 - 35*m**3 - 5705*m.
-5*(m - 19)*(m - 9)*(7*m + 2)
Let k = -4172 + 4176. Let j(s) = -s + 13. Let d be j(8). Let 1/2*u + 2*u**2 - 1 + 1/2*u**d - u**3 - u**k = 0. Calculate u.
-1, 1, 2
Let m be (44/66)/((-2)/(-225)). Suppose -63*k = -m*k. Factor k*f + 1/7 - 1/7*f**2.
-(f - 1)*(f + 1)/7
Factor -1/4*c**2 + 7/4 - 3/2*c.
-(c - 1)*(c + 7)/4
Let g(s) = -2*s**3 - 11*s**2 - s + 22. Let y be g(-5). Let o(f) be the third derivative of -1/3*f**4 - 3*f**y + 1/6*f**5 + 0*f**3 + 0*f + 0. Factor o(k).
2*k*(5*k - 4)
Find l such that -6*l**2 + 54 + 3/8*l**5 + 48*l - 15/8*l**4 - 27/2*l**3 = 0.
-2, 2, 9
Let i(y) be the second derivative of 5*y**4/36 + 325*y**3/18 + 295*y**2 + 2233*y. Determine c, given that i(c) = 0.
-59, -6
Factor -439 - 285*d - 185 + 7*d + 28 - 256 + 2*d**2.
2*(d - 142)*(d + 3)
Let n(a) be the first derivative of -a**4/28 - 71*a**3/21 - 134*a**2/7 + 6405. Factor n(y).
-y*(y + 4)*(y + 67)/7
Let r(l) be the second derivative of -5*l**6/6 - 63*l**5/4 - 535*l**4/6 - 70*l**3 + 180*l**2 - 167*l. Let r(x) = 0. Calculate x.
-6, -1, 2/5
Let n = 10739 + -10736. Let q(v) be the second derivative of 0*v**2 + 6*v + 0 + 1/20*v**4 + 1/10*v**n. Factor q(c).
3*c*(c + 1)/5
Let k = -8756 - -70049/8. Let o(c) be the first derivative of 0*c**3 + 0*c**2 - k*c**4 + 0*c - 16. Factor o(h).
-h**3/2
Let -2/9*f**5 + 3822*f - 2396/9*f**3 + 2058 + 1484*f**2 + 122/9*f**4 = 0. What is f?
-1, 21
Let a be (2/30)/((-1)/(-6)*(-240)/(-120)). Let v(l) be the second derivative of 7/60*l**4 + 7/30*l**3 + 1/50*l**5 + 33*l + 0 + a*l**2. Factor v(m).
(m + 1)*(m + 2)*(2*m + 1)/5
Suppose 3*p = 4*p - 5*k - 36, 2*p + k - 28 = 0. Suppose -7*h + 6*h = m - 1, -3*m = -4*h + 18. Find j, given that -5*j**4 + p*j**h + j - j + j**4 = 0.
0, 4
Let d(i) be the first derivative of 7*i**4/16 + 297*i**3/4 + 127*i**2/4 - 386. Factor d(p).
p*(p + 127)*(7*p + 2)/4
Let x be 1/((-8)/840*-21). Let w(l) be the third derivative of -1/160*l**x + 0*l + 1/16*l**4 - 1/4*l**3 + 0 - 11*l**2. Let w(t) = 0. What is t?
2
Suppose 112