/240). Let j(k) be the first derivative of 25*k + 5/3*k**3 + 15*k**2 - r. Solve j(t) = 0.
-5, -1
Suppose -28*m + 30*m - 5*o = 9, -4 = 4*o. Let s = 73 + -69. Let 2/7*x**3 + 0*x**m + 2/7*x**s + 0*x + 0 = 0. What is x?
-1, 0
What is q in -125*q**4 + 240*q**2 + 41816*q**5 - 115*q**4 - 41821*q**5 + 235*q - 230*q**3 = 0?
-47, -1, 0, 1
Suppose -h - 4*s = -16, -3*h - s - 2*s = -57. Let w be (h/(-50))/(1 + (-433)/432). Determine q so that -4/5*q**3 + w + 72/5*q**2 - 432/5*q = 0.
6
Let z(b) = 5*b**2 - 10098*b - 1997636. Let r(s) = -s**2 + 1686*s + 332940. Let a(n) = 34*r(n) + 6*z(n). Find p such that a(p) = 0.
-408
Let o(a) be the second derivative of 0 + 50*a**2 + 63*a + 2*a**4 - 1/10*a**5 - 15*a**3. Factor o(x).
-2*(x - 5)**2*(x - 2)
Let m(x) be the third derivative of 1/1050*x**7 + x**2 + 1/600*x**6 - 10*x + 0*x**5 + 0 + 0*x**4 + 0*x**3. Factor m(w).
w**3*(w + 1)/5
Let x = -1238035/4 + 309509. Factor 1/4*w**2 + 1/2*w**3 - 1/2*w - x*w**4 + 0.
-w*(w - 2)*(w - 1)*(w + 1)/4
Let n be (64 + -2)*1/2. Let k(t) = -t**3 + 6*t**2 + 2*t - 7. Let v be k(6). Factor 11 - n - v*h**2 + 8 + 15*h + 2.
-5*(h - 2)*(h - 1)
Let g(b) = 6*b**2 - 49*b + 9. Let w be g(5). Let a be (-16)/88 - (-6)/(-660)*w. Factor 6/5*k**3 + 0*k**2 - 3/5*k**4 - 6/5*k + a.
-3*(k - 1)**3*(k + 1)/5
Let a(s) be the first derivative of -s**3/27 + s**2/2 + 22*s/9 + 168. Factor a(p).
-(p - 11)*(p + 2)/9
Let -4*d + 16*d**2 + 24*d + 84 - 14*d**2 - 6*d**2 + 5*d**2 = 0. Calculate d.
-14, -6
Suppose 5*x + 4*d = -2 + 21, -x + 2 = -d. What is v in 31*v**2 - v**3 + 0*v + 8 + 2*v**4 + 8*v - 3*v**x - 37*v**2 = 0?
-1, 2
Let w = 105312 + -737136/7. Find b such that -2/7*b**2 - 288/7 + w*b = 0.
12
Let h(j) be the second derivative of -j**4/54 - 23*j**3/27 + 248*j**2/9 + 2161*j. Find p, given that h(p) = 0.
-31, 8
Let q = 161 + -155. Factor 16 + q*j**2 - 4*j**2 + 121*j - 67*j - 66*j.
2*(j - 4)*(j - 2)
Suppose -180 = -2836*x + 2791*x. Let p(u) be the third derivative of 1/330*u**5 + 0 + 0*u - 21*u**2 + 0*u**3 - 1/132*u**x. Suppose p(b) = 0. What is b?
0, 1
Let m(s) be the third derivative of -s**2 - 27 - 1/12*s**5 + 25/12*s**4 - 15/2*s**3 + 0*s. Let m(u) = 0. What is u?
1, 9
Factor 3/7*l**4 - 249/7*l**3 - 948/7*l + 0 + 960/7*l**2.
3*l*(l - 79)*(l - 2)**2/7
Suppose 0 = -2*s - 3*s - 5, 0 = 5*d - 3*s - 13. Factor -v**d - 13*v + 39*v - 15*v - 6*v - 4.
-(v - 4)*(v - 1)
Let r = 139 + -138. Let g(i) = -3*i**5 - 3*i**4 - 9*i**3 - 3*i**2 - 6. Let j(q) = q**5 + q**3 + q**2 + 1. Let f(v) = r*g(v) + 6*j(v). Factor f(t).
3*t**2*(t - 1)**2*(t + 1)
Let l(i) = 14*i**2 - 136*i + 736. Let f(t) = 8*t**2 + t - 2. Let d(v) = 2*f(v) - l(v). Factor d(o).
2*(o - 5)*(o + 74)
Suppose 0 = 8*q - 4*q + d - 59, 0 = 3*q - 5*d - 50. Let b be 1/2 - ((-2615)/(-170) - q). Factor -4/17*i**3 + 0*i**2 + 0*i**4 + b*i + 0 + 2/17*i**5.
2*i*(i - 1)**2*(i + 1)**2/17
Let p(v) be the third derivative of -15*v**2 + v + 0*v**3 + 3/4*v**5 + 1/4*v**4 + 11/70*v**7 + 3/5*v**6 + 0. Determine w so that p(w) = 0.
-1, -2/11, 0
Let 632*b - 67*b**4 + 185*b**3 - 1197*b + 72*b**4 - 370 - 15*b**2 = 0. Calculate b.
-37, -1, 2
Let r(z) = 17*z**3 + 1292*z**2 + 5791*z - 1760. Let b(i) = i**3 - 2*i**2 + i. Let m(p) = 6*b(p) - 2*r(p). Factor m(f).
-4*(f + 5)*(f + 88)*(7*f - 2)
Let v(g) be the third derivative of -8*g**8/21 - 368*g**7/105 - 97*g**6/60 + 341*g**5/15 - 163*g**4/12 + 10*g**3/3 + 812*g**2. Find a, given that v(a) = 0.
-5, -2, 1/8, 1
Let g be ((-25)/(-33))/(38396/(-2784) - -14). Determine o, given that g*o + 8/11 + 18/11*o**2 = 0.
-2, -2/9
Let l(z) be the first derivative of 3/5*z**2 + 44 - 1/5*z**3 + 0*z. What is w in l(w) = 0?
0, 2
Let n = -1 + 3. Suppose n*h + 44 - 54 = 0. Factor h + 10*r**2 + 15*r - r**5 - 6*r**3 - 4*r**3 - 15*r**4 - 4*r**5.
-5*(r - 1)*(r + 1)**4
What is o in -40*o + 1/2*o**3 + 288 - 7/2*o**2 = 0?
-9, 8
Suppose 9*z - 11 - 7 = 0. Let f(s) be the second derivative of 0 + 1/165*s**6 + 1/33*s**4 + 0*s**z - 3/110*s**5 + 6*s + 0*s**3. What is r in f(r) = 0?
0, 1, 2
Let u be (-41322)/(-10476) + 4/(-18)*-1. Suppose u*t**4 + 13/3*t**3 + 0*t + 5/6*t**2 + 0 + 2/3*t**5 = 0. Calculate t.
-5, -1, -1/4, 0
Let a be (-5 - -6)/((-1)/3) - -7. Let -30*i**2 + 6*i**4 + 68*i**3 + 256*i - 290*i**2 + i**4 - 11*i**a = 0. What is i?
0, 1, 8
Let s(j) be the third derivative of 1/210*j**5 - j**2 + 125 + 0*j**4 + 0*j - 1/420*j**6 + 0*j**3. Factor s(g).
-2*g**2*(g - 1)/7
Let t(y) be the first derivative of y**4/2 - 14*y**3 + 74*y**2 + 192*y + 1608. Suppose t(h) = 0. What is h?
-1, 6, 16
Let m = 10551/7913 - 1/23739. Let q(h) be the second derivative of 33*h - 1/2*h**3 + 0 + 1/36*h**4 + m*h**2. Factor q(o).
(o - 8)*(o - 1)/3
Find g, given that -4/7*g**3 + 88/7*g + 0 + 36/7*g**2 = 0.
-2, 0, 11
Find y such that 1538 - 74*y**4 + 510 - 76*y**4 - 2046*y**2 - 128*y + 148*y**4 + 128*y**3 = 0.
-1, 1, 32
Let o(d) be the second derivative of -d**5/50 + 23*d**4/30 + 518*d**3/15 - 317*d. Factor o(t).
-2*t*(t - 37)*(t + 14)/5
Let g be (5/(-7))/((-7175)/20090). Determine j, given that 3/5*j**g - 84/5*j + 81/5 = 0.
1, 27
Let b(w) be the first derivative of -w**5/5 + w**4 + 20*w**3/3 + 8*w + 2. Let i(a) be the first derivative of b(a). Let i(m) = 0. Calculate m.
-2, 0, 5
Let n(t) be the first derivative of -t**3/3 + 13*t**2 - 2*t + 108. Let z(j) = 3*j**2 - 27*j + 3. Let k(v) = 3*n(v) + 2*z(v). Factor k(u).
3*u*(u + 8)
Suppose 109 + 641 = 10*d. Let w(z) = -3*z - 4. Let u be w(-2). Solve 2*y + 1 + d*y**u + 2 - 76*y**2 = 0.
-1, 3
Determine f so that 114*f**3 - f**4 + 4866*f + 3*f**4 + 1608*f + 1176*f**2 + 5760 - 2026*f = 0.
-45, -4
Suppose -101 + 115 = -7*r. Let m be (-7)/15*r - (-4)/10. Factor -4/3*d**2 - 1/3 - m*d.
-(2*d + 1)**2/3
Let j(i) be the third derivative of -7/60*i**5 + 0 - 5/72*i**6 + 0*i - 1/24*i**4 + 1/9*i**3 - 56*i**2 - 1/70*i**7. Find d such that j(d) = 0.
-1, 2/9
Suppose -3*t = -10*t - 35. Let w be 2 + t/((-5)/2). Factor 10/3*m**3 - 5/3*m**w - 10/3*m + 0 + 5/3*m**2.
-5*m*(m - 2)*(m - 1)*(m + 1)/3
Let n(l) = 18*l**4 + 53*l**3 - 141*l**2 - 225*l - 7. Let h(g) = -20*g**4 - 52*g**3 + 140*g**2 + 228*g + 8. Let d(o) = 7*h(o) + 8*n(o). Factor d(s).
4*s*(s - 3)*(s + 1)*(s + 17)
Find b such that 16 + 1/4*b**2 + 5*b = 0.
-16, -4
Let z be (-45)/60 + (-143)/(-4). Let c be 14/(-2)*5/z*-2. Factor 1/5*a - 2/5*a**c + 0 + 1/5*a**3.
a*(a - 1)**2/5
Let j be (-4 - 104/(-28))/(25*57/(-11305)). Determine a, given that -2/15*a**5 - 48/5 + 16/15*a**4 - 28/15*a**2 + 56/5*a - j*a**3 = 0.
-2, 2, 3
Suppose -5 = -3*v - 17, -5*v + 10304 = 2*t. Find w such that 4*w**2 + 5086*w - 1444 - 5*w**2 - t*w = 0.
-38
Let m(a) be the third derivative of a**5/30 + 253*a**4/16 - 95*a**3/6 - 443*a**2 - 2*a. Determine t so that m(t) = 0.
-190, 1/4
Let p(w) = 17*w - 3907. Let v be p(230). Factor 2/3 + 1/3*d**v + 5/3*d + 4/3*d**2.
(d + 1)**2*(d + 2)/3
Let q(j) be the first derivative of 87 - 1/12*j**3 - 7/8*j**2 - 5/2*j. Find i, given that q(i) = 0.
-5, -2
Let o(c) = c**3 + 30*c**2 - c - 19. Let g be o(-30). Let p be (86/g - 8) + (-27)/(-88). Factor 0*h + p*h**3 - 1/8*h**4 + 0 + 3/4*h**2.
-h**2*(h - 3)*(h + 2)/8
Factor 20106*s - 5*s**4 - 1218*s**2 + 86*s**3 - 13952*s - 8092 + 3*s**4.
-2*(s - 17)**2*(s - 7)*(s - 2)
Let r(c) be the first derivative of 2*c**6/3 - 184*c**5/5 - 48*c**4 + 184*c**3/3 + 94*c**2 - 6599. Suppose r(j) = 0. What is j?
-1, 0, 1, 47
Let s(i) be the first derivative of i**4/20 - 224*i**3/5 - 1347*i**2/10 - 674*i/5 - 11541. Factor s(a).
(a - 674)*(a + 1)**2/5
Let d(t) be the second derivative of -t**5/10 - 89*t**4/6 + t**3/3 + 89*t**2 + 59*t + 7. Factor d(a).
-2*(a - 1)*(a + 1)*(a + 89)
Let x be ((-16)/(-6))/8 + 1105/105 + -10. Suppose 4/7*l + 0 - x*l**2 + 2/7*l**3 = 0. What is l?
0, 1, 2
Let v = 20622 - 20620. Let i(n) be the second derivative of -1/20*n**5 - 1/12*n**4 + 0*n**v + 0 - 21*n + 0*n**3. What is z in i(z) = 0?
-1, 0
Suppose 7*d + 29*d = 13*d + 92. Let t(b) be the second derivative of -b + 0 - 2/9*b**2 - 1/9*b**3 - 1/54*b**d. Factor t(m).
-2*(m + 1)*(m + 2)/9
Let n(w) be the third derivative of 0*w + 2/3*w**3 - 1/300*w**5 - 71*w**2 + 2 + 1/15*w**4. Factor n(m).
-(m - 10)*(m + 2)/5
Factor -1060*n + 45483 - 45483 - 5*n**2.
-5*n*(n + 212)
Let w(y) be the third derivative of -y**6/120 + 37*y**5/60 + 471*y**2 + y. Factor w(n).
-n**2*(n - 37)
Suppose -12*v + 188 = -2*i - 16*v, 0 = -2*v + 10. Let g be (