 q be 30/9*(-3)/12*-6. Let d be (45/(-6))/q*6/(-3). Factor -2*s**4 - 7*s**d + 6*s - 9*s - s**3 + 11*s + 8 - 6*s**2.
-2*(s - 1)*(s + 1)*(s + 2)**2
Let f(c) be the second derivative of -c**4/48 + 107*c**3/24 - 175*c**2/2 + 1840*c - 3. Factor f(r).
-(r - 100)*(r - 7)/4
Let n(k) be the third derivative of k**8/2184 + 22*k**7/1365 + 2*k**6/13 + 3*k**5/5 + 45*k**4/52 + k**2 - 88*k. Solve n(p) = 0.
-15, -3, -1, 0
Let f = 218 + -214. Factor 87*m - 75*m + f*m**2 - 11 - 5*m**2.
-(m - 11)*(m - 1)
Let t(d) be the third derivative of d**6/240 - 317*d**5/40 + 100489*d**4/16 - 31855013*d**3/12 - 13*d**2 - 15*d. Find b such that t(b) = 0.
317
Let g = 133 - 98. Suppose -9*k**3 - 6 - 34*k**2 - 2 - 26*k**4 + g*k**4 - 2*k**3 + 44*k = 0. Calculate k.
-2, 2/9, 1, 2
Let m(r) = 10*r**2 - 73*r + 59 - 141 + 159. Let k(u) = -5*u**2 + 37*u - 38. Let w(n) = 7*k(n) + 3*m(n). Factor w(i).
-5*(i - 7)*(i - 1)
Suppose -615 + 619 = 2*j. Let z be j/27 - (-520)/270. Factor 5/2*r**3 - 5/2*r + 0 - 5/2*r**4 + 5/2*r**z.
-5*r*(r - 1)**2*(r + 1)/2
Factor -4176*c + 8165*c + 5*c**5 + 455*c**3 - 4369*c + 490*c**2 - 680 + 110*c**4.
5*(c - 1)*(c + 2)**3*(c + 17)
Let m(c) be the second derivative of -c**5/10 + 2*c**4/7 - c**3/7 - 2*c**2/7 - 5*c - 208. Find p such that m(p) = 0.
-2/7, 1
Let w(l) = -15*l**3 + 33 + 225*l**2 - 556*l - 42 - 1578*l + 181*l. Let b(s) = 7*s**3 - 112*s**2 + 976*s + 4. Let c(j) = -9*b(j) - 4*w(j). Factor c(v).
-3*v*(v - 18)**2
Let l be ((-495)/440)/(3/(-24)) - (-240)/(-32). Factor -3/5*t**2 + 1/10*t**3 - l*t + 10.
(t - 5)**2*(t + 4)/10
Factor 1 - 3*w + 9*w**2 + 13*w**2 - 23*w**2 + 3*w.
-(w - 1)*(w + 1)
Let r be (16/14)/((-6)/(-21)). Suppose 0 = -r*z + 7*z - 6. Find d, given that 7*d**4 - 15*d**z - 2*d**4 + 10*d**2 = 0.
-1, 0, 1
Suppose 36 + 96 = 11*d. Let q be 8*(2/d - (-10)/(-15)). Let b(r) = r**3 + r**2 + r. Let c(l) = 5*l**3 - l**2 + 12*l - 4. Let u(x) = q*b(x) + c(x). Factor u(k).
(k - 2)**2*(k - 1)
Let r be (-2)/(-13) - (680975/715)/(-5). Let t = 191 - r. Factor -2/11*a**5 + 2/11 + 2/11*a**4 - t*a**2 - 2/11*a + 4/11*a**3.
-2*(a - 1)**3*(a + 1)**2/11
Let r(g) = -59*g**3 - 118*g**2 + 6*g + 15. Let v be r(-2). Solve 21/4*s**2 - 3/2*s**5 - 5/4*s**4 + 13/2*s**v - 2*s - 1 = 0 for s.
-2, -1, -1/3, 1/2, 2
Let m(d) be the second derivative of -2*d**6/15 - 4*d**5/5 - 5*d**4/3 - 4*d**3/3 + 6*d - 87. Factor m(b).
-4*b*(b + 1)**2*(b + 2)
Factor 986/7*a**2 + 0 + 984/7*a + 2/7*a**3.
2*a*(a + 1)*(a + 492)/7
Let -48*i**4 - 2835*i - 7197*i + 925*i**2 - 114*i**3 + 23232 + 51*i**4 + 686*i**2 = 0. What is i?
8, 11
Let q(k) = -31 + 4 + 15 + k + 13. Let a be q(1). Determine w so that 9/4*w**a - 3/4*w + 0 = 0.
0, 1/3
Let v(s) be the first derivative of -s**4/4 + 27*s**3 + 41*s**2 - 5715. Factor v(b).
-b*(b - 82)*(b + 1)
Let m(n) be the second derivative of -n**7/126 - 89*n**6/90 - 652*n**5/15 - 670*n**4 + 1800*n**3 + 9000*n**2 + 50*n - 4. Factor m(z).
-(z - 2)*(z + 1)*(z + 30)**3/3
Let z(p) = -p**2 + 19*p - 14. Let c be z(18). Suppose u - 22 = -c*m, -48 = -2*u - 2*u + 4*m. Factor 16*r + 2*r**5 - u*r - 4*r**4 - 4*r**5 + 4*r**2.
-2*r*(r - 1)*(r + 1)**3
Let a = 1009 + -1554. Let h = a + 547. Factor 2/3*r**h + 0*r - 2/3.
2*(r - 1)*(r + 1)/3
Let h = 2/1124991 - -1124981/5624955. Factor -h*f**3 - 19/5*f + 12/5 + 8/5*f**2.
-(f - 4)*(f - 3)*(f - 1)/5
Suppose -762 = -732*r + 351*r. Suppose 0*f - 2/9*f**r - 2/9*f**3 + 0 = 0. Calculate f.
-1, 0
Let t(g) be the third derivative of g**6/60 - 77*g**5/6 - 773*g**4/12 - 129*g**3 - 601*g**2. Determine q, given that t(q) = 0.
-1, 387
Factor 0*u + 0 - 2/7*u**2 + u**4 + 5/7*u**3.
u**2*(u + 1)*(7*u - 2)/7
Let q = 5817854/7999519 + -2/727229. Solve 8/11*d**3 + 2/11*d**4 + 6/11*d**2 - 8/11*d - q = 0 for d.
-2, -1, 1
Suppose 20*x - 5 = -30*x + 49*x. Suppose 2/9*l**4 + 2/9*l**2 + 10/9*l - 4/9 - 14/9*l**3 + 4/9*l**x = 0. What is l?
-2, -1, 1/2, 1
Determine i, given that -24 - 523*i**2 + 246*i + 1042*i**2 - 456*i**2 = 0.
-4, 2/21
Let r(i) be the first derivative of -2*i**3/9 + 6*i**2 - 64*i/3 - 736. Suppose r(g) = 0. What is g?
2, 16
Let g(p) be the second derivative of p**6/1440 + p**5/160 - p**4/24 - p**3/6 + 20*p**2 - 6*p + 10. Let x(k) be the second derivative of g(k). Factor x(i).
(i - 1)*(i + 4)/4
Factor 88*n**3 - 89*n**2 + 267*n**2 - 72*n + 468*n**2 - 648 + 2*n**4 - 16*n**3.
2*(n - 1)*(n + 1)*(n + 18)**2
Factor 1760/3*b - 1/3*b**3 + 14/3*b**2 + 7200.
-(b - 54)*(b + 20)**2/3
Let d = 134341 - 134337. Solve -2/3*a**4 + 0 - d*a**3 + 64/3*a + 0*a**2 = 0.
-4, 0, 2
Let c(u) = -6*u + 86. Let g be c(11). Solve -16*f**2 + g*f**5 + 28*f**4 - 6*f**5 - 12*f**4 - 50*f**5 + 36*f**3 = 0.
-1, 0, 4/9, 1
Let o(r) be the first derivative of r**4/6 + 98*r**3/3 - 148*r**2/3 + 2452. Determine h, given that o(h) = 0.
-148, 0, 1
Let t be (-672)/360*(-6)/21. Find i, given that -4/15*i**3 - t*i**4 + 8/15*i**2 + 0 - 2/15*i**5 + 2/5*i = 0.
-3, -1, 0, 1
Let t(u) be the second derivative of -25*u**5/4 - 450*u**4 - 2115*u**3/2 - 945*u**2 - 351*u. Factor t(d).
-5*(d + 42)*(5*d + 3)**2
Let p = -624 + 17473/28. Let v = p - -1/4. Solve -1/7*y**5 + v*y**4 - 2/7*y**2 + 0*y**3 + 0 + 1/7*y = 0.
-1, 0, 1
Let o(r) be the third derivative of 1/6*r**4 + 1/24*r**3 - 5*r**2 + 4/15*r**5 + 4*r + 0. Determine y so that o(y) = 0.
-1/8
Suppose 0 = 3*v - 5*p - 5075, 8*v = 6*v - 5*p + 3400. Let 3*d**2 + v - 53*d + 33 - 115*d + 624 = 0. Calculate d.
28
Let q(r) = -5*r**2 - 340*r + 651. Let w(b) = -2*b**2 - 112*b + 218. Let p(m) = -2*q(m) + 7*w(m). Factor p(n).
-4*(n - 2)*(n + 28)
Let 6*x**3 + 7 - 71 + 31 + 16*x**4 + 33 = 0. What is x?
-3/8, 0
Solve 165/2 - 329/2*t + 1/2*t**3 + 163/2*t**2 = 0.
-165, 1
Let g(z) be the second derivative of 4*z**6/21 + 97*z**5/5 + 11492*z**4/21 - 2312*z**3/21 - 1749*z. Let g(b) = 0. What is b?
-34, 0, 1/10
Solve 14/11*b + 20/11 + 2/11*b**2 = 0.
-5, -2
Let n = -169 + 176. What is v in -2*v**2 + n*v - v**2 + 5*v**2 - 2*v**3 - 3*v = 0?
-1, 0, 2
Suppose -77*r - 20*r = 18*r. Let p(k) be the third derivative of r*k**4 - 4*k**2 + 0*k**5 + 0*k + 0*k**3 + 0 + 0*k**6 - 1/105*k**7 - 1/168*k**8. Factor p(h).
-2*h**4*(h + 1)
Suppose 0 = 26*g - 104*g. Let y(i) be the third derivative of 0*i + 1/48*i**4 + 1/240*i**5 + g*i**3 + 0 + 5*i**2. Factor y(q).
q*(q + 2)/4
Let q(k) be the second derivative of -k**5/90 - 23*k**4/27 - 131*k**3/27 - 86*k**2/9 + 5*k + 37. Determine d, given that q(d) = 0.
-43, -2, -1
Let p(o) be the third derivative of o**8/112 - o**7/70 - 3*o**6/10 - o**5/5 + 2*o**4 - 2*o**2 + 451*o. Factor p(m).
3*m*(m - 4)*(m - 1)*(m + 2)**2
Let z(i) be the third derivative of 2*i**7/105 + i**6/15 - 7*i**5/15 - 4*i**4/3 + 8*i**3 + 215*i**2 + 2*i. Solve z(k) = 0 for k.
-3, -2, 1, 2
Let i be ((-24)/14)/(4*2/56). Let z be -1 + 1 - i/20. Factor z - 1/5*k**2 + 2/5*k.
-(k - 3)*(k + 1)/5
Suppose 273*r**2 - 218*r**3 - 45*r**2 - 7*r**3 + 123*r**4 + 63*r**3 - 3*r**5 - 186*r**3 = 0. What is r?
0, 1, 2, 38
Factor 258*i + 57/2*i**2 + 230 + 1/2*i**3.
(i + 1)*(i + 10)*(i + 46)/2
Let v be 10*(15/(-5) + (-130)/(-39)). Let g(y) = y**2 - 6*y - 5. Let r be g(7). Find a such that 4/9 - r*a + v*a**2 + 2/3*a**4 - 22/9*a**3 = 0.
2/3, 1
Let s(u) be the third derivative of u**7/210 - 47*u**6/120 + 191*u**5/20 - 437*u**4/24 - 529*u**3/3 + 3623*u**2. Factor s(a).
(a - 23)**2*(a - 2)*(a + 1)
Let g(i) be the second derivative of -1/8*i**4 + i**3 - 2 - 4*i - 9/4*i**2. Factor g(o).
-3*(o - 3)*(o - 1)/2
Suppose 426*v = -37*v + 34*v + 858. Find f, given that 32/9*f + 1/9*f**v + 256/9 = 0.
-16
Let t be (3/1)/24 + (-3598)/(-16). Let c be ((-36)/t)/((-1)/20). Suppose 4/5*r**2 - c*r + 4/5*r**3 - 16/5 = 0. What is r?
-2, -1, 2
Factor -22*w - 4*w**2 - 16*w + 5*w**2 - 56 + w**2 + 14*w.
2*(w - 14)*(w + 2)
Let a = 6639611/13031130 - -2/434371. Let j = a + 11/70. Factor -j*m + 4/5 + 2/15*m**2.
2*(m - 3)*(m - 2)/15
Let y(n) be the first derivative of 4*n**3/3 + 62*n**2 + 710. Factor y(r).
4*r*(r + 31)
Suppose -6*h - 9*h = -1080. Let u = h + -69. Factor -2/5*i - 4/5*i**2 + 0 - 2/5*i**u.
-2*i*(i + 1)**2/5
Let j = -161794 - -323589/2. Determine m, given that -11/2*m - 3 - j*m**3 - 3*m**2 = 0.
-3, -2, -1
Factor -2/5*c**3 + 34/5*c**2 - 32/5*c + 0.
-2*c*(c - 16)*(c - 1)/5
Let k = -305/52 - 18/13. Let g = 143/12 + k. Factor 2/3 + 2*a**4 + 16/3*a**2 + 3*a + 1/3*a**5 + g*a**3.
(a + 1)**4*(a + 2)/3
Let n(g) be the third derivative of g**