 - -72. Let 24*w - 35*w**2 - u*w**2 - 85*w**2 + 147*w**4 + 44*w**2 + 210*w**3 = 0. Calculate w.
-2, 0, 2/7
Let l(x) be the first derivative of 63 - 2/27*x**3 - 5/9*x**2 + 0*x. Factor l(c).
-2*c*(c + 5)/9
Let b(p) = 3*p**2 + 12*p - 14. Let l be b(4). Let a = 86 - l. Factor a*v**2 + 8 + 5 - 17.
4*(v - 1)*(v + 1)
Suppose 56*c = 6*c + 76*c. Let c*s**2 - 9/10*s + 1/10*s**3 + 0 = 0. What is s?
-3, 0, 3
Factor -36 + 27/2*p - 1/2*p**2.
-(p - 24)*(p - 3)/2
Let q = -111653/21 + 5317. Let v(p) be the second derivative of 13*p + 0 + q*p**3 - 6/7*p**2 + 1/21*p**4. Factor v(y).
4*(y - 1)*(y + 3)/7
Let x(h) = -h**3 + 275*h**2 + 405*h - 35604. Let l be x(276). Factor -1/8*z + l + 1/8*z**2.
z*(z - 1)/8
Let z(y) be the third derivative of -y**5/80 + 437*y**4/16 - 190969*y**3/8 - y**2 + 1975. Solve z(k) = 0 for k.
437
Let s(c) = -4*c**2 + 31206*c - 60839996. Let b(f) = 16*f**2 - 124827*f + 243359982. Let g(m) = -2*b(m) - 9*s(m). Factor g(a).
4*(a - 3900)**2
Let c(o) be the second derivative of -24/11*o**3 - 2/11*o**4 + 0*o**2 + 56*o + 0 + 1/11*o**5 - 1/165*o**6. Solve c(m) = 0.
-2, 0, 6
Let b be 1/(((-5)/(-10))/(22/2)). Factor -b*l**3 + 12*l + 11*l**2 - 18*l - 3*l**2 + 20*l**3.
-2*l*(l - 3)*(l - 1)
Let u(r) = 8*r**2 + 2*r - 1. Let x(l) = -27*l**2 + 333*l - 333. Let w(c) = 3*u(c) + x(c). Factor w(d).
-3*(d - 112)*(d - 1)
Determine c so that 0*c + 0 + 66/13*c**4 + 28/13*c**3 + 0*c**2 - 10/13*c**5 = 0.
-2/5, 0, 7
Suppose -460*f = -212 - 1628. Factor 2*u - 2*u**2 + 1/2*u**f - 1/2*u**3 + 0.
u*(u - 2)*(u - 1)*(u + 2)/2
Let n(g) be the first derivative of 3*g**4/20 + 34*g**3/5 + 96*g**2 + 1536*g/5 - 2690. Factor n(l).
3*(l + 2)*(l + 16)**2/5
Factor -156792/5*x**2 + 77284/5*x**3 + 4464/5*x - 32/5.
4*(x - 2)*(139*x - 2)**2/5
Suppose 11552/17*h**3 - 894/17*h - 18/17 - 10640/17*h**2 = 0. Calculate h.
-3/76, 1
Let p(i) be the second derivative of i**6/75 + i**5/50 - 39*i**4/5 + 612*i**3/5 - 4104*i**2/5 + 751*i. Factor p(b).
2*(b - 6)**3*(b + 19)/5
Let l(f) = f + 7. Let u be l(-5). Factor 15*d**3 - 18 - 14*d**3 + 3*d**u - 4*d + 6.
(d - 2)*(d + 2)*(d + 3)
Factor -920/3 + 176/9*a**2 + 4/9*a**3 - 428/9*a.
4*(a - 5)*(a + 3)*(a + 46)/9
Let n = 220645 - 16990066/77. Let w = n - -62/11. Find s such that -12/7*s**4 + 12/7*s**2 + 0 + 3/7*s - w*s**3 = 0.
-1, -1/4, 0, 1
Let q(i) = 75*i**3 - 10607*i**2 + 4229*i - 417. Let l(m) = 975*m**3 - 137892*m**2 + 54975*m - 5418. Let t(x) = 2*l(x) - 27*q(x). What is h in t(h) = 0?
1/5, 141
Let l be ((-2)/(-6)*3)/(6/12). Determine g so that -37*g**l - 4*g + 8*g - 2 + 71*g**2 - 36*g**2 = 0.
1
Suppose 36*y**3 + 424*y**4 + 357*y**4 - 37*y**2 - 780*y**4 = 0. What is y?
-37, 0, 1
Let u(b) be the first derivative of -2*b**6/3 - 7*b**5/5 + b**4/3 + 2*b**3 + 61*b - 44. Let k(t) be the first derivative of u(t). Suppose k(j) = 0. Calculate j.
-1, 0, 3/5
Suppose 0 = 4*v - l + 10, -v + 35*l - 36*l + 10 = 0. Determine r, given that 3/2*r**3 + 135/2*r**2 + v*r + 0 = 0.
-45, 0
Let u(g) be the third derivative of -g**5/330 + g**4/3 - 44*g**3/3 + 783*g**2. Let u(p) = 0. What is p?
22
Let z be (-2)/((-8 - -10)/2). Let q be (-3 - -2 - 0)*z/6. Factor 4/3 + q*k**4 - k**3 - 5/3*k**2 + k.
(k - 4)*(k - 1)*(k + 1)**2/3
Let p be ((-6)/4 - 1)*-2. Let u(j) = -13*j**3 + 9*j**2 - 14*j - 2. Let y(s) = -1 + 23*s - 47*s - 2*s**3 + 23*s. Let q(g) = p*y(g) - u(g). Factor q(a).
3*(a - 1)**3
Suppose 0 = -2*v + 3*q + 567, -1407 = -5*v - q - 2*q. Let p be (7 - v/30)/(-4). Factor -1/5*x**3 - p*x**2 + 0 - 2/5*x.
-x*(x + 1)*(x + 2)/5
Let t(w) = -6088*w - 12174. Let m be t(-2). Solve -3/2*h**m + 27 + 9/2*h = 0 for h.
-3, 6
Factor 0 - 2/5*r**2 - 1842/5*r.
-2*r*(r + 921)/5
Let k(z) be the third derivative of 0 + 3/55*z**5 + 17/660*z**6 - 14*z - 3*z**2 + 0*z**4 + 0*z**3 - 1/1155*z**7. Determine a so that k(a) = 0.
-1, 0, 18
Let d(g) be the second derivative of 3*g**5/20 - 11*g**4/4 + 7*g**3/2 + 441*g**2/2 + 304*g. Let d(t) = 0. What is t?
-3, 7
Let j(v) be the second derivative of -v**4/9 - 16*v**3/9 - 1230*v. Factor j(k).
-4*k*(k + 8)/3
Let w(u) be the first derivative of 2/65*u**5 - 11/26*u**4 + 0*u**2 - 128 + 0*u + 20/39*u**3. Factor w(y).
2*y**2*(y - 10)*(y - 1)/13
Let k be -10*((-7)/2 - -4). Let z be ((-1)/(2/k))/((-1)/(-2)). Factor -8 + 3*o**2 + z*o + o - o**2.
2*(o - 1)*(o + 4)
Suppose p = 6*d - 8*d + 33, -d + 399 = 128*p. Solve 2/3*m**5 + 2/3*m**4 - 2/3*m**2 - 2*m**p + 4/3*m + 0 = 0.
-2, -1, 0, 1
Let z(q) be the first derivative of 16/3*q**2 + 2/15*q**5 + 16/9*q**3 - 7/6*q**4 + 0*q + 55. Factor z(w).
2*w*(w - 4)**2*(w + 1)/3
Let i(x) = -x**3 - 8*x**2 + 13*x + 110. Let q be i(-8). Suppose 0 = -21*m + 90 - q. Factor 0*d**3 - 1/7*d**m + 1/7*d**5 + 0*d**2 + 0*d + 0.
d**4*(d - 1)/7
Let l(z) be the first derivative of 2*z**5/35 + 2554*z**4/7 + 5797012*z**3/7 + 4930355300*z**2/7 - 9878111854*z/7 - 1711. Factor l(q).
2*(q - 1)*(q + 1703)**3/7
Let l(f) be the second derivative of -15*f**7/14 - 23*f**6 - 481*f**5/4 + 460*f**4/3 - 160*f**3/3 + 2394*f + 2. Find t, given that l(t) = 0.
-8, 0, 1/3
Let n be 2*((84/(-60) - 7758/630) + 14). Factor 0*k**3 + 8/7*k**4 + 0*k + n*k**5 + 0 + 0*k**2.
4*k**4*(k + 2)/7
Let f(l) be the third derivative of -8/21*l**4 - 1/588*l**8 - 12*l**2 - 8/7*l**3 + 0*l + 0 + 3/70*l**6 + 1/21*l**5 - 2/735*l**7. Solve f(t) = 0.
-3, -1, 2
Let l(b) be the third derivative of 1/12*b**5 + 0 + 0*b**3 + 0*b - 5/24*b**4 - 75*b**2. Suppose l(p) = 0. What is p?
0, 1
Suppose 18*n + 12 = 22*n. Suppose -2*w + 4 = 2*h, 4*h - n*h + 5*w = -10. Factor 30*t + 259*t**3 - 1 - 294*t**4 - 343*t**h + 9 + 54*t + 286*t**2.
-(t - 1)*(t + 1)*(7*t + 2)**3
Let r be 4/(-14) + 530/91. Let i = 1000291 - 1000291. Factor r*u + i + 24/13*u**2 + 2/13*u**3.
2*u*(u + 6)**2/13
Let y(k) be the first derivative of k**6/9 + 60*k**5 + 51071*k**4/6 + 199804*k**3/9 - 17024*k**2 - 200704*k/3 - 1916. Find w such that y(w) = 0.
-224, -2, -1, 1
Let i = 74567 - 74565. Factor -10/21*k**2 - 8/21 - i*k.
-2*(k + 4)*(5*k + 1)/21
Let f(h) be the third derivative of 3*h**8/56 - 412*h**7/105 - 947*h**6/60 - 311*h**5/15 - 8*h**4 + 12*h**2 + 7*h - 16. Find d, given that f(d) = 0.
-1, -2/9, 0, 48
Let o = 3822156/6842143 + 39/5227. Let l = o - -1/187. Factor 2/7*y**2 - l*y - 6/7.
2*(y - 3)*(y + 1)/7
Let t(f) be the first derivative of 3*f**6/2 - 246*f**5/5 - 47*f**4 + 568*f**3/3 - 112*f**2 + 2683. Determine u, given that t(u) = 0.
-2, 0, 2/3, 28
Factor -59/3*r**2 + 57 - 1/3*r**3 - 37*r.
-(r - 1)*(r + 3)*(r + 57)/3
Let b = -3562/11 - -10862/33. Factor -b + 136/3*n - 289/3*n**2.
-(17*n - 4)**2/3
Suppose s - 16 = -4*c + 6*s, 2*c + 4*s - 8 = 0. Factor c*m**5 + 19*m - 29*m + 100*m**3 - 40*m**4 + 10*m.
4*m**3*(m - 5)**2
Let t(w) be the third derivative of 13*w**4/24 - 16*w**3/3 - w**2 + 7*w. Let h be t(4). Factor -h*l**2 + 32*l**3 + 4*l**4 - 8*l**3 + 56*l**2.
4*l**2*(l + 3)**2
Let y(z) = z**3 + z + 3. Let s(x) = 5*x**3 - 258*x**2 + 22192*x - 636044. Let p(v) = 3*s(v) - 12*y(v). Factor p(b).
3*(b - 86)**3
Let k(d) be the first derivative of -3*d**5/2 + 219*d**4/8 - 120*d**3 + 69*d**2 + 120*d + 905. Determine m, given that k(m) = 0.
-2/5, 1, 4, 10
Factor 0 + 46/5*l - 1/5*l**2.
-l*(l - 46)/5
Let n(s) be the first derivative of -s**5/2 + 15*s**4 - 115*s**3/6 + 9076. Factor n(j).
-5*j**2*(j - 23)*(j - 1)/2
Let v = 8487 - 8479. Factor 20/7 - v*c - 12/7*c**2.
-4*(c + 5)*(3*c - 1)/7
Find n such that -1/6*n**2 + 13/6*n + 15 = 0.
-5, 18
Let x(h) = 11*h**2 + 895*h + 2508. Let m(v) = -13*v**2 - 910*v - 2509. Let u(k) = -3*m(k) - 4*x(k). Suppose u(l) = 0. What is l?
-167, -3
Let s = 401197/312053 - -2/44579. What is q in -6/7*q**4 + 0*q + 3/7*q**5 - s*q**3 + 0*q**2 + 0 = 0?
-1, 0, 3
Let a(i) be the third derivative of -i**5/630 + i**4/63 + 32*i**3/63 + 83*i**2 + 6*i - 3. Factor a(v).
-2*(v - 8)*(v + 4)/21
Suppose -488 + 515 = 9*v. Suppose 4*r = -3*z + 16 - 1, v*z = 3. Solve -4/7*h**r + 6/7*h**2 - 4/7*h + 1/7*h**4 + 1/7 = 0 for h.
1
Let n(k) = -3*k**3 - 2856*k**2 - 910116*k - 96472302. Let l(b) = 3*b**3 + 2855*b**2 + 910116*b + 96472303. Let p(c) = 6*l(c) + 7*n(c). Factor p(h).
-3*(h + 318)**3
Suppose 677*n - 5*n**4 + 228 - 105*n**2 - 187*n - 228 - 60*n**3 = 0. What is n?
-7, 0, 2
Let q(c) be the third derivative of -32 - 1/32*c**4 - 1/240*c**5 - 2*c**2 + 1/6*c**3 + 0*c. Factor q(y).
-(y - 1)*(y + 4)/4
Let d(a) be the third derivative of a**6/40 - 49*a