4
Let y be (-2*1/4)/((-108)/1176). Let q = -16/3 + y. Solve 0*l**3 + 0*l - 16/9 + 8/9*l**2 - q*l**4 = 0.
-2, 2
Let j(r) = -2*r**3 + 4*r**2 - r + 6. Let v(a) = -10*a**3 + 412*a**2 + a - 382. Let k(z) = -3*j(z) + v(z). Factor k(c).
-4*(c - 100)*(c - 1)*(c + 1)
Suppose -4*j + 8 = 0, 1 = 5*a - 2*j - 5. Let -81 + 30*q + 29 + 20 + 3*q**a - 1 = 0. What is q?
-11, 1
Find w, given that 28/3 - 8/3*w**2 - 20/3*w**4 - 2/3*w**5 - 44/3*w**3 + 46/3*w = 0.
-7, -2, -1, 1
Let c(a) be the third derivative of -5*a**2 - 5*a + 0 - 48/13*a**3 - 5/78*a**5 + 10/13*a**4. Find q, given that c(q) = 0.
12/5
Let m be (-24)/28 - 78/(-91). Let s(j) be the first derivative of -12/5*j**5 + 0*j**2 + m*j + 10/3*j**6 - 8 - 32*j**4 - 16*j**3. Suppose s(t) = 0. What is t?
-2, -2/5, 0, 3
Let w(s) = s**2 - 17*s + 15. Let c be w(17). Factor -33*l**2 + l + 3*l**4 + c*l + 5*l**2 - 2*l**4 + 12*l**3 - l**5.
-l*(l - 2)**2*(l - 1)*(l + 4)
Let y(j) be the third derivative of j**6/300 + 1526*j**5/75 + 582169*j**4/15 - 68*j**2 + 9*j - 4. Solve y(o) = 0 for o.
-1526, 0
Let l(s) be the third derivative of 0*s**3 + 23/56*s**4 + 0*s + 0 - 151*s**2 + 1/140*s**5. Solve l(p) = 0.
-23, 0
Let f(v) be the second derivative of -v**6/70 + 3*v**5/10 - 61*v**4/28 + 6*v**3 - 54*v**2/7 + 1466*v. Factor f(i).
-3*(i - 6)**2*(i - 1)**2/7
Let f(d) be the second derivative of -25/12*d**4 + 0*d**2 + 3 + 11*d + 10/3*d**3 + 1/4*d**5. Suppose f(v) = 0. What is v?
0, 1, 4
Let x(z) = 2*z**4 + 22*z**2 + 4*z - 24. Let t(h) = -h**4 - h**2 + h. Suppose -9*w - 4*y + 3 = -12*w, -y + 4 = -4*w. Let f(m) = w*x(m) - 4*t(m). Factor f(r).
2*(r - 3)*(r - 1)*(r + 2)**2
Let b(h) = -h**2 - 242*h - 14616. Let y be b(-126). Let 2/19*d**4 + y*d**2 - 2/19 - 4/19*d**3 + 4/19*d = 0. Calculate d.
-1, 1
Let t be 5*1/(-1)*(-3 - (-4)/20). Let w(f) be the first derivative of -14*f**3 + 9*f**4 - t + 54/5*f**5 + 8*f - 8*f**2. What is a in w(a) = 0?
-1, -2/3, 1/3, 2/3
Suppose 7*n = -56 + 84. Suppose -7*c - n = -4*v - 8*c, -4*c = 16. Solve 1/3*z**v + 0 + z = 0 for z.
-3, 0
Let w be (28/28)/((-7)/4381). Let j = w - -628. Let -j*p + 3/7*p**2 + 0 = 0. Calculate p.
0, 5
Factor 602/9*t**2 + 20/9*t + 118/3*t**3 + 0.
2*t*(3*t + 5)*(59*t + 2)/9
Find r such that 6*r - 243/2*r**2 - 3/2*r**3 + 486 = 0.
-81, -2, 2
Let y(d) = 2*d**2 + 48*d + 299. Let o(w) = -49 + 100 - 50. Let f(s) = -22*o(s) + 2*y(s). Suppose f(c) = 0. Calculate c.
-12
Let c(k) be the first derivative of k**6/105 - 9*k**5/70 + 5*k**4/14 - k**3/3 + 70*k + 85. Let v(j) be the first derivative of c(j). Factor v(a).
2*a*(a - 7)*(a - 1)**2/7
Let b(m) = 4*m**4 - 20*m**3 + 137*m**2 - 207*m + 98. Let w(s) = -8*s**4 + 45*s**3 - 275*s**2 + 413*s - 196. Let l(h) = 7*b(h) + 4*w(h). Factor l(a).
-(a - 2)*(a - 1)*(2*a - 7)**2
Let z = 967 + -965. Suppose -13*w - 2 = -2*b - 14*w, -z*b + 4*w + 12 = 0. Factor -1/8*o - 1/8*o**b + 3/4.
-(o - 2)*(o + 3)/8
Let o(t) be the third derivative of t**7/70 - 7*t**6/20 + 33*t**5/20 - 2*t**2 - 30*t. Find r such that o(r) = 0.
0, 3, 11
Let f(y) be the second derivative of -y**6/24 - 3*y**5/80 - 747*y. Solve f(c) = 0 for c.
-3/5, 0
Let m(k) be the first derivative of k**4/3 - 22*k**3/3 + 18*k - 117. Let x(g) be the first derivative of m(g). Factor x(t).
4*t*(t - 11)
Let w(n) be the first derivative of n**6/2 + 87*n**5/5 - 3*n**4/2 - 58*n**3 + 3*n**2/2 + 87*n - 1752. Determine d so that w(d) = 0.
-29, -1, 1
Suppose 7*g - 12*g + 3*w + 192 = 0, -w - 4 = 0. Let j be g + (-1)/(-2)*0. Let -25*y + 4 + 2 - j + 5*y**2 = 0. Calculate y.
-1, 6
Let p(x) be the second derivative of 1/360*x**5 - 9/2*x**2 + 0*x**3 - 36*x - 1/144*x**4 + 0. Let c(g) be the first derivative of p(g). Factor c(s).
s*(s - 1)/6
Suppose -67 = 4*r - 275. Suppose -2*z + 2 = -r. Find g, given that -5*g - 2*g**3 + 3*g - 27 + z - 4*g**2 = 0.
-1, 0
Let l(z) be the second derivative of 1/3*z**4 + 179*z + 98/3*z**3 + 0 + 96*z**2. Let l(b) = 0. What is b?
-48, -1
Let u = 529571/211830 - -2/105915. Factor -1/2*g**2 + 12 + u*g.
-(g - 8)*(g + 3)/2
Let g(d) be the third derivative of -d**5/15 - 487*d**4/3 + 12069*d**2. Factor g(z).
-4*z*(z + 974)
Suppose 2*q + 0*q + f = 1500, -q + 750 = -5*f. Let c = q + -748. Solve -1/6 + 1/3*o - 1/6*o**c = 0.
1
Factor 182/5*z + 2/5*z**2 + 528/5.
2*(z + 3)*(z + 88)/5
Let c = -55470452/21 + 2642316. Let j = 866 - c. Find d such that 0 + 0*d + j*d**2 - 4/21*d**4 - 2/21*d**3 = 0.
-1, 0, 1/2
Factor -6*j**4 + 3/4*j**5 + 0*j**2 + 0*j + 0 + 9*j**3.
3*j**3*(j - 6)*(j - 2)/4
Suppose -5*o + 28 = 4*v + 9, -3*v = -4*o + 9. Find b such that -32/3 + 2*b**o + 296/9*b - 80/3*b**2 = 0.
2/3, 12
Let h(i) be the first derivative of i**5/4 - 5*i**4/3 - 55*i**3/6 - 15*i**2 + 68*i - 73. Let n(f) be the first derivative of h(f). Solve n(m) = 0.
-1, 6
Let k(x) = -6*x + 112. Let j be k(18). What is u in -9*u**2 - 6*u - 32*u**4 + 19*u**4 + 16*u**j = 0?
-1, 0, 2
Let p(v) = 127*v**2 + 440*v + 2391. Let o(q) = 28*q**2 + 110*q + 598. Let z(g) = 9*o(g) - 2*p(g). Solve z(m) = 0.
-5, 60
Factor 5071*x - 11047 + 3*x**2 - 385244 - 457*x + 1598163 + 572211.
3*(x + 769)**2
Let t(g) be the first derivative of g**6/1080 - g**5/60 + 16*g**3/3 + 45. Let n(z) be the third derivative of t(z). Let n(q) = 0. Calculate q.
0, 6
Let t(c) be the second derivative of c**8/112 - c**7/35 - c**6/40 + c**5/10 - 99*c**2/2 + 121*c. Let d(k) be the first derivative of t(k). Factor d(v).
3*v**2*(v - 2)*(v - 1)*(v + 1)
Factor 8/9*c**3 - 1340/9*c + 242/9*c**2 - 350/9.
2*(c - 5)*(c + 35)*(4*c + 1)/9
Let l(g) be the second derivative of -g**4/48 - 13*g**3/6 + 53*g**2/8 - 10596*g. Factor l(z).
-(z - 1)*(z + 53)/4
Let s(q) = q**4 - q**3 + q**2 - 15*q + 1. Let g(d) = 4*d**4 + 2*d**3 - 8*d**2 - 42*d + 2. Let u(t) = g(t) - 2*s(t). Find h, given that u(h) = 0.
-3, -1, 0, 2
Find y such that 6*y - 5*y**3 + 1486*y**5 - 1485*y**5 + 0*y**3 + 5*y**2 - 2*y**3 - 5*y**4 = 0.
-1, 0, 1, 6
Factor -4*o**4 - 431*o**2 + 2463*o**2 - 384*o**3 - 233*o**3 - 1411*o**3.
-4*o**2*(o - 1)*(o + 508)
Let m(o) be the third derivative of -o**5/75 + 21*o**4/2 + 632*o**3/15 - 2*o**2 + 85*o - 6. Factor m(x).
-4*(x - 316)*(x + 1)/5
Let r = 26 + 46. Let y = 74 - r. Solve -6*h**2 - 11*h**3 + 7*h + 0*h**y - 2 + 4*h + 8*h**2 = 0 for h.
-1, 2/11, 1
Let c(q) be the second derivative of q**4/84 - 23*q**3/42 + 11*q**2/7 + 376*q + 2. Solve c(o) = 0 for o.
1, 22
Let u = -117 - -119. Factor -c**2 + 7*c**2 - c**3 - 4*c**u.
-c**2*(c - 2)
Let m(v) be the second derivative of -v**5/180 + v**4/9 - 5*v**3/6 - 3*v**2/2 + v - 35. Let h(q) be the first derivative of m(q). Factor h(n).
-(n - 5)*(n - 3)/3
Suppose 2*k + 63*b - 55*b - 88 = 0, 52 = 3*k + 4*b. Factor -5*a**2 + 0 - 3*a - 1/3*a**k - 7/3*a**3.
-a*(a + 1)*(a + 3)**2/3
Determine s, given that -34*s**3 + 2*s**4 - 18 + 20*s - 2*s**3 + 16*s**3 + 16*s**2 = 0.
-1, 1, 9
Suppose 3*o = 3*r - 27, -21*r + 26*r - 3*o - 37 = 0. Let w(q) be the second derivative of 0*q**2 + 1/2*q**3 - r*q + 1/4*q**4 + 0. What is a in w(a) = 0?
-1, 0
Let t(n) = 1103*n - 17640. Let d be t(16). Determine w, given that -d*w**3 + 61/8*w**2 - 7/2*w**4 - 3/4 + 1/8*w = 0.
-3, -2/7, 1/2
Factor -5/4*y**2 - 3735/4*y + 0.
-5*y*(y + 747)/4
Let k = -13198 - -13200. Let v(p) be the second derivative of 1/54*p**4 + 43*p + 0*p**3 + 0 + 1/180*p**5 + 0*p**k. Suppose v(u) = 0. Calculate u.
-2, 0
Let w(g) be the third derivative of 16*g**2 - 1/60*g**6 - 1/15*g**5 + 1/210*g**7 + 1/12*g**4 + 1/2*g**3 + 0*g + 1. Solve w(t) = 0.
-1, 1, 3
Let d(a) be the third derivative of -a**4/24 + a**3/3 + 11*a**2. Let k be d(0). Factor 2*v**k - 120*v**3 - v**4 + 119*v**3 - 2*v**2.
-v**3*(v + 1)
Factor -5/2 - 27/4*k - 3/4*k**3 - 5*k**2.
-(k + 1)*(k + 5)*(3*k + 2)/4
Factor -233*v**2 + 101*v**2 - 295 - 635 + 137*v**2 - 125*v.
5*(v - 31)*(v + 6)
Suppose 3*a - 4*n = -49 + 57, 4*n + 8 = a. Let x(f) be the first derivative of 0*f**3 + 16 + 0*f**2 - 1/4*f**4 + a*f. Factor x(y).
-y**3
Let m(u) be the second derivative of 3*u**7/28 - 13*u**6/2 + 307*u**5/10 - 47*u**4 + 80*u**3/3 - 314*u + 3. Determine n so that m(n) = 0.
0, 2/3, 2, 40
Let w be (1218/(-50))/((-8)/760). Let y = -2314 + w. Factor 3/5*z**2 - 27/5 + 9/5*z - y*z**3.
-(z - 3)**2*(z + 3)/5
Let w(y) = -25*y**3 + 1147*y**2 + 944*y + 172. Let n(q) = -1 - 37*q + q**2 + 38*q - 2*q**2 - 1. Let j(z) = -40*n(z) + 5*w(z). Find c such that j(c) = 0.
-2/5, 47
Find k such that 495/2*