k).
3*(k + 1)*(k + 13)**2
Let z(o) be the third derivative of -o**5/48 + 6605*o**4/96 - 275*o**3 - 3060*o**2. Solve z(p) = 0.
1, 1320
Let i = -197/273715 - -310277923/372799830. Let u = i - -2/1135. Factor 0 + 0*p + u*p**4 + 0*p**3 - 5/6*p**2.
5*p**2*(p - 1)*(p + 1)/6
Determine o so that o**2 + 409*o - 348 - o**2 - o**2 - 466 = 0.
2, 407
Let u(l) = 425*l + 130475. Let i be u(-307). Factor 2/13*x**4 + 0*x + i*x**2 + 0*x**3 + 0.
2*x**4/13
Let w(c) be the second derivative of -129*c + 62/3*c**3 + 0 - 4*c**5 - 8*c**2 - 37/2*c**4 + 16/15*c**6. Factor w(g).
2*(g - 4)*(g + 2)*(4*g - 1)**2
Let r = -1063 + 3197/3. Let q(f) be the second derivative of -1/10*f**5 + 5/6*f**4 + 4*f**2 - r*f**3 - 3*f + 0. Determine c so that q(c) = 0.
1, 2
Let y = -98480 - -98482. Factor 2/7*s**y - 30/7*s - 32/7.
2*(s - 16)*(s + 1)/7
Let p(v) be the second derivative of 5/12*v**4 - 205/3*v**3 + 8405/2*v**2 - 51*v - 3. Factor p(o).
5*(o - 41)**2
Let o(r) be the second derivative of r**6/20 + 63*r**5/20 + 481*r**4/8 + 210*r**3 + 300*r**2 + 578*r. Factor o(w).
3*(w + 1)**2*(w + 20)**2/2
Let z = -3361244 + 870560808/259. Let f = -8/37 - z. Factor -2/7*c**3 - 8/7*c**2 + f + 6/7*c.
-2*(c - 2)*(c + 3)**2/7
Let t(v) be the third derivative of -v**5/390 + 1325*v**4/26 - 5266875*v**3/13 - 8*v**2 + 303. Solve t(a) = 0.
3975
Suppose 3*g = 3 + 3. Let a(s) = s**3 - 39*s**2 - 23*s + 903. Let k be a(39). Factor -k*h + 6 + 0*h - h + 12*h - h**g.
-(h - 6)*(h + 1)
Let y(o) be the second derivative of -o**7/77 - 12*o**6/55 - 51*o**5/110 + 15*o**4/11 + 1561*o. Find q such that y(q) = 0.
-10, -3, 0, 1
Suppose 0 = -3*f - h - 2 - 25, 1 = -2*f + 5*h. Let b be -8 - f/(240/258). Determine q so that 0 + 6/5*q - b*q**4 + 3/5*q**2 - 6/5*q**3 = 0.
-2, -1, 0, 1
Let z(w) be the second derivative of -1/30*w**5 + 4 - 8*w - 56/9*w**3 + 13/18*w**4 + 80/3*w**2. Factor z(u).
-2*(u - 5)*(u - 4)**2/3
Let q(w) be the second derivative of -2*w**7/119 - 53*w**6/255 - 3*w**5/170 + 253*w**4/51 - 172*w**3/17 + 72*w**2/17 + 9300*w. Solve q(m) = 0 for m.
-6, 1/6, 1, 2
Let x(k) = 66*k**3 + 170*k**2 + 75*k - 41. Let h(v) = 64*v**3 + 168*v**2 + 74*v - 38. Let r(z) = -3*h(z) + 2*x(z). Suppose r(w) = 0. Calculate w.
-2, -1, 4/15
Let w be (1 - -2) + 0 + -3. Suppose -z - 3*z + 8 = w. Suppose -5*v**z + 10*v - 4 + v**2 - 4*v + 2*v = 0. What is v?
1
Let x(d) be the first derivative of 2*d**3/39 + 70*d**2/13 + 114*d + 4602. Factor x(u).
2*(u + 13)*(u + 57)/13
Suppose -9*p + 8*p + 8 = 0. Factor 16*b**2 + p*b**4 - b**3 - 6*b**4 + 10*b**3 + 9*b**3.
2*b**2*(b + 1)*(b + 8)
Let p(m) be the first derivative of -m**6/90 + m**5/10 + 2*m**4/3 - 32*m**3/3 - 87. Let b(n) be the third derivative of p(n). Determine z, given that b(z) = 0.
-1, 4
Let j(i) be the second derivative of -7*i**6/25 + 41*i**5/50 + 149*i**4/30 + 91*i**3/15 + 4*i**2/5 + 329*i. Determine z, given that j(z) = 0.
-1, -1/21, 4
Let r be 6/(-15) + 3412/5. Let a = -4768/7 + r. Find s, given that a*s**3 + 0*s + 4/7*s**2 - 10/7*s**4 + 0 = 0.
-2/5, 0, 1
Let i be 47 + ((-2)/(-4))/((-1)/(-2)). Factor 8 + 4*r - i*r**2 + 89*r**2 - 45*r**2.
-4*(r - 2)*(r + 1)
Let v be (14/(-4) - -2) + (-450)/(-12). Factor v*t**3 + 0*t**3 + 30*t**4 + 3*t**5 - 10720*t**2 + 10504*t**2.
3*t**2*(t - 2)*(t + 6)**2
Solve 7/2*g + 11/2*g**2 - 147/2 + 1/2*g**3 = 0 for g.
-7, 3
Suppose 2*c - 3*g - 62 = 0, -24*c + 3*g - 13 = -25*c. Suppose c*y + 40 = 35*y. What is p in 7/2*p**3 - 5/2*p**4 + 2 - y*p + 1/2*p**5 + 1/2*p**2 = 0?
-1, 1, 2
Factor -8099/8*t + 181/8*t**2 - 8281/8 - 1/8*t**3.
-(t - 91)**2*(t + 1)/8
Let n be (3915/(-1566))/(11/(-2)). Factor -n*c + 0 - 1/11*c**2.
-c*(c + 5)/11
Let i(r) be the second derivative of -r**7/14 - 11*r**6/40 - 7*r**5/20 - r**4/8 + 75*r**2/2 + 192*r. Let a(o) be the first derivative of i(o). Factor a(z).
-3*z*(z + 1)**2*(5*z + 1)
Let o(s) be the second derivative of 5*s**4/12 + 35*s**3/3 + 225*s**2/2 + 580*s. Find q, given that o(q) = 0.
-9, -5
Let y(u) = 10*u**2 - 20*u + 4. Suppose 5*g - g - 76 = 0. Let q(a) = -8*a**2 + g*a + 0*a**2 - 4 - 2*a**2. Let n(b) = 4*q(b) + 6*y(b). Factor n(d).
4*(d - 2)*(5*d - 1)
Factor -52960 + 7414*v**3 - 3662*v**3 + 26560*v - 3747*v**3 - 3350*v**2.
5*(v - 662)*(v - 4)**2
Let z(j) be the third derivative of -j**6/660 - 13*j**5/330 + 11*j**4/12 + 133*j**3/33 + 8*j**2 - 97*j. Suppose z(i) = 0. What is i?
-19, -1, 7
Let i(x) = 4*x**2 + 6329*x + 10004602. Let b(r) = 11*r**2 + 18986*r + 30013795. Let f(q) = -3*b(q) + 8*i(q). Factor f(z).
-(z + 3163)**2
Let c(n) be the second derivative of -n**5/10 + 7*n**4/3 + n**3/3 - 14*n**2 - 518*n. Find v such that c(v) = 0.
-1, 1, 14
Let v = 13488/737 - 1214/67. Factor 0*q + 4/11*q**3 + 0 + 16/11*q**2 - v*q**4.
-2*q**2*(q - 4)*(q + 2)/11
Suppose a = k + 152 - 150, -k - 14 = -4*a. Factor -87/2*h + 15/4*h**k - 18.
3*(h - 12)*(5*h + 2)/4
Let n(d) = d**3 - 2*d**2 - 8*d + 33. Let x be n(3). Factor -40 - 20*k + x*k**2 - 16*k**2 - 16*k + 3*k**2 - k**2.
4*(k - 10)*(k + 1)
Factor 970*s**3 - 3*s**4 - 226175939328 + 5318*s**3 - 2303938*s**2 - 2638430*s**2 + 566310403*s + 1160223485*s.
-3*(s - 524)**4
Suppose -341 = -28*w - 285. Let f be (-28)/(-154) + 226/88. Factor -f*i + i**3 - 3/4 - w*i**2.
(i - 3)*(2*i + 1)**2/4
Let b = -9 + 16. Let a(z) = z**2 + 29*z + 18. Let y(h) = -4 - 10 - 13 - 18*h + h**2 - 25*h - 3*h**2. Let v(m) = b*a(m) + 5*y(m). Let v(g) = 0. What is g?
-3, -1
Factor 1496*a - 41330 + 308006 + 2*a**2 + 13076.
2*(a + 374)**2
Let 121/5*q**4 + 24*q - 119/5*q**3 - 121/5*q**2 + 0 - 1/5*q**5 = 0. What is q?
-1, 0, 1, 120
Let a = 27269/8181 + 1/8181. Factor 8/3 + a*b**2 + 2/3*b**3 + 16/3*b.
2*(b + 1)*(b + 2)**2/3
Let t(l) be the third derivative of -l**6/1020 + l**5/10 + 40*l**4/51 + 36*l**3/17 - 5*l**2 - 9*l. Factor t(d).
-2*(d - 54)*(d + 1)*(d + 2)/17
Let z(b) be the third derivative of -b**7/210 - 13*b**6/60 - 14*b**5/5 + 13*b**4/12 + 169*b**3/6 + 1429*b**2. Find t, given that z(t) = 0.
-13, -1, 1
Let p be -2 + (-6)/((-24)/(-62)). Let h = p + 19. Factor 1/2*x**2 + 1/2*x**4 - 1 + h*x - 3/2*x**3.
(x - 2)*(x - 1)**2*(x + 1)/2
Let n(o) be the third derivative of 2/21*o**3 - 1/840*o**6 - 12*o**2 + 1/24*o**4 + 1/210*o**5 + 0 - 3*o. Find d, given that n(d) = 0.
-1, 4
Let r(m) be the first derivative of m**8/560 + 3*m**7/280 - m**6/30 + 19*m**3 + 13. Let x(t) be the third derivative of r(t). Factor x(b).
3*b**2*(b - 1)*(b + 4)
Let g = 68 - 2. Let n = 75 - g. Let r(z) = -7*z**2 + 30*z - 47. Let o(s) = -29*s**2 + 120*s - 189. Let d(p) = n*r(p) - 2*o(p). Factor d(c).
-5*(c - 3)**2
Let u = 4505/52 - 2233/26. Suppose 0 + 0*j**2 + 3/4*j**3 - u*j**4 + 0*j = 0. Calculate j.
0, 1
Let q(c) = -55*c**3 - 65*c**2 - 175*c - 195. Let m(i) = -2*i**3 - 4*i**2 - i. Let h(a) = 30*m(a) - q(a). Solve h(n) = 0.
-13, -1, 3
Let q(d) = -d**4 - 2*d**2 - d - 2. Let p(i) = 28*i**4 + 60*i**3 + 128*i**2 + 32*i + 64. Let g(a) = -p(a) - 32*q(a). Factor g(r).
4*r**2*(r - 16)*(r + 1)
Let u(h) be the second derivative of -h**5/20 + 29*h**4/12 - 9*h**3 + 490*h. Factor u(z).
-z*(z - 27)*(z - 2)
Let v(d) be the first derivative of -1/5*d**3 + 19/5*d**2 + 13/5*d + 69. Factor v(a).
-(a - 13)*(3*a + 1)/5
Let d(f) be the third derivative of -f**5/210 - f**4 - 83*f**3/21 - f**2 - 1479*f. Determine y, given that d(y) = 0.
-83, -1
Let g = 1672310/63 + -185806/7. Factor g*n - 14/3 + 2/9*n**2.
2*(n - 3)*(n + 7)/9
Let k(d) = -3*d + 19. Let g be k(3). Suppose -2*f = -3*c + 16, -c = g*f - 8*f - 16. Factor -13*s**4 - 5*s**2 + 12*s**4 - 7*s**2 + 6*s**3 + c*s.
-s*(s - 2)**3
Let r(n) be the first derivative of -2*n**7/21 - 2*n**6/15 + n**5/5 + n**4/3 - 55*n + 109. Let a(l) be the first derivative of r(l). Let a(m) = 0. Calculate m.
-1, 0, 1
Suppose 6*y - y = 30. Suppose 0*z - 5*d = z + 6, 3*d + y = 0. Find a such that -738*a - 7*a**4 - 864*a**2 - 158*a - 15*a**z + 2*a**4 + 512 - 232*a**3 = 0.
-4, 2/5
Let y be (3464/(-2165))/(192/(-90)). Find u, given that 1/4*u**2 - y - 1/2*u = 0.
-1, 3
Let c(n) be the second derivative of 3/2*n**5 + 0 + 3/5*n**6 + 7/6*n**4 + 0*n**2 + 0*n**3 + 113*n + 1/21*n**7. Find t, given that c(t) = 0.
-7, -1, 0
Let q(y) be the second derivative of y**7/105 + 7*y**6/75 + 3*y**5/50 - 23*y**4/30 - 32*y**3/15 - 12*y**2/5 - 1076*y + 5. Factor q(a).
2*(a - 2)*(a + 1)**3*(a + 6)/5
Let t(j) be the first derivative of 118 - 2/13*j**3 + 32/13*j**2 - 40/13*j. Find w s