 375. Suppose 37*h - 29*h = 16. Let l(n) = -n**3 - 105*n**2 - 440*n - 750. Let j(w) = h*l(w) + 5*b(w). Factor j(i).
3*(i + 5)**3
Let w be (-14)/(-70) - (2 + (-194)/80). Let k(l) be the first derivative of 24 + w*l**4 - 1/2*l + 11/12*l**3 - 1/8*l**2. Suppose k(q) = 0. Calculate q.
-1, -1/2, 2/5
Let p(x) be the second derivative of -x**7/630 + 8*x**6/45 - 31*x**5/30 - 71*x**4/3 + 5*x - 5. Let i(t) be the third derivative of p(t). Factor i(o).
-4*(o - 31)*(o - 1)
Solve 228*t**3 + 40804 - 22*t**3 - 6766*t**2 + t**4 + 7093*t**2 + 24437*t + 10686*t**2 + 17175*t = 0 for t.
-101, -2
Factor -28*h**2 + 2/17*h**3 + 0 + 1410/17*h.
2*h*(h - 235)*(h - 3)/17
Suppose -n + f + 4 = 0, -38 = 5*f - 13. Let x = n - -3. Find z such that z - 2*z**3 + 9*z**x - 4*z + 7*z**2 - 29*z = 0.
0, 4
Let u(a) be the third derivative of 2*a**2 + 0*a**4 + 0*a**3 + 10*a + 1/20*a**5 + 0 + 1/672*a**8 - 1/70*a**7 - 1/240*a**6. Suppose u(x) = 0. What is x?
-1, 0, 1, 6
Let r be (-1)/(2/2)*13. Let o(t) = t**2 + 14*t + 15. Let d be o(r). Solve 35*n**d + 2*n - 2*n + 4*n**3 - 39*n**2 = 0.
0, 1
Let m(r) be the first derivative of -r**5/4 - 25*r**4/2 - 375*r**3/2 - 74*r - 81. Let b(z) be the first derivative of m(z). Factor b(d).
-5*d*(d + 15)**2
Let b(x) be the third derivative of 22*x**5/15 - x**4/6 - 14*x**3 - 7144*x**2. Factor b(u).
4*(u - 1)*(22*u + 21)
Let o be 40/(-30)*(2 - 20). Determine m, given that 34*m + 21*m**2 + o*m**3 - 7*m**2 - 11 + 29 - 26*m**3 = 0.
-1, 9
Let p(b) = b**3 - 3*b**2 + 2*b - 1. Let i be p(3). Factor -124 + a**2 + a**4 + a**2 + a**2 + 5*a**3 + 120 - i*a.
(a - 1)*(a + 1)**2*(a + 4)
Let s be (-42)/(-30) + (-27)/(-45) - (-141)/(-72). Let b(w) be the second derivative of 17*w - 1/12*w**3 + 1/2*w**2 - s*w**4 + 0. Factor b(y).
-(y - 1)*(y + 2)/2
Factor -5*d**4 + 15*d**2 + 261*d**3 - 535*d + 398*d**3 + 350 - 484*d**3.
-5*(d - 35)*(d - 1)**2*(d + 2)
Let c be (-24)/(-40) + 2*5086/(-20). Let k = 512 + c. Let -17/3*b - 23/3*b**3 - 1 - 2*b**k - 31/3*b**2 = 0. What is b?
-3/2, -1, -1/3
Let r(w) be the first derivative of w**4/12 + 52*w**3/3 + 960*w**2 - 25600*w/3 + 2055. Let r(i) = 0. What is i?
-80, 4
Let l(b) be the first derivative of -9*b**4/4 + 25*b**3 + 189*b**2 + 216*b + 913. Factor l(u).
-3*(u - 12)*(u + 3)*(3*u + 2)
Let o(k) = 7*k**4 - 147*k**3 + 5324*k**2 + 5480*k - 2. Let n(l) = 17*l**4 - 294*l**3 + 10646*l**2 + 10962*l - 5. Let u(z) = -2*n(z) + 5*o(z). Factor u(h).
h*(h - 74)**2*(h + 1)
Let p(r) = -63*r - 40. Let y be p(-4). Factor -33124 + y*b - 624*b**2 + 620*b**2 - 613*b - 327*b.
-4*(b + 91)**2
Let -7301 - 7403 + 23*k**2 - 204*k - 20*k**2 + 10672 = 0. What is k?
-16, 84
Find s such that -s**2 + 1071648 - 829*s - 2702*s + 3*s**2 + 603*s = 0.
732
Let c(x) = -5*x**2 - 702*x. Let d(i) = -4*i**2 - 739*i. Let z(f) = -3*c(f) + 4*d(f). Let z(l) = 0. Calculate l.
-850, 0
Let i be -7*(-795)/(-315) + 18. Let b be (-6)/21 - (-68)/42. Solve -b + 5/3*x**2 + x - x**3 - i*x**4 = 0 for x.
-4, -1, 1
Suppose 0*h = -3*h + 12, q = 5*h - 18. Suppose 7*u**3 - 4*u**3 + 13 - 4 + 15*u**q - 124*u + 145*u = 0. What is u?
-3, -1
Suppose 0 = 172*w - 176*w - 224. Let t(l) = l**2 + 61*l + 283. Let y be t(w). Determine s, given that 1/3*s**2 + 1/6*s**4 - 1/2*s**y + 0 + 0*s = 0.
0, 1, 2
Let w be ((-40752)/(-47544))/((-3)/((-210)/38)). Solve -w*x + 12/19*x**2 + 16/19 + 2/19*x**3 = 0 for x.
-8, 1
Let p(t) = 10*t**3 + 265*t**2 + 35*t - 265. Let n(i) = -15*i**3 - 397*i**2 - 57*i + 397. Let l(f) = 5*n(f) + 8*p(f). Factor l(h).
5*(h - 1)*(h + 1)*(h + 27)
Let u(s) be the second derivative of s**4/66 - 742*s**3/33 - 743*s**2/11 - 4274*s. Let u(k) = 0. Calculate k.
-1, 743
Let n(y) be the second derivative of -y**4/12 - 2*y**3 + 14*y**2 - 1314*y. Factor n(p).
-(p - 2)*(p + 14)
What is t in -59/2*t**2 - 39/4*t - 3/4*t**3 + 0 = 0?
-39, -1/3, 0
Suppose -72*w**2 + 829*w**3 - 93*w - 412*w**3 - 413*w**3 + 21 - 151*w - 189 = 0. Calculate w.
-2, -1, 21
Let o(j) be the first derivative of 15 - j**4 - 8/3*j**3 + 8*j**2 + 12*j. Let n(u) be the first derivative of o(u). Factor n(q).
-4*(q + 2)*(3*q - 2)
Let q(j) be the second derivative of j**4/20 - 223*j**3/10 - 2061*j**2/5 + 2438*j. Factor q(v).
3*(v - 229)*(v + 6)/5
Let i(h) = -243*h**2 + h**3 + 490*h**2 - 1 - h - h**4 - 247*h**2. Let k(c) = 15*c**4 + 72*c**2 + 96*c + 45. Let r(p) = 18*i(p) + k(p). Factor r(d).
-3*(d - 9)*(d + 1)**3
What is p in 31*p**3 + 0 - 5/2*p**5 + 0*p + 97/2*p**4 - 20*p**2 = 0?
-1, 0, 2/5, 20
Let a(g) be the third derivative of 0*g - 1/105*g**5 - 6728/21*g**3 + 0 - 58/21*g**4 - 190*g**2. Find c such that a(c) = 0.
-58
Find v, given that 1156*v + 0 - 1/4*v**4 - 135/4*v**3 - 1122*v**2 = 0.
-68, 0, 1
Let w(k) be the first derivative of 2*k**6/3 + 12*k**5/5 - 2*k**4 - 16*k**3 - 16*k**2 - 175. Solve w(i) = 0.
-2, -1, 0, 2
Let v(o) be the third derivative of -o**6/120 + 3*o**5/20 + o**4/24 - 7*o**3/6 - o**2 - 7. Let p be v(9). Solve 0 + 0*a - 1/2*a**3 - a**p = 0.
-2, 0
Factor -1/2*z**3 - 133/2 + 1/2*z + 133/2*z**2.
-(z - 133)*(z - 1)*(z + 1)/2
Let -512/3*l + 2/3*l**4 + 0*l**3 - 160 - 48*l**2 = 0. What is l?
-6, -2, 10
Factor 28 + 48*z**2 + 173 + 51 - 27*z + 282*z.
3*(z + 4)*(16*z + 21)
Let h(c) = 7*c**4 + 2*c + 1. Let m(z) = -38*z**4 + 16*z**3 - 48*z**2 - 140*z + 250. Let p(b) = -6*h(b) - m(b). Solve p(i) = 0.
-4, 2
Let l be (28 - (-756)/(-21) - 192/(-25))*5/(-4). Factor -m**3 + l*m + 0 - 9/10*m**2 + 3/10*m**4.
m*(m - 4)*(m + 1)*(3*m - 1)/10
Let r(m) be the third derivative of m**7/210 - 7*m**6/24 - m**5/20 + 103*m**4/24 + 35*m**3/3 + 9*m**2 - 70*m. Suppose r(a) = 0. What is a?
-1, 2, 35
Suppose 5*x = 5*s + 30, -2*x + 4*s - 8*s = -36. Factor 5*y + 10 - 10*y + 4*y**2 + 15*y**3 - 9*y**2 - x*y - 5*y**4.
-5*(y - 2)*(y - 1)**2*(y + 1)
Let u(v) be the third derivative of -v**6/24 - 47*v**5/60 - 3*v**4/4 - 13*v**2 + 66. Factor u(x).
-x*(x + 9)*(5*x + 2)
Let t(x) be the second derivative of 1/150*x**6 + 361/5*x**4 + 0*x**2 + 27436/15*x**3 + 57/50*x**5 - 236 + x. Factor t(j).
j*(j + 38)**3/5
Factor 6/7*u**2 - 282/7*u - 286/7 + 2/7*u**3.
2*(u - 11)*(u + 1)*(u + 13)/7
Let p be (48/35 + 0)*51750/8280. What is w in 33/7*w**3 + p + 21*w + 117/7*w**2 + 3/7*w**4 = 0?
-5, -4, -1
Suppose -195 = -3*m + g - 4050, g = 5*m + 6425. Let a = m - -1285. Solve -3/8*t**3 + 0*t + a*t**2 + 1/8*t**4 + 0 = 0.
0, 3
Let p(s) be the third derivative of -196/51*s**3 - 14/17*s**4 + 9/170*s**5 + 2*s + 0 + 79*s**2 - 1/1020*s**6. Determine g, given that p(g) = 0.
-1, 14
Let u(o) be the third derivative of o**8/1008 + 23*o**7/315 + 161*o**6/180 + 35*o**5/9 + 613*o**4/72 + 95*o**3/9 - 2*o**2 + 257*o - 5. Factor u(x).
(x + 1)**3*(x + 5)*(x + 38)/3
Let u = 11155 + -11155. Let q(o) be the third derivative of u + 0*o - 1/60*o**5 - 5/6*o**3 - 18*o**2 + 1/4*o**4. Factor q(g).
-(g - 5)*(g - 1)
Let q = -29 - -29. Let g = -165767/6 + 27629. Suppose -2*r + 8/3*r**2 - g*r**3 + q + 1/6*r**4 = 0. Calculate r.
0, 2, 3
Suppose -4*g - q + 23 = 0, -5*g + 3*q + 15 = -35. Let f be 5 + (-8 - -4) + 3/g. Suppose -2/7*i**2 + f*i - 8/7 = 0. What is i?
1, 4
Let j = -5 + 20. Suppose -12*l - 6 = -j*l. Let 3*h + 35*h - 2*h - 13 + 3*h**3 + 18*h**l + 37 = 0. What is h?
-2
Let y(a) = -134*a - 804. Let r be y(-6). Let f(n) be the second derivative of 5/9*n**3 + 25/6*n**2 + 1/36*n**4 + 16*n + r. Factor f(w).
(w + 5)**2/3
Let i(m) be the first derivative of 10 - 6/7*m**2 + 2/105*m**6 + 4*m + 0*m**5 - 16/21*m**3 - 2/7*m**4. Let a(p) be the first derivative of i(p). Factor a(z).
4*(z - 3)*(z + 1)**3/7
Suppose 205304*r = 205314*r - 30. Factor -3888 - 106/3*x**r - 3240*x + 2/3*x**4 + 612*x**2.
2*(x - 18)**3*(x + 1)/3
Suppose -4*i + 3 = -o + i, 0 = -3*o + i + 5. Solve 40*b**5 + 22*b**2 + 223*b**2 - 12*b + 612*b**3 - 77*b**2 + 282*b**4 - 18 + 208*b**o = 0 for b.
-3, -1, -1/4, 1/5
Let g = 819 + 255. Let d = g + -1074. Solve d*v - 2/5*v**2 + 8/5 = 0.
-2, 2
Let r(s) be the first derivative of s**4/6 - 2*s**3 + 26*s**2/3 - 16*s - 1584. Factor r(a).
2*(a - 4)*(a - 3)*(a - 2)/3
Suppose -35*g = -30*g - 3190. Let f be 6/(-4) + 1073/g. Factor 8/11 + 8/11*q + f*q**2.
2*(q + 2)**2/11
Let n be -4 + (25 - 4) + -56*(-29)/(-116). Factor 0*l - 4*l**n - 4/3*l**4 + 0 + 16/3*l**2.
-4*l**2*(l - 1)*(l + 4)/3
Let w(b) be the second derivative of b**6/45 + 11*b**5/30 - 2*b**4/3 + 3*b - 219. Factor w(q).
2*q**2*(q - 1)*(q + 12)/3
Let r(i) = 20*