58*v**4 + 144 + 436*v**2 = 0.
2/3, 1, 2, 18
Let b(g) = -2*g**2 - 3*g + 10. Let s be b(-4). Let a be -1 - (1/s)/((-8)/(-300)). Factor 5/4 + a*u + 7/4*u**2 + 1/4*u**3.
(u + 1)**2*(u + 5)/4
Let o(u) be the third derivative of 11*u - 5/8*u**4 + 0*u**3 + 4*u**2 - 1/12*u**5 + 5/42*u**7 + 7/24*u**6 + 0. Factor o(h).
5*h*(h + 1)**2*(5*h - 3)
Let v(r) = -9*r**2 + 27*r. Let q(z) = -z. Let k(f) = -f**2 + 6*f. Let o(n) = -k(n) - 5*q(n). Let w(x) = -40*o(x) - 5*v(x). Factor w(i).
5*i*(i - 19)
Let y = -9234 - -9236. Let z(u) be the first derivative of 4/3*u**3 - 1/2*u**y + 0*u - 1/6*u**6 - 3/2*u**4 - 19 + 4/5*u**5. Solve z(j) = 0.
0, 1
Let a = -146379 - -146469. Factor a + 2/5*v**2 - 12*v.
2*(v - 15)**2/5
Let u(q) be the first derivative of 31/7*q**2 + 24/7*q - 4 - 5/28*q**4 + 1/7*q**3. Factor u(n).
-(n - 4)*(n + 3)*(5*n + 2)/7
Factor 8*s - 20*s - 9*s**3 - 9*s**2 + 13*s**3 - s**3.
3*s*(s - 4)*(s + 1)
Let a = 1104045 + -7728311/7. Factor 2/21*d**3 - 10/21*d**2 + 0 + a*d.
2*d*(d - 3)*(d - 2)/21
Let y(o) = 15*o**2 + 563*o + 1122. Let a(g) = -7*g**2 - g - 2. Let h(r) = 2*a(r) + y(r). What is j in h(j) = 0?
-559, -2
Let h = 9109/3 + -3036. Let b(z) be the first derivative of -5/18*z**6 - h*z**2 - 1/3*z**3 - 7 + 0*z + 7/12*z**4 + 1/5*z**5. Determine n, given that b(n) = 0.
-1, -2/5, 0, 1
Let t(r) be the second derivative of 11*r**7/105 + 2*r**6/75 - 99*r**5/50 + 13*r**4/15 + 28*r**3/3 + 24*r**2/5 + 7*r + 119. Determine a, given that t(a) = 0.
-3, -1, -2/11, 2
Suppose -615*r + 680*r = 0. Let u(p) be the second derivative of -3/2*p**3 - 1/4*p**4 + r - 20*p + 15*p**2. Factor u(o).
-3*(o - 2)*(o + 5)
Determine j so that -226/15*j**2 + 0 - 56/3*j - 2/15*j**4 + 52/15*j**3 = 0.
-1, 0, 7, 20
Let v = 1695 + -1675. Let j be (v/36 + -1)/(280/(-180)). Factor 16/7*o - j*o**2 - 2.
-2*(o - 7)*(o - 1)/7
Let c be (-4)/450*(1313 - 1328). Factor 6/5*u**2 - 18/5*u + 2/5*u**3 + 0 - c*u**4.
-2*u*(u - 3)**2*(u + 3)/15
Let l be ((-32)/(-6) - 1) + 18576/(-13932). Find x such that 32/9*x**2 - 154/9*x + 196/9 - 2/9*x**l = 0.
2, 7
Let p be 1/5 + 57*(-1)/(-15). Let r(d) = 2*d**3 - 6*d**2 + 2. Let x(l) = -6*l**3 + 19*l**2 - 7. Let c(t) = p*x(t) + 14*r(t). Factor c(s).
4*s**2*(s - 2)
Let t(h) = -9*h - 354. Let z(y) = 4*y + 1. Let g(o) = -4*t(o) + 28*z(o). Let b(m) = -m**2 + 147*m + 1444. Let p(d) = 4*b(d) - 5*g(d). Solve p(j) = 0 for j.
-19
Find b, given that 48*b**3 + 213*b**2 + 243/2 + 288*b + 3/2*b**4 = 0.
-27, -3, -1
Factor -h**4 + 2256*h**2 - 319*h**3 - 4234*h + 7*h**4 - 41*h**3 + 3072 - 342*h - 10*h**4.
-4*(h - 2)**3*(h + 96)
Let f(t) = -5*t + 84. Let v be f(8). Let i be v/70 + 44/77. Factor 21/5*l**2 + 0 - i*l.
3*l*(7*l - 2)/5
Let o(g) be the third derivative of g**5/270 - 19*g**4/54 + 115*g**3/9 + 2759*g**2 + g. Let o(m) = 0. What is m?
15, 23
Let f(k) be the second derivative of -k**5/60 - k**4/36 + 5*k**3/18 - k**2/2 - 28*k + 5. Factor f(p).
-(p - 1)**2*(p + 3)/3
Let d(n) be the third derivative of -383*n**5/360 - 191*n**4/36 + n**3/9 - 3*n**2 + 75*n. Factor d(a).
-(a + 2)*(383*a - 2)/6
Let a(q) = -5*q - 103. Let j be a(-17). Let v be 18 + -19 - j/14. Determine d, given that -2*d + 8/7 + v*d**3 + 4/7*d**2 = 0.
-4, 1
Let z(h) be the second derivative of -h**6/150 + 13*h**5/100 + 17*h**4/10 + 22*h**3/3 + 76*h**2/5 + 1843*h. What is g in z(g) = 0?
-2, 19
Suppose 536*p = 1058*p - 586*p. Factor 3/5*g**4 + 27/5*g**2 + 0*g + 18/5*g**3 + p.
3*g**2*(g + 3)**2/5
Suppose -5*b - 57 = 5*o + 13, 44 = -4*o + 2*b. Let v(w) = -1. Let j(a) = a**2 + 17*a + 4. Let u(s) = o*v(s) - 3*j(s). Find i, given that u(i) = 0.
-17, 0
Determine w so that -2/13*w**4 - 240/13 - 18/13*w**3 + 18/13*w**2 + 242/13*w = 0.
-8, -5, 1, 3
Let w(d) = d**3 - 25*d**2 + 24*d - 1. Let j be w(24). Let r be 8/j + 172/18. Factor 2*y**4 - 10/3*y**3 - 2/9*y + r*y**2 + 0.
2*y*(y - 1)*(3*y - 1)**2/9
Suppose -613*i + 618*i + 64 = 4*k, 5*i - 5*k = -80. Determine n so that 1/5*n + i + 3/10*n**2 + 1/10*n**3 = 0.
-2, -1, 0
Let c be (-3)/(-9)*(-6)/28 - 6*34/(-357). Suppose 16 - c*x**4 - 20*x + x**3 + 6*x**2 = 0. What is x?
-4, 2
Let q(g) be the third derivative of g**5/12 - 25*g**4/6 + 125*g**3/2 + 825*g**2. Factor q(y).
5*(y - 15)*(y - 5)
Let k(f) be the second derivative of f**7/42 - 19*f**6/90 - 83*f**5/60 + 71*f**4/36 + 40*f**3/3 + 18*f**2 - 38*f + 8. Solve k(y) = 0.
-3, -1, -2/3, 2, 9
Let u(k) be the third derivative of 17*k**6/40 + 33*k**5/20 + 15*k**4/8 - k**3/2 + 2*k**2 - 799*k. Determine h, given that u(h) = 0.
-1, 1/17
Let h(x) = -4*x**2 - 1968*x - 120. Let w(y) = -y + 10. Let g(n) = h(n) + 12*w(n). Let g(m) = 0. Calculate m.
-495, 0
Factor 224/11*m + 256/11 + 1/11*m**3 - 31/11*m**2.
(m - 16)**2*(m + 1)/11
Let b be 1*4 - 9/(-54)*-30. Let p(g) = g + 1. Let x(s) = -25*s**3 + 110*s**2 - 25*s + 15. Let f(l) = b*x(l) + 15*p(l). Find t such that f(t) = 0.
0, 2/5, 4
Let y(l) be the second derivative of 2*l**7/105 - 4*l**6/75 - 12*l**5/25 + 38*l**4/15 - 74*l**3/15 + 24*l**2/5 - 422*l - 1. Find j, given that y(j) = 0.
-4, 1, 3
Let w be (-3)/(-4) - (10/(-8) + -2). Let i be 2/(55/15*w/22). Factor -2/13*o**4 + 0*o + 0 + 2/13*o**2 + 0*o**i.
-2*o**2*(o - 1)*(o + 1)/13
Determine g, given that -200/3*g + 1/6*g**2 + 133/2 = 0.
1, 399
Factor 0 + 9/2*u**3 + 63*u + 569/2*u**2.
u*(u + 63)*(9*u + 2)/2
Let f(u) = u**2 - 25*u - 32. Let l be f(30). Factor -l*z**3 + 207*z**3 + z**4 + 24*z - 115*z**3 - 3*z**5 + z**5 - 20*z**2 + 5*z**5.
z*(z - 3)*(z + 2)**2*(3*z - 2)
Let h(m) be the first derivative of 43 + 2/33*m**3 + 3/11*m**2 - 20/11*m. Factor h(j).
2*(j - 2)*(j + 5)/11
Let f(x) = -3*x**3 + 151*x**2 + 100*x + 104. Let y be f(51). Let r(n) be the first derivative of 0*n + 1/18*n**4 + 0*n**3 - 18 + 0*n**y. Solve r(u) = 0 for u.
0
Let f(q) be the third derivative of -q**5/20 - 87*q**4/8 + 279*q**3 - 6475*q**2. Factor f(j).
-3*(j - 6)*(j + 93)
Let f(m) be the second derivative of m**4/6 - 220*m**3 + 108900*m**2 - m - 309. Factor f(y).
2*(y - 330)**2
Let h = -6457 - -6465. Let b(r) be the third derivative of 0*r - 2/2415*r**7 + 0*r**3 + 0*r**4 - 19*r**2 - 1/3864*r**h - 1/1380*r**6 + 0*r**5 + 0. Factor b(l).
-2*l**3*(l + 1)**2/23
Suppose 5*p + 4*z + 8 - 35 = 0, 0 = -4*p - 5*z + 27. Factor -15*o**2 - 8*o + 8*o + o**3 - o**4 - 2*o**3 + 17*o**p.
-o**2*(o - 15)*(o - 1)
Factor 0 + 2/7*z**2 - 40/7*z.
2*z*(z - 20)/7
Suppose -22 = w - 4*t, -w + 30 = -t + 43. Let c be (w/25)/(18/500*-2). Suppose 10/9*f**2 + 8/9 - c*f**3 + 32/9*f = 0. Calculate f.
-2/5, 1
Factor -147/5 - 17/5*u**2 - 1/5*u**3 - 91/5*u.
-(u + 3)*(u + 7)**2/5
Suppose 68*w - 47*w = 6*w + 30. Let d(q) be the first derivative of 0*q + 3/28*q**4 + 4/7*q**3 + 24 - 15/14*q**w. Factor d(u).
3*u*(u - 1)*(u + 5)/7
Let j(y) be the first derivative of -1/12*y**3 + 1/2*y - 1/20*y**5 + 3/8*y**2 - 42 - 3/16*y**4. Find l, given that j(l) = 0.
-2, -1, 1
Suppose -53320*f + 53332*f - 288 = 0. Determine w so that f + 2/3*w**2 - 8*w = 0.
6
Let k(w) be the second derivative of -4*w**7/21 - 6*w**6 - 19*w**5/5 + 22*w**4 - 2703*w. Find u such that k(u) = 0.
-22, -3/2, 0, 1
Let s(m) be the first derivative of -m**3/9 - 19*m**2/6 + 20*m/3 + 591. Factor s(v).
-(v - 1)*(v + 20)/3
Let t be 0*((-4)/8 - -1) - -2. Determine h so that 18*h**2 + 17*h**t + 2*h - 65*h**2 = 0.
0, 1/15
Let j be 1845/378 - (-2 + (-12)/(-7)). Let q = -119/30 + j. Factor -n - 2/5*n**2 - 1/5*n**4 + 3/5 - 1/5*n**5 + q*n**3.
-(n - 1)**3*(n + 1)*(n + 3)/5
Let o(s) be the first derivative of -s**4 + 16*s**3 - 22*s**2 + 3010. Factor o(y).
-4*y*(y - 11)*(y - 1)
Let j be 18884/44 - (-4)/176*-8. Factor -138*p**2 + 10*p**3 + 3125 + 214*p**2 + j*p**2 + 6500*p.
5*(p + 25)**2*(2*p + 1)
Suppose 0 = 30*l - 21*l. Suppose 26*w - 21*w = l. Factor -4/5*h**5 - 12/5*h**3 + 0 - 4/5*h**2 + w*h - 12/5*h**4.
-4*h**2*(h + 1)**3/5
Let h be (24/15)/(4/10). Suppose 0 = -2*o - 0*o - 5*d + 3, -h*o = -4*d - 20. Factor 3*a**2 - 3*a**3 - a + 5*a**2 - 2*a**2 + a**o - 3*a**2.
a*(a - 1)**3
Let j(k) be the third derivative of -k**5/300 + 11*k**4/20 - 384*k**2. Factor j(r).
-r*(r - 66)/5
Let l(f) = -f**2 + 4*f + 29. Let h be l(5). Let x be (h/(-80))/(18/(-10)). Factor x - 1/6*n**2 - 1/6*n + 1/6*n**3.
(n - 1)**2*(n + 1)/6
Find v such that 315/2*v - 1/2*v**2 - 313 = 0.
2, 313
Let j = -310 + 457. Let a = 150 - j. Factor a*f**2 + 66 + 9*f - 66.
3*f*(f + 3)
Let w(o) be the second derivative of o**5/105 - 