- 342. Let u(c) = 2*g(c) + 3*k(c). Find r such that u(r) = 0.
-17, -2
Let u be 6/14 + (-1953)/(-931). Let i = 307/114 - u. Solve -1/6*y + i*y**3 - 1/6*y**2 + 0 + 1/6*y**4 = 0 for y.
-1, 0, 1
Let g(x) = 20*x + 282. Let u be g(-14). Let d(b) be the first derivative of -3 - b**u - 2*b + 2/3*b**3 + 1/2*b**4. Factor d(l).
2*(l - 1)*(l + 1)**2
Let f be 630/(-2100) + (-1 - 6/(-4)). What is y in -3/5*y**4 + 0 - f*y**5 + 0*y**2 - 2/5*y**3 + 0*y = 0?
-2, -1, 0
Suppose -5*r - 13 + 19 = -z, 0 = 4*r - 5*z + 12. Factor -20/7*a + 8/7 - 4/7*a**3 + 16/7*a**r.
-4*(a - 2)*(a - 1)**2/7
Suppose 2*r = 5*p + 31, 71*p + 3 = -4*r + 68*p. Factor 0*s + 2/11*s**r - 6/11*s**2 + 8/11.
2*(s - 2)**2*(s + 1)/11
Suppose 4*c**4 + 20 - 168*c**2 + 44 - 26*c**3 - 14*c**4 - 80*c - 50*c**3 = 0. What is c?
-4, -2, 2/5
Determine p so that 81/4*p**3 - 9/2 - 6*p**4 + 3/8*p**5 - 57/2*p**2 + 147/8*p = 0.
1, 12
Let f = 39 - 37. Factor -u**3 - 3*u**3 + 5 + 12*u**f - 21.
-4*(u - 2)**2*(u + 1)
Let i(g) = g**4 - g**3 + g**2 - g. Let u(w) = 9*w**4 + 25*w**3 + 7*w**2 - 7*w. Let q(a) = 14*i(a) - 2*u(a). Factor q(h).
-4*h**3*(h + 16)
Suppose -5*i + n + 4*n + 50 = 0, -10 = -4*i - 2*n. Factor -64*q**5 - 68*q**i + 127*q**5.
-5*q**5
Let n(o) be the first derivative of 18*o + 6 + 15/2*o**2 + o**3. Find h, given that n(h) = 0.
-3, -2
Let m(h) = -h**3 - 26*h**2 - 25*h - 2. Let n be m(-25). Let i be ((-1)/(-2))/(-3 - n - -2). Factor 0*p + p**2 + i*p**3 + 0.
p**2*(p + 2)/2
Let p = 629 + -623. Let m(k) be the third derivative of 0 + 1/30*k**5 + 0*k - 1/60*k**p + 0*k**3 - 5*k**2 + 0*k**4. Factor m(j).
-2*j**2*(j - 1)
Suppose 2*b - 4*b = -200. Let c be (5 + 0)*40/b. Factor -47 + 2*o**3 + 24 - 2*o - c*o**2 + 25.
2*(o - 1)**2*(o + 1)
Factor 26*i**2 + 31*i**3 - 28*i + 93*i + 15*i + 5*i**3 + 70*i**2 + 4*i**4.
4*i*(i + 2)**2*(i + 5)
Let v(r) be the second derivative of -r**6/45 + 2*r**5/5 + 3*r**4/2 + 14*r**3/9 + 20*r. What is l in v(l) = 0?
-1, 0, 14
Suppose -3*f = 32 - 29. Let g be (108/42)/((-10)/14*f). Suppose g + 12/5*c + 2/5*c**2 = 0. Calculate c.
-3
Factor d**5 + 2*d**5 - 13*d**4 + 4*d**2 - 16 - 2*d**3 + 10*d**3 + 20*d**2 - 16*d.
(d - 2)**3*(d + 1)*(3*d + 2)
Let b(k) = k**3 + 216*k**2 + 15554*k + 373250. Let l(z) = 5*z**3 + 1080*z**2 + 77771*z + 1866251. Let n(x) = 22*b(x) - 4*l(x). Factor n(u).
2*(u + 72)**3
Suppose -6*a + 5*a + 2 = 0. Determine g so that 7*g**a + 26*g - 6 + 12*g**4 - 4*g**2 - 5*g**2 - 26*g**3 - 4*g**4 = 0.
-1, 1/4, 1, 3
Find l such that -2 - 51*l - 14 - 16 - 5*l - 12203*l**2 + 12183*l**2 = 0.
-2, -4/5
Let m(i) be the third derivative of -i**5/180 - i**4/4 - 9*i**3/2 + 26*i**2. Factor m(y).
-(y + 9)**2/3
What is k in -1592*k**4 + 4*k**2 - 20*k**3 + 20*k + 1596*k**4 - 16 + 8*k**2 = 0?
-1, 1, 4
Factor 24/13 - 2/13*t + 2/13*t**3 - 24/13*t**2.
2*(t - 12)*(t - 1)*(t + 1)/13
Suppose 5*n + 4*b - 16 = 0, -2*b = -4*n - 2 - 6. Let z(d) = d**3 - 2*d**2 - d + 2. Let h be z(n). Let -2/5*y**h + 6/5*y - 4/5 = 0. What is y?
1, 2
Let a(u) = 7*u**4 + 18*u**2 + 4*u + 9. Let s(c) = 6*c**4 + c**3 + 17*c**2 + 5*c + 8. Let x(b) = 5*a(b) - 6*s(b). Factor x(z).
-(z + 1)**3*(z + 3)
Let h(m) be the third derivative of m**7/630 - m**5/30 - m**4/9 - m**3/6 + 74*m**2 - 4*m. Factor h(q).
(q - 3)*(q + 1)**3/3
Let a = -1/5970 - -2389/5970. Factor -4/5*w**3 - w**2 + a + 7/5*w.
-(w - 1)*(w + 2)*(4*w + 1)/5
Let x(k) = 2*k**3 + 18*k**2 + 17*k + 12. Let b be x(-8). Let 0 - w - 3/2*w**3 + 7/2*w**b - 7/2*w**2 + 5/2*w**5 = 0. What is w?
-1, -2/5, 0, 1
Let s(g) be the third derivative of 1/30*g**5 - 1/90*g**6 + 7*g**2 + 0*g + 0 + 1/3*g**4 + 5/6*g**3. Let k(l) be the first derivative of s(l). Factor k(r).
-4*(r - 2)*(r + 1)
Find b such that 23/7*b - 10/7 + 1/7*b**4 - 15/7*b**2 + 1/7*b**3 = 0.
-5, 1, 2
Let v(l) be the first derivative of -5*l**6/4 - 69*l**5/10 - 15*l**4/8 + 51*l**3/2 - 27*l**2/2 - 357. Suppose v(t) = 0. Calculate t.
-3, 0, 2/5, 1
Suppose 5*q - y = -5, 5 + 5 = 2*y. Suppose -s + 3*t = 7*t - 3, -t = q. Factor 1/2*l**s + 1/2*l**2 + 0 + 0*l.
l**2*(l + 1)/2
Let u(a) = 135*a**2 - 55*a - 80. Let i = 58 + -60. Let b(f) = -5*f**2 + 2*f + 3. Let g(v) = i*u(v) - 55*b(v). Determine q, given that g(q) = 0.
-1, 1
Let l(g) be the second derivative of g**6/180 - g**5/60 - g**4/18 + g**3/18 + g**2/4 - 5*g. Solve l(f) = 0 for f.
-1, 1, 3
Let 81/7 + 1/7*g**4 - 144/7*g + 46/7*g**2 + 16/7*g**3 = 0. Calculate g.
-9, 1
Let u(w) be the first derivative of -8/3*w**6 + 4/3*w**3 + 7*w**4 - 6*w**2 - 16 - 4*w + 0*w**5. Find v, given that u(v) = 0.
-1, -1/2, 1
Let w = 5/11 - -8/55. Let g(z) be the first derivative of 3*z + 3*z**2 + 0*z**3 - 3/2*z**4 - 1 - w*z**5. Find o, given that g(o) = 0.
-1, 1
Let n = -14 + 21. Suppose 4*l - 115 = 3*z + n, -l - 4*z = -21. Factor 448*v**5 - 2 - 16*v**4 + 149*v**2 - 9 - 365*v**3 + 81*v**3 + 13 - l*v.
(v + 1)*(4*v - 1)**3*(7*v - 2)
Let b be (-9 - (-63)/6)/198. Let v(f) be the third derivative of 0*f + 1/165*f**5 + 0*f**3 - 5*f**2 - b*f**4 + 0 - 1/660*f**6. Solve v(g) = 0 for g.
0, 1
Let m(c) = c**2 - 7*c + 11. Let a be m(5). Let t be 36/(-40)*a/(3/(-5)). Let -3/2*n**2 + 3*n - t*n**3 + 0 = 0. Calculate n.
-2, 0, 1
Let q(m) = 6*m**2 + 1. Let k(y) = 7*y**2 - 2*y + 2. Let a(n) = 5*k(n) - 6*q(n). Let r be a(-10). Solve 3/2*f**3 - 7/2*f**2 + f + 0 + 7/2*f**r - 5/2*f**5 = 0.
-1, 0, 2/5, 1
Let k be (31 + -35)*18/(-228). Suppose k - 26/19*s + 8/19*s**2 = 0. What is s?
1/4, 3
Let t(k) be the second derivative of 1/20*k**5 + 0*k**3 + 0 - 22*k - 1/12*k**4 + 0*k**2. Determine w, given that t(w) = 0.
0, 1
Let y(c) = -15*c**2 + 7*c + 2. Let t be y(-3). Let l be ((-74)/(-44) + 28/t)/3. Find g such that 0*g + 2 - l*g**2 = 0.
-2, 2
Let u(m) be the first derivative of m**7/280 + m**6/60 + m**5/40 - m**3/3 - 6. Let o(j) be the third derivative of u(j). Factor o(t).
3*t*(t + 1)**2
Let s(u) = -150*u + 505. Let b(g) = -g**2 - 151*g + 506. Let z(l) = -5*b(l) + 6*s(l). Let z(c) = 0. What is c?
4, 25
Factor 0 + 12/7*k + 4/7*k**2.
4*k*(k + 3)/7
Let w(j) be the third derivative of j**6/30 + 52*j**5/5 + 1352*j**4 + 281216*j**3/3 + 19*j**2 + j. Factor w(q).
4*(q + 52)**3
Let b(l) = -l + 47 + 4*l + 0. Let u be b(-15). Factor 2/5*w**3 - 4/5 + 0*w**u - 6/5*w.
2*(w - 2)*(w + 1)**2/5
Factor 133 - 65 - 120 + 2*g**2 - 4*g**2 + 30*g.
-2*(g - 13)*(g - 2)
Let q = 25/103 + 137/1133. Factor -2/11 - 2/11*y**2 + q*y.
-2*(y - 1)**2/11
Let r(m) = m**3 - m**2 - 2*m - 4. Let q be r(3). Let l = 10 - q. Find k such that -10*k + 9*k**2 + 3*k**3 - 4*k**4 + l*k**4 - k**4 + 6 - 5*k = 0.
-2, 1
Suppose 2 = -5*t - h, -4*t + 42*h - 6 = 45*h. Factor t*b + 2/3*b**3 - 1/6*b**4 + 0 - 2/3*b**2.
-b**2*(b - 2)**2/6
Let u(o) be the second derivative of 0 + 3/10*o**2 - 15*o - 1/20*o**4 + 0*o**3. Factor u(z).
-3*(z - 1)*(z + 1)/5
Let n be (-45)/350*285/(-38). Let g(f) be the first derivative of 0*f**2 + 2 + 0*f**3 + 18/35*f**5 + 0*f + 1/14*f**6 + n*f**4. Solve g(a) = 0.
-3, 0
Let u(q) be the first derivative of q**8/840 - q**7/140 + q**6/60 - q**5/60 + 5*q**3 - 14. Let l(i) be the third derivative of u(i). Factor l(v).
2*v*(v - 1)**3
Factor 23/8*k + 0 + 1/8*k**2.
k*(k + 23)/8
Factor 9 + 1/2*s**2 + 9/2*s.
(s + 3)*(s + 6)/2
Let u = 59871/5 + -12162. Let v = u + 188. Factor 6/5*x**4 + 0 + 0*x - 1/5*x**3 - v*x**2.
x**2*(2*x - 1)*(3*x + 1)/5
Let x = 647 - 645. Factor 15/4*v**x - 6*v + 9/4.
3*(v - 1)*(5*v - 3)/4
Let s(o) be the first derivative of o**5/240 - 5*o**4/96 + o**3/4 + 27*o**2/2 + 38. Let d(h) be the second derivative of s(h). Find f, given that d(f) = 0.
2, 3
Let t be (0/(-1))/(-1)*7/(-14). Let j(m) be the second derivative of t + 1/4*m**5 - 8*m + 0*m**2 + 5/6*m**4 + 5/6*m**3. Solve j(i) = 0 for i.
-1, 0
Let q = -24653/5 + 4933. Suppose 0 + 8/5*g**2 + 0*g - q*g**3 = 0. What is g?
0, 2/3
Suppose 0 = 3*o + o - 4*g - 12, -6 = 5*o + 2*g. Let k be ((-1)/(-2))/(4/20). Suppose -k*m**3 - 1/2*m**4 + o - 4*m**2 - 2*m = 0. Calculate m.
-2, -1, 0
Let c = -81/5 + 84/5. Factor -c*m**4 + 0*m**3 + 0 + 0*m + 3/5*m**2.
-3*m**2*(m - 1)*(m + 1)/5
Factor 2/5*d**4 - 32/5*d + 0 + 14/5*d**3 + 16/5*d**2.
2*d*(d - 1)*(d + 4)**2/5
Let k(z) be the first derivative of -15/2*z**6 + 80/3*z**3 + 43 + 70*z**4 + 160*z - 200*z**2 - 6*z**5. Find l such that k(l) = 0.
-2, 2/3, 2
Let f(s) be the first derivative of s**5/10 + 23*s**4/4 + 22*s**3/3 - 23*s**2/2 - 45*s/2 + 837. Suppose f(c) = 0. Calculate c.
-