106 - 109. Let t be (-19 + 18)*(u + 1). What is j in -6/13*j + 0 + 4/13*j**t + 2/13*j**3 = 0?
-3, 0, 1
Determine v, given that 4*v**2 + 334*v + 335*v - 48 + 3*v**3 + v**3 - 701*v = 0.
-2, 3
Let l(m) be the first derivative of 2*m**3/39 - 3*m**2/13 - 56*m/13 - 69. Determine x so that l(x) = 0.
-4, 7
Suppose 1757*v - 1703*v - 162 = 0. Solve 1/5*d**v + 7/5*d**2 - 16/5 + 8/5*d = 0 for d.
-4, 1
Let o(k) = k**2 + k. Let a(h) = -h**3 + 5*h**2 + 7*h - 7. Let v be a(6). Let g(j) = -2*j**2 - 16 - 7*j - 10 + 18 - 3*j. Let f(b) = v*g(b) + 2*o(b). Factor f(c).
4*(c + 1)*(c + 2)
Let h(v) be the first derivative of 19 - 2/7*v**2 + 0*v + 4/21*v**3 + 1/7*v**4 - 4/35*v**5. Factor h(n).
-4*n*(n - 1)**2*(n + 1)/7
Suppose -2*k - 15 + 3 = -2*y, 2*y + k = 0. Suppose -2*l + 1 + 1 = 4*g, -3*g - y = -2*l. Solve 3/2*q**4 + g*q + 0 + 3*q**2 + 9/2*q**3 = 0.
-2, -1, 0
Let l(q) be the third derivative of q**6/300 - 2*q**5/75 - q**4/4 + 6*q**3/5 + 179*q**2. Factor l(z).
2*(z - 6)*(z - 1)*(z + 3)/5
Suppose -2*p = p - 4*o - 17, -8 = -2*o. Factor -5 + 5*w**2 + 6*w + p + 14*w + 9.
5*(w + 1)*(w + 3)
Let n(m) = 3*m - 7. Let b be n(2). Let g(v) = v**4 + 1. Let u(s) = 18*s**4 - 6*s**3 - 15*s**2 + 6*s + 3. Let t(x) = b*u(x) + 3*g(x). Factor t(y).
-3*y*(y - 1)*(y + 1)*(5*y - 2)
Let m = -20 - -25. Factor 27*h**2 - 16*h - 67*h**2 + 25*h**2 + 6*h - m*h**3.
-5*h*(h + 1)*(h + 2)
Let d(f) = 16*f**2 + 3740*f - 1072. Let v(q) = -19*q**2 - 3741*q + 1072. Let r(p) = 3*d(p) + 4*v(p). Factor r(x).
-4*(x + 134)*(7*x - 2)
Let y(h) = 8*h + 504. Let s be y(-63). Let b(l) be the second derivative of s + 1/12*l**4 + 1/2*l**2 + 1/3*l**3 + 8*l. Find o such that b(o) = 0.
-1
Let v(x) be the second derivative of -5*x**4/12 - 35*x**3/6 + 45*x**2 - 57*x + 1. What is m in v(m) = 0?
-9, 2
Suppose -5*t + 41 + 24 = 0. Factor t + 9*f + 15*f**3 - 48*f**2 - 33 + 20.
3*f*(f - 3)*(5*f - 1)
Suppose 0 + 1/2*v**2 - v = 0. Calculate v.
0, 2
Let o(u) = -2*u**3 - 13*u**2 - 10*u + 25. Let g be o(-5). Factor -2/11*b**4 + 0*b + 2/11*b**3 + g*b**2 + 0.
-2*b**3*(b - 1)/11
Suppose -s - 20 = -4*c, -c = 3*c - 20. Let k be s + 8/308*7. What is h in 0 + 2/11*h - 2/11*h**3 - 2/11*h**4 + k*h**2 = 0?
-1, 0, 1
Factor -4 - 1/5*r**2 - 21/5*r.
-(r + 1)*(r + 20)/5
Let o(u) = -3*u**2 - 29*u - 14. Let h be o(-9). Let y(c) be the first derivative of -15/2*c**2 - 3/4*c**4 - h*c**3 - 1 - 6*c. Factor y(t).
-3*(t + 1)**2*(t + 2)
Let c(d) be the third derivative of -d**9/5040 - d**8/560 + 2*d**4/3 + 7*d**2. Let g(s) be the second derivative of c(s). Factor g(y).
-3*y**3*(y + 4)
Let i(c) = -2*c**4 + c**3 - c**2 + c - 1. Let f(k) = -11*k**4 - 809*k**3 - 73714*k**2 - 2259896*k - 2187004. Let j(v) = f(v) - 4*i(v). Factor j(l).
-3*(l + 1)*(l + 90)**3
Suppose 162*s = 160*s + 4. Let d = -9 + 9. Determine p so that d*p + 0 + 2/9*p**s = 0.
0
Let o(x) = 1. Let u be (-8)/(-6) - 6/(-9)*10. Let w(m) = 2*m**2 + 12*m + 18. Let v(l) = u*o(l) - w(l). Factor v(n).
-2*(n + 1)*(n + 5)
Factor 2/15*u**3 + 4/15 - 2/5*u + 0*u**2.
2*(u - 1)**2*(u + 2)/15
Let k(z) be the first derivative of -z**6/6 - 3*z**5/5 + z**4 + 4*z**3 + 197. Factor k(b).
-b**2*(b - 2)*(b + 2)*(b + 3)
Let h(m) be the third derivative of 15*m**2 + 0 + 5/16*m**4 + m**3 + 1/40*m**5 + 0*m. Factor h(i).
3*(i + 1)*(i + 4)/2
Let u(g) be the third derivative of -g**9/37800 + g**7/3150 - g**5/300 - 7*g**4/12 - 13*g**2. Let m(z) be the second derivative of u(z). Factor m(w).
-2*(w - 1)**2*(w + 1)**2/5
Let t be 35 + -41 + (-43)/(-6). Let i(v) be the first derivative of 9/4*v**2 - t*v**3 + 2 - v. Factor i(s).
-(s - 1)*(7*s - 2)/2
Solve 62*x**2 - 32*x**3 - 5*x**2 + 52*x**2 + 62*x + 3*x**2 + 8 = 0.
-1/4, 4
Let k = 593 + -1778/3. Let n(d) be the first derivative of 1/6*d**4 + 0*d - 6 - 2/9*d**3 + 2/15*d**5 - k*d**2. Factor n(m).
2*m*(m - 1)*(m + 1)**2/3
Let k = 453 - 2261/5. Factor 6/5*i - 2/5*i**2 - k.
-2*(i - 2)*(i - 1)/5
Determine g, given that -32*g + 2*g**3 + 56/5 + 46/5*g**2 = 0.
-7, 2/5, 2
Let c(s) = 3*s**3 - s**2 - s + 1. Let x be c(1). Factor q**2 + 2 - 4*q + x*q**2 - q**2.
2*(q - 1)**2
Let m(x) be the third derivative of -x**6/900 - 11*x**5/450 + 5*x**4/36 - 13*x**3/45 + 2*x**2 - 33*x. What is l in m(l) = 0?
-13, 1
Find b such that -6*b**2 + 24*b**3 + 13 - 15*b - 17*b**2 - 15 + 16*b**4 = 0.
-2, -1/4, 1
Let p(b) be the first derivative of 4*b + 23*b**3 - 7 - 22*b**2 + 169/5*b**5 + 143/2*b**4. Factor p(i).
(i + 1)**2*(13*i - 2)**2
Let q(v) = 28*v**3 - 4*v + 3. Let w be q(2). Let o be w/231 + 1/(-11). Find h, given that -6/7*h**3 - 2/7*h**4 + 0 - 2/7*h - o*h**2 = 0.
-1, 0
Let g(i) be the third derivative of i**8/168 - 4*i**7/105 + i**6/20 + 2*i**5/15 - i**4/3 - 115*i**2. Solve g(l) = 0 for l.
-1, 0, 1, 2
Let d be 192/15 + 2/10. Let x = -11 + d. Factor 8*p**3 + p**3 + 3*p**x + 0*p**3 - 20*p**4 + 8*p**4.
-3*p**2*(p - 1)*(4*p + 1)
Let t(d) be the first derivative of d**7/420 - d**5/40 + d**4/24 + 21*d**2/2 - 18. Let z(q) be the second derivative of t(q). Factor z(r).
r*(r - 1)**2*(r + 2)/2
Let t(h) be the first derivative of h**6/30 - 4*h**5/25 + 3*h**4/10 - 4*h**3/15 + h**2/10 - 269. Factor t(i).
i*(i - 1)**4/5
Suppose 103*k**4 - 11*k**3 - 106*k**4 + 24*k**2 - 154*k + 174*k = 0. What is k?
-5, -2/3, 0, 2
Let a = -1372 + 1375. Let f(h) be the second derivative of -1/4*h**4 + h**a + 0*h**2 + 0 + 5*h. Factor f(l).
-3*l*(l - 2)
Suppose 2/17*s**2 + 450/17 - 60/17*s = 0. What is s?
15
Let -12/7*v + 0*v**2 + 4/7*v**3 - 8/7 = 0. Calculate v.
-1, 2
Let j be 24/10 + 20/(-50). Factor 12*u + 3*u - 29*u - u**j.
-u*(u + 14)
Let w = -31294 - -125179/4. Let -3/2*p**3 + w*p**4 + 3/4*p**2 + 0 + 0*p = 0. Calculate p.
0, 1
Let h(r) = -4*r**2 + 28*r - 111. Let l(c) = -2*c**2 + 14*c - 52. Let j(g) = -4*h(g) + 9*l(g). Factor j(v).
-2*(v - 4)*(v - 3)
Let z(i) = 10*i**3 - 8*i**2 - i + 2. Let j(h) = 16*h**3 - 14*h**2 - h + 4. Let w(g) = 3*j(g) - 5*z(g). What is x in w(x) = 0?
-1, 1
Let f be (-174)/(-406) + (-1)/(-14)*-6*1. Find d, given that -2/5*d**4 + 4*d**3 + 0 + f*d - 10*d**2 = 0.
0, 5
Let l(p) = -5*p**4 - 9*p**2 - 2*p + 4. Let u(g) = -g**2 + 1 - 5*g**3 - g**4 - 6*g**3 + 10*g**3 - g. Let y(w) = l(w) - 4*u(w). What is b in y(b) = 0?
0, 1, 2
Let k be 2*(139/8)/((-3)/(-12)). Let z = -692/5 + k. Factor 0 + z*v**2 - 3/5*v.
3*v*(v - 1)/5
Let p(n) be the second derivative of n**4/15 + 3*n**3/5 - 7*n**2 - 2*n + 375. Solve p(w) = 0.
-7, 5/2
Let x(d) be the third derivative of -1/70*d**7 + 18*d**2 + 0*d**3 + 0*d + 0*d**5 + 1/20*d**6 + 0 + 0*d**4. Factor x(m).
-3*m**3*(m - 2)
Let h be (1 + -7)*(-24)/216. Factor 0 + o**2 - h*o + 2/3*o**3.
o*(o + 2)*(2*o - 1)/3
Let i = -3881 + 19407/5. Factor -i*k**2 + 2/5 + 0*k.
-2*(k - 1)*(k + 1)/5
Let r(i) = i**5 + i**4 - 3*i**3 - i**2 - 1. Let x(a) = 4*a**5 + a**4 - 9*a**3 - a**2 - a - 3. Let k(t) = 3*r(t) - x(t). Factor k(w).
-w*(w - 1)**3*(w + 1)
Find h such that -16406 + 32864 + 4*h**4 - 16428 + 113*h**3 - 208*h**2 + 61*h = 0.
-30, -1/4, 1
Let q(j) = 117*j + 21. Let a(f) = -f**2 + 117*f + 19. Let y(n) = -4*a(n) + 5*q(n). Find t such that y(t) = 0.
-29, -1/4
Let p(y) = 2*y**3 - 17*y**2 - 7*y - 19. Let u be p(9). Let i be 6/63*(4 + u)*1. Suppose 0 - 4/7*v**2 + 2/7*v**3 + i*v = 0. What is v?
0, 1
Suppose -k + 13 = -7. Let w = k + -20. Factor 0 + 1/2*h**2 + w*h - 3/2*h**3.
-h**2*(3*h - 1)/2
Suppose -4*j - z = -2*z - 647, 4*j + 4*z - 632 = 0. Suppose -j*f + 164*f - 12 = 0. Factor 0*q**3 + 0 + 0*q + 0*q**2 - 2/7*q**f.
-2*q**4/7
Let o(h) = -h**4 - h**3 + 3*h + 1. Let t(f) = -7*f**4 - 26*f**3 - 9*f**2 - 3*f - 1. Let b(j) = -5*o(j) - 5*t(j). Factor b(w).
5*w**2*(w + 3)*(8*w + 3)
Determine q, given that 27*q**4 + 3/2*q**5 + 363/2*q**3 + 0 + 540*q**2 + 600*q = 0.
-5, -4, 0
Determine t, given that 6*t**2 - 6*t**2 - 4*t**2 - 2*t**4 + 6*t**3 = 0.
0, 1, 2
Let j(t) = 3*t**5 - 6*t**4 - 3*t**3 - 6*t - 3. Let g(m) = -9*m**5 + 18*m**4 + 8*m**3 - 2*m**2 + 17*m + 8. Let n(q) = -3*g(q) - 8*j(q). Factor n(l).
3*l*(l - 1)**3*(l + 1)
Let n = -14030 - -14032. Factor -10/3*s + 0 + 5/3*s**n.
5*s*(s - 2)/3
Let s(y) be the second derivative of -3*y - 1/120*y**6 + 1/8*y**4 + 0*y**5 - 3 + 3/8*y**2 + 1/3*y**3. Factor s(k).
-(k - 3)*(k + 1)**3/4
Let d(k) = -k**2 + k. Let y(b) = -2*b**3 + 11*b**2 - 11*b. Suppose 154 = -13*l + 6*l. Let h(z) = l*d(z) - 2*y(z). Solve h(f) = 0.
0
Let q(r) be the first derivative of 5/3*r**3 + 4*r - 1/4*r**