). Determine l so that -28/3*l**4 + 0 - 64/3*l**3 - v*l**2 - p*l = 0.
-1, -2/7, 0
Let c = 33/68 + -49/136. Let x = 10 - 39/4. Determine m, given that 1/8*m**3 - x*m**2 + c*m + 0 = 0.
0, 1
Solve 72 + 5*i**4 - 6*i**5 - 8*i**4 - 35*i**4 + 134*i**2 - 31*i**3 - 11*i**3 + 264*i = 0.
-3, -2, -1/3, 2
Let k(m) be the second derivative of 0*m**2 - 1/18*m**4 - 15*m + 1/9*m**3 + 0. What is u in k(u) = 0?
0, 1
Let t be (158/(-1461))/((-10)/185) + -2. Let j = t + 20443/16071. Solve -8/11 + 38/11*o**2 - 16/11*o - j*o**3 = 0 for o.
-2/7, 1, 2
Let x(d) = -28*d + 3. Let q be x(-1). Suppose 72*z - 37*z - 4*z**2 - q*z = 0. Calculate z.
0, 1
Let y(x) = -66*x - 264. Let d be y(-4). Let -2/13*u**3 + 0*u - 4/13*u**2 + 2/13*u**4 + d = 0. Calculate u.
-1, 0, 2
Let j(q) = -q**3 + 2*q**2 + 2*q + 5. Let r be j(3). Suppose 40*b - 40*b - b**r + 1 = 0. Calculate b.
-1, 1
Let j = 11 - 9. Suppose -5*s + j*s = 9, -3*s + 11 = 4*c. Factor 0 - 2/9*u**c - 2/9*u**3 + 4/9*u**4 + 0*u**2 + 0*u.
-2*u**3*(u - 1)**2/9
Find o such that -2/3*o**3 - 50*o**2 - 1250*o - 31250/3 = 0.
-25
Let j be (-6)/2 + (-342)/4. Let n = -877/10 - j. What is c in -n*c**2 + 0 - 2/5*c**3 - 2/5*c = 0?
-1, 0
Let o(q) be the third derivative of q**5/100 + 17*q**4/5 + 2312*q**3/5 - 190*q**2. Determine s so that o(s) = 0.
-68
Suppose -63 = -29*x + 20*x. Let d be 3 + -9 + x - 1. What is u in -4/5*u**4 + 6/5*u**3 + 4/5*u**2 + d - 6/5*u**5 + 0*u = 0?
-1, -2/3, 0, 1
Suppose -6*t - 10 = -11*t. Factor -11 - 18*s + 2*s**t + s**2 + 17 + 21.
3*(s - 3)**2
Factor 576/7 + 340/7*g**2 + 2112/7*g + 2*g**3.
2*(g + 12)**2*(7*g + 2)/7
Let t(d) be the third derivative of -d**6/30 + 4*d**5/15 + 5*d**4/6 - 70*d**2. Solve t(h) = 0 for h.
-1, 0, 5
Let c = 11807/7874 + 2/3937. Suppose -3/4*t + 3/2 + 3/4*t**3 - c*t**2 = 0. What is t?
-1, 1, 2
Let o(l) be the second derivative of l**8/336 + l**7/42 + l**6/24 - l**5/6 - 5*l**4/6 - 13*l**3/6 - 4*l. Let f(m) be the second derivative of o(m). Factor f(s).
5*(s - 1)*(s + 1)*(s + 2)**2
Find r, given that -2/3*r - 8/9 - 1/9*r**2 = 0.
-4, -2
Let h = -26 + 34. Suppose -8*f**3 + 20*f**2 - 26*f - h*f**3 - 8 - 72*f**2 - 18*f = 0. What is f?
-2, -1, -1/4
Suppose 554 = 15*x - 1231. Let b = 119 - x. Determine a so that -2/5*a**2 + 0*a + b - 2/5*a**3 = 0.
-1, 0
Let f be 8/(-2) + 11 + 0. Suppose 4*n = 2*n + 2*w + 28, -2*n - f = 5*w. Factor 4*s - 5 + n - 4 - 4*s**3.
-4*s*(s - 1)*(s + 1)
Let j(y) = -y**2 - 47*y - 480. Let b be j(-32). Determine a so that b - 9/5*a + 3/5*a**3 - 6/5*a**2 = 0.
-1, 0, 3
Let n(q) be the third derivative of -q**7/21 - 19*q**6/60 - 11*q**5/30 + q**4/4 + 158*q**2. Factor n(l).
-2*l*(l + 1)*(l + 3)*(5*l - 1)
Let r(l) = 5*l**3 - 15*l**2 - 6*l + 23. Let i be r(3). Determine a, given that 0*a + 0*a**4 - 3/4*a**3 - 1/2*a**2 + 1/4*a**i + 0 = 0.
-1, 0, 2
Let p(k) be the second derivative of -5*k**4/24 + 65*k**3/6 - 845*k**2/4 + k + 4. Factor p(o).
-5*(o - 13)**2/2
Suppose 86 = -5*r + 4*o, 0*o - 64 = 4*r - 2*o. Let d be r/(-6)*(-20)/(-350). Find u, given that -d*u - 4/15 + 2/15*u**2 = 0.
-1, 2
Let g(w) be the first derivative of -w**7/84 - w**6/60 + w**5/40 + w**4/24 + 9*w + 1. Let q(n) be the first derivative of g(n). Factor q(p).
-p**2*(p - 1)*(p + 1)**2/2
Let m = -5507/9 - -612. Let o(x) be the second derivative of 0 + 2*x - 1/30*x**5 + 4/9*x**3 + m*x**4 - 8/3*x**2. Factor o(j).
-2*(j - 2)**2*(j + 2)/3
Factor 16*j**2 + 26*j + 2*j**3 + 66 + 12*j - 42*j**2.
2*(j - 11)*(j - 3)*(j + 1)
Suppose -2*c - 54 = -4*x, 0 = 5*x - 6*x - 4*c + 18. Let b(g) be the first derivative of -g**4 + 4 + 12*g - x*g**2 + 20/3*g**3. Factor b(l).
-4*(l - 3)*(l - 1)**2
Let s(z) be the first derivative of 5*z**4/12 + 5*z**3/6 + 22*z - 9. Let u(j) be the first derivative of s(j). Factor u(w).
5*w*(w + 1)
Suppose 11*u + 620 = u. Let b = 127/2 + u. Factor 0*g - g**3 + 0*g**2 + b*g**5 + 0 - 1/2*g**4.
g**3*(g - 1)*(3*g + 2)/2
Let y(b) be the first derivative of -3 + 2/5*b**5 + 0*b**2 + 0*b**3 + 0*b**4 + 0*b + 1/6*b**6. Solve y(x) = 0 for x.
-2, 0
Determine s, given that 606*s**2 - 614*s**2 - 12*s**3 - 2*s**4 - 2*s**4 = 0.
-2, -1, 0
Let m(v) = -v**3 - v**2 - 26. Let o be m(5). Let n = -172 - o. Let 9/5*c**3 - 3/5*c**n + 6/5 - 3/5*c**2 - 9/5*c = 0. Calculate c.
-1, 1, 2
Suppose 4*f = 10*f - 9*f. Let c(o) be the second derivative of f - 7/15*o**3 + 7/50*o**5 - 2/5*o**2 + 5*o + 1/15*o**4. Factor c(i).
2*(i - 1)*(i + 1)*(7*i + 2)/5
Let t(p) be the second derivative of -p**4/84 - 11*p**3/42 - 5*p**2/7 + 32*p. Factor t(l).
-(l + 1)*(l + 10)/7
Let j be (-70)/(-5) + -8 + -4. Let q(d) be the second derivative of 4*d + 1/24*d**3 + 0*d**j + 0 + 1/24*d**4 + 1/80*d**5. Factor q(l).
l*(l + 1)**2/4
Let x(r) = -11*r**3 + 53*r**2 - 140*r + 114. Let h(t) = 9*t**3 - 52*t**2 + 140*t - 116. Let p(c) = 3*h(c) + 2*x(c). Find u, given that p(u) = 0.
2, 6
Let k(m) = 19*m + 439. Let n be k(-23). Let l(p) be the first derivative of -4*p - 1/3*p**3 + 2*p**n - 4. What is i in l(i) = 0?
2
Let -2/9*w**4 - 32 - 176/3*w - 194/9*w**2 + 44/9*w**3 = 0. What is w?
-1, 12
Let c(b) be the first derivative of b**4 - 2*b**2 - 8*b - 25 + 8/3*b**3. Factor c(t).
4*(t - 1)*(t + 1)*(t + 2)
Find o such that -554*o - 145*o**3 + 25 + 34*o + 590*o**2 - 28*o + 15 - 72*o = 0.
2/29, 2
Let b(v) be the first derivative of v**6/180 - 2*v**5/45 + 5*v**4/36 - 2*v**3/9 - 12*v**2 + 10. Let q(c) be the second derivative of b(c). Solve q(j) = 0.
1, 2
Let m(x) = -x**3 - 187*x**2 + 2095*x + 5005. Let u(y) = -y**3 + y**2 - y + 1. Let i(v) = -m(v) + 5*u(v). Suppose i(p) = 0. What is p?
-2, 25
Let t(p) be the second derivative of 2/35*p**7 - 13/100*p**5 - 1/60*p**4 + 1/30*p**3 - 24*p + 1/150*p**6 + 0*p**2 + 0. Suppose t(l) = 0. Calculate l.
-1, -1/3, 0, 1/4, 1
Let q(v) = -v**2 - 17*v - 2. Let b be q(-9). Let n be ((-2)/6)/(b/21 + -5). Factor 3/5*z**2 - 2/5*z + 1/5*z**5 + n*z**3 + 0 - 3/5*z**4.
z*(z - 2)*(z - 1)**2*(z + 1)/5
Let q(h) be the second derivative of -h**5/20 + h**4/12 - h**3/3 - h**2 - 28*h. Let y(c) = -5*c**3 + 4*c**2 - 8*c - 9. Let m(k) = 18*q(k) - 4*y(k). Factor m(r).
2*r*(r - 1)*(r + 2)
Let i(w) be the second derivative of 2/33*w**4 + 0*w**2 + 1/231*w**7 + 16/33*w**3 - 6/55*w**5 + 0 + 1/165*w**6 + 52*w. What is z in i(z) = 0?
-4, -1, 0, 2
Suppose 4*k - 5 = r - 2*r, -k = -5*r + 25. Factor 9*o**3 + o**r + 6*o**2 + o**2 - 27*o + 29*o + 5*o**4.
o*(o + 1)**3*(o + 2)
Solve -24*t**4 + 2493*t**2 + 80*t**3 - 10*t**3 + 2*t**5 - 2541*t**2 = 0 for t.
0, 1, 3, 8
Factor 3 - 7*w - 18*w**3 + 37*w**3 - 20*w**3 + 5*w**2.
-(w - 3)*(w - 1)**2
Determine c, given that -12 - 58*c + 15*c**4 - 11*c**4 - 44*c**2 + 4*c**4 - 4*c**3 + 14*c = 0.
-1, -1/2, 3
What is i in -30*i**3 + 135*i - 20 + 4281*i**5 - 10*i**2 + 110 - 30*i**3 - 4276*i**5 = 0?
-3, -1, 2, 3
Find y such that 2*y - 5/3*y**2 - 1/3*y**5 - 5/3*y**3 + 5/3*y**4 + 0 = 0.
-1, 0, 1, 2, 3
Let r(q) be the third derivative of q**9/60480 + q**8/5376 + q**7/1260 + q**6/720 + 2*q**4/3 + 2*q**2. Let u(t) be the second derivative of r(t). Factor u(o).
o*(o + 1)*(o + 2)**2/4
Let m = 945 + -8485/9. Let r be (-16)/18 - (1 + -3). Suppose -2/9*v**5 + 2/9 + m*v**2 - 20/9*v**3 + r*v**4 - 10/9*v = 0. What is v?
1
Factor -135*n - 106*n + 0*n**2 - 182*n - 2*n**2 + 63*n - 16200.
-2*(n + 90)**2
Let v(p) = 13*p**3 - 71*p**2 + 311*p - 401. Let y(d) = 80*d**3 - 425*d**2 + 1865*d - 2405. Let z(i) = 25*v(i) - 4*y(i). Solve z(a) = 0 for a.
3, 9
Determine l, given that -10/7*l**2 + 0 + 16/7*l**3 - 4*l - 2/7*l**4 = 0.
-1, 0, 2, 7
Suppose -5*r + 109/2*r**3 + 133/2*r**2 - 12 - 5*r**4 = 0. What is r?
-1, -1/2, 2/5, 12
Let l(h) = -7*h**3 - 3*h + 10. Let b(c) = -2*c**3 + c**2 + c. Let j(q) = -4*b(q) + l(q). Factor j(z).
(z - 5)*(z - 1)*(z + 2)
Let g be (-14)/(-63) - (-1356)/(-27). Let y = 50 + g. Determine r so that -1/4*r**3 + y*r**2 + 1/2 + 3/4*r = 0.
-1, 2
Let r = 58 + -55. Solve -3 - 2*d**3 + 6*d**r - 2*d**3 + 11 + 18*d + 12*d**2 = 0.
-4, -1
Let -128/9*m - 2/9*m**5 - 8/3*m**4 - 64/3*m**2 + 0 - 104/9*m**3 = 0. Calculate m.
-4, -2, 0
Let n = -502 - -504. Let j(c) be the first derivative of 5 + 9/7*c**n + 2/3*c**3 + 4/7*c. Factor j(f).
2*(f + 1)*(7*f + 2)/7
Let a(x) be the third derivative of 0*x**3 - 1/42*x**8 - 1/30*x**5 + 0*x + 0*x**4 + 1/15*x**6 + 18*x**2 + 1/105*x**7 + 0. Determine s so that a(s) = 0.
-1, 0, 1/4, 1
Let -23*n**2 - 14/3*n + 1 = 0. Calculate n.
-1/3, 3/23