t l(y) = 4*y + 99. Let i be l(-24). Find v, given that 0 - 6/11*v**i - 2/11*v + 6/11*v**2 + 2/11*v**4 = 0.
0, 1
Suppose 11*c + 0*c = 0. Let a = 57/106 + -2/53. Determine w, given that -1/2*w**4 + c*w - w**3 + 0 - a*w**2 = 0.
-1, 0
Let b = 7 - 3. Factor 2*m**4 + 9*m**3 + 15*m**2 - 3*m**5 + 6*m - 3*m**4 - 2*m**b.
-3*m*(m - 2)*(m + 1)**3
Let j(n) be the second derivative of n**7/189 - 4*n**6/135 + n**5/18 - n**4/27 + 37*n. Solve j(z) = 0 for z.
0, 1, 2
Let f(o) be the third derivative of o**8/42 + 8*o**7/35 + 7*o**6/20 + o**5/6 - o**2 - o. Suppose f(u) = 0. Calculate u.
-5, -1/2, 0
Factor 0 + 8/7*y + 4/7*y**4 + 16/7*y**3 + 20/7*y**2.
4*y*(y + 1)**2*(y + 2)/7
Let b(u) be the first derivative of -4*u**5 - 3*u**4 + 8*u**3/3 + 7. Factor b(r).
-4*r**2*(r + 1)*(5*r - 2)
Let z(t) = -23*t**2 + 11*t. Let j(s) = -8*s**2 + 4*s. Let b = 2 + -8. Let l(o) = b*z(o) + 17*j(o). Factor l(i).
2*i*(i + 1)
Let g(o) = 3*o + 3. Let x be g(2). Let 65*c**2 - 2*c - 4*c + x - 64*c**2 = 0. What is c?
3
Let j(i) be the first derivative of i**5/120 - i**4/72 - i**3/36 + i**2/12 - 2*i - 1. Let l(m) be the first derivative of j(m). Factor l(v).
(v - 1)**2*(v + 1)/6
Let g(y) be the second derivative of y**5/160 - y**4/32 - 3*y**3/16 - 5*y**2/16 + 6*y. Factor g(s).
(s - 5)*(s + 1)**2/8
Let y(z) be the first derivative of z**4/2 + 11*z**3/9 + 2*z**2/3 - 5*z - 1. Let x(s) be the first derivative of y(s). Factor x(r).
2*(r + 1)*(9*r + 2)/3
Suppose 9*x - 4*x = 3*x. Solve 1/2*c - 3/2*c**4 + x - c**5 + 3/2*c**2 + 1/2*c**3 = 0.
-1, -1/2, 0, 1
Factor 4/3 - 1/3*i**2 + 0*i.
-(i - 2)*(i + 2)/3
Let v(m) be the first derivative of -m**6/4 - 3*m**5/10 + 3*m**4/4 + 10. Factor v(y).
-3*y**3*(y - 1)*(y + 2)/2
Let r be 30/36*10/25. Let u = 3 - 1. Determine g so that 0 - r*g**u - 2/3*g = 0.
-2, 0
Suppose -4*i + 2*h = -12, i + 6*h + 8 = h. Let f(n) be the third derivative of -i*n**2 + 1/24*n**4 + 1/9*n**3 + 0 + 1/180*n**5 + 0*n. Solve f(z) = 0.
-2, -1
Let m(s) be the first derivative of s**8/1344 - s**6/240 + s**4/96 - s**2/2 + 4. Let w(g) be the second derivative of m(g). Factor w(r).
r*(r - 1)**2*(r + 1)**2/4
Determine v so that 0*v + 2/5*v**5 + 2/5*v**4 - 2/5*v**2 + 0 - 2/5*v**3 = 0.
-1, 0, 1
Let v(l) = -l**4 + l**3 - l**2. Let a(u) = 6*u**4 - 3*u**3 + 6*u**2. Suppose -3*w + 51 = 21. Let i(q) = w*v(q) + 2*a(q). Factor i(d).
2*d**2*(d + 1)**2
Let m = 327 - 653/2. Determine c so that -1/2 - 1/2*c**5 + c**2 + c**3 - m*c - 1/2*c**4 = 0.
-1, 1
Let n(w) be the second derivative of -w**4/78 - 2*w**3/39 - w**2/13 - 2*w. Let n(y) = 0. What is y?
-1
Let w(b) be the first derivative of -1 - 1/16*b**4 + 0*b + 1/24*b**6 + 0*b**2 - 1/6*b**3 + 1/10*b**5. Find t such that w(t) = 0.
-2, -1, 0, 1
Let y(b) be the first derivative of -b**4 + 16*b**3/3 - 10*b**2 + 8*b + 4. Solve y(c) = 0.
1, 2
Let x(d) be the third derivative of d**6/80 + d**5/20 + d**4/16 - 12*d**2. Let x(i) = 0. What is i?
-1, 0
Suppose -4*p + 14*p = 0. Let b(s) be the third derivative of p - 1/120*s**6 - 2*s**2 + 0*s + 2/3*s**3 - 1/3*s**4 + 1/12*s**5. Factor b(k).
-(k - 2)**2*(k - 1)
Let r(q) be the first derivative of -1/5*q**5 + 0*q + 1/2*q**4 - 1/3*q**3 + 0*q**2 + 2. Find m such that r(m) = 0.
0, 1
Let b(c) = -22*c - 3*c**2 + 6 - c - 7*c**3 + 10*c**2 - 1. Let o(q) = 20*q**3 - 22*q**2 + 68*q - 14. Let g(h) = 14*b(h) + 5*o(h). Let g(m) = 0. What is m?
0, 3
Let b(j) be the second derivative of j**4/3 - 2*j**3 + 4*j**2 + 13*j. Factor b(g).
4*(g - 2)*(g - 1)
Suppose -17*x = -12*x - 30. Let u(a) be the second derivative of 0 + 1/12*a**4 - 1/8*a**5 + 0*a**2 - a + 0*a**3 + 1/20*a**x. Factor u(b).
b**2*(b - 1)*(3*b - 2)/2
Let u = 787 + -784. Factor 0*s - 3/4*s**2 + 7/4*s**u + 0 + 1/4*s**5 - 5/4*s**4.
s**2*(s - 3)*(s - 1)**2/4
Factor -23 + 30*z**2 - 8 + 9*z**3 + 60*z - 72*z**2 + 7.
3*(z - 2)**2*(3*z - 2)
Let d be (-3 - -1) + 0 + 4. Suppose 0 = -2*y - 2*n + 6, -d*y + n = -0 - 6. Find z such that -3*z**3 - y*z + 5*z**3 + z = 0.
-1, 0, 1
Let h be (-22)/33 + 19/(-3). Let p(v) = -v**2 - 6*v + 7. Let b be p(h). Factor 2/3*d**4 + 0*d + b*d**2 + 0 + 0*d**3.
2*d**4/3
Let w(z) = 3*z - 1. Let u(g) = g**3 + 2*g**2. Let h be u(-1). Let n be w(h). What is f in f**3 + 4*f**2 - 2*f**n - 2*f**3 - f**3 - 2*f**4 + 2*f = 0?
-1, 0, 1
Let u(d) = -2*d**2 + 6*d - 4. Let x(z) = z**2 - 3*z + 2. Let m(b) = -2*u(b) - 5*x(b). Factor m(a).
-(a - 2)*(a - 1)
Let n(h) be the third derivative of -3*h**7/490 + h**6/56 - h**5/70 + 29*h**2. Let n(v) = 0. Calculate v.
0, 2/3, 1
Let o(c) be the first derivative of -c**6/3 - 6*c**5/5 - 3*c**4/2 - 2*c**3/3 + 5. Factor o(s).
-2*s**2*(s + 1)**3
Determine j so that -6*j**4 - 146/7*j**3 + 48/7*j + 34/7*j**2 + 8/7 + 14*j**5 = 0.
-1, -2/7, 1
Let f = 146371/210 + -697. Let q(r) be the third derivative of 0 + 0*r - f*r**5 - 1/21*r**4 - 4/21*r**3 + 2*r**2. Find o such that q(o) = 0.
-2
Let f(q) be the third derivative of 5*q**2 - 1/20*q**5 + 0 + 0*q + 0*q**4 + 1/40*q**6 + 0*q**3. Let f(x) = 0. What is x?
0, 1
Let p(f) = -f**3 + 2*f**2 + 4*f - 5. Let m(k) = -k**3 - 4*k**2 - k - 2. Let t be m(-4). Let n be p(t). Suppose 1/4*l + 1/4*l**n + 1/2*l**2 + 0 = 0. What is l?
-1, 0
Let n(g) = g - 1. Let j(m) = -2*m**2 - 7*m + 1. Let x(t) = -j(t) - 3*n(t). Solve x(h) = 0.
-1
Let h(g) be the second derivative of 3*g**5/20 + 5*g**4/2 - 11*g**3/2 + 40*g. Solve h(l) = 0.
-11, 0, 1
Let o(x) be the first derivative of x**4/34 - 10*x**3/51 + 3*x**2/17 + 18*x/17 + 10. What is g in o(g) = 0?
-1, 3
Let b(u) be the second derivative of 3*u**5/20 + u**4/4 - u**3/2 - 3*u**2/2 + 23*u. Factor b(y).
3*(y - 1)*(y + 1)**2
Let k(y) be the first derivative of 1/15*y**5 + 1/12*y**4 - 4 + 0*y - 1/6*y**2 - 1/9*y**3. Factor k(w).
w*(w - 1)*(w + 1)**2/3
Let t be 2/4 - 15/6. Let b be t + (6/3 - 0). Factor 2*q**3 + b*q**2 - q**2 + 3*q**3 - 4*q**3.
q**2*(q - 1)
Find c such that -c**3 + 4/3*c + 4/3 - 5/3*c**2 = 0.
-2, -2/3, 1
What is k in -49/2 + 63/2*k - 15/2*k**2 + 1/2*k**3 = 0?
1, 7
Let a(l) = -l**5 - l**3 - 1. Let v(o) = -11*o**5 - 12*o**4 - 10*o**3 + 10*o**2 + 9*o - 4. Let m(p) = -30*a(p) + 5*v(p). Suppose m(w) = 0. What is w?
-1, -2/5, 1
Let q(d) = 5*d**3 - 2*d**2 + 4*d + 4. Let l(f) = -f**3 - f + 1 - 2 + 0. Let b(h) = 4*l(h) + q(h). Factor b(n).
n**2*(n - 2)
Let c be 3/6 + 39/2. Let x be (4/(-45))/((-4)/c). Determine b, given that -2/9*b**4 + x*b**3 - 8/9*b + 2/3*b**2 - 8/9 = 0.
-1, 2
Let r(g) be the first derivative of -4 + 2*g**3 + 2*g - 1/2*g**4 - 3*g**2. Suppose r(h) = 0. What is h?
1
Let o = 51 - 49. Let f(p) be the first derivative of 5/4*p**4 - 8/3*p**3 + 3 - o*p**2 + 0*p. Determine h, given that f(h) = 0.
-2/5, 0, 2
Let -4*d**2 + 2*d**3 + 3*d**2 - 15*d**2 + 32*d = 0. What is d?
0, 4
Suppose -5*f = -p - 13, -2*f = 3*f + p - 17. Suppose -2*l + 4*v = f*l + 12, 4*l + 3*v - 9 = 0. Suppose -2/5*m**2 - 4/5*m**3 - 2/5*m**4 + l + 0*m = 0. What is m?
-1, 0
Let p = 261 - 7045/27. Let k(v) be the first derivative of -3 - 1/9*v**2 - 4/9*v + p*v**3. Factor k(s).
2*(s - 2)*(s + 1)/9
Let a(m) be the third derivative of 0 + 1/10*m**6 - 1/10*m**5 + 1/2*m**3 + 0*m + 1/70*m**7 + 4*m**2 - 1/56*m**8 - 1/4*m**4. Let a(v) = 0. What is v?
-1, 1/2, 1
Let l(f) be the second derivative of -f**7/14 - 7*f**6/30 + f**5/20 + 7*f**4/12 + f**3/3 + 10*f. Determine x so that l(x) = 0.
-2, -1, -1/3, 0, 1
Suppose -4 + 7 = -z. Let p(r) = r**3 - 4*r**3 + 4*r**3 + 1. Let a(q) = -q**3 + 8*q**2 + 4*q - 4. Let c(o) = z*a(o) - 12*p(o). Suppose c(g) = 0. Calculate g.
-2, -2/3, 0
Let f(k) be the first derivative of k**4/14 - 2*k**3/7 + 2*k**2/7 - 20. Factor f(i).
2*i*(i - 2)*(i - 1)/7
Let s(q) = -q**2 + 7*q + 30. Let v be s(10). Factor v + 1/3*d**4 + d**2 + d**3 + 1/3*d.
d*(d + 1)**3/3
Let p(g) be the third derivative of g**8/840 - 2*g**7/525 + g**6/300 - 31*g**2. Factor p(i).
2*i**3*(i - 1)**2/5
Let q be 548/91 - (25/35 - 1). Find y such that -48/13*y**2 + 0 - q*y**3 - 8/13*y - 42/13*y**4 = 0.
-1, -2/3, -2/7, 0
Let u(w) be the first derivative of 2*w**5/65 + 2*w**4/13 + 10*w**3/39 + 2*w**2/13 - 28. Factor u(v).
2*v*(v + 1)**2*(v + 2)/13
Let w(y) be the second derivative of 3*y**2 - 4*y + 0 - 16/3*y**3 + 32/9*y**4. Factor w(l).
2*(8*l - 3)**2/3
Let k = -295 - -886/3. Let n(i) = -i**3 + 5*i**2 - 4*i + 2. Let r be n(4). Factor k - 2/3*p + 1/3*p**r.
(p - 1)**2/3
Let q(x) be the first derivative of -x**4 + 8*x**3/3 - 2*x**2