3). Let s(x) = -x - 4. Let f be s(-7). Factor 0 + 0*n + l*n**2 - 1/2*n**f.
-n**2*(n - 1)/2
Suppose 0*j + 2*j = 0. Let s(f) be the first derivative of -8*f**2 - 40/3*f**3 + 162/5*f**5 + 9*f**4 - 1 + 18*f**6 + j*f. Let s(u) = 0. Calculate u.
-2/3, 0, 1/2
Let x(n) = -9*n**2 - 17*n - 5. Let d(k) = -5*k**2 - 9*k - 3. Let w(c) = -7*d(c) + 4*x(c). Let m be w(-4). Let 2*l**5 - 3*l + l**3 + m*l - 5*l**3 = 0. What is l?
-1, 0, 1
Let l = 2 - -2. Suppose u - 4*c - 2 = 0, -4*u - u + l*c = -10. Determine q so that 3*q - 6*q**u - q + 0*q + 4 = 0.
-2/3, 1
Let r be 2/(-12) - 20/72. Let p = 2/9 - r. Suppose 0 + p*y**2 + 0*y - 2/3*y**3 = 0. Calculate y.
0, 1
Let r(m) be the third derivative of -m**8/224 - m**7/70 + m**5/20 + m**4/16 - 27*m**2. Solve r(q) = 0.
-1, 0, 1
What is y in 49/4 + 1/4*y**2 - 7/2*y = 0?
7
What is u in 3*u**4 - 51*u - 43*u - 9*u**2 + 100*u = 0?
-2, 0, 1
Let n(c) = -c**2 + 3*c - 2. Let y(x) be the second derivative of x**3/6 - x**2/2 + 5*x. Let f be (-46)/14 - (-2)/7. Let v(b) = f*y(b) + n(b). Factor v(j).
-(j - 1)*(j + 1)
Suppose 4*f + g - 2*g - 49 = 0, -g = 5. Suppose -2*d = q - f, -2*q - 18 + 4 = -5*d. Solve 4 + 2*t + 2*t**2 + d*t + 0*t = 0 for t.
-2, -1
Let d(q) be the second derivative of 0*q**2 - 1/100*q**5 + q - 1/210*q**7 + 0*q**3 + 0*q**4 + 0 - 1/75*q**6. What is z in d(z) = 0?
-1, 0
Let g(o) = -2*o - 4. Let i be g(-4). Factor 0*v**3 + 2*v**2 + 2*v + 2*v**3 + 2 - 4*v**2 - i*v**3.
-2*(v - 1)*(v + 1)**2
Let n(f) be the third derivative of f**6/30 + f**5/30 + f**3/3 + 3*f**2. Let p(j) = 13*j**3 + 6*j**2 + 7. Let x(q) = -7*n(q) + 2*p(q). Factor x(h).
-2*h**2*(h + 1)
Solve -4*m**5 + 2*m**2 - 4*m**5 + 2*m**4 + 4*m**3 - 4*m**4 + 4*m**3 = 0.
-1, -1/4, 0, 1
Let j = -5 - -7. What is f in 9*f - j*f**2 - 2*f - 3*f = 0?
0, 2
Let h(k) be the second derivative of k**4/12 + 2*k**3 + 8*k**2 - 2*k. Let d be h(-11). Factor b**4 + b**3 + 1/3*b**d + 0*b + 1/3*b**2 + 0.
b**2*(b + 1)**3/3
Let k(n) be the third derivative of 1/132*n**4 + 0*n + 0*n**3 - 6*n**2 + 2/165*n**6 + 0 - 1/66*n**5 - 4/1155*n**7. Let k(c) = 0. What is c?
0, 1/2, 1
Let n be (1/(-8))/(17/(-34)). What is y in -1/4*y + n*y**3 + 0*y**2 + 0 = 0?
-1, 0, 1
Let b(d) be the second derivative of -49*d**8/3840 - 7*d**7/240 - 7*d**6/240 - d**5/60 - d**4/4 - 2*d. Let v(l) be the third derivative of b(l). Factor v(p).
-(7*p + 2)**3/4
Suppose -67 - 5*a**4 - 15*a + 77 - 5*a**3 + 20*a**3 - 5*a**2 = 0. Calculate a.
-1, 1, 2
Let o = -10 + 10. Let d(l) be the third derivative of -2/105*l**5 + 0 + o*l - 1/21*l**3 + 1/21*l**4 + 2*l**2. Factor d(u).
-2*(2*u - 1)**2/7
Let q be (2 + -3)*-1*2. Suppose q*j = 5*j - 6. Solve 4*c - 2*c**2 - 5 + j + 1 = 0.
1
Let z(b) be the first derivative of -b**3/12 + 3*b**2/8 - b/2 - 7. Factor z(s).
-(s - 2)*(s - 1)/4
Suppose -2*a**5 - 5*a**2 + 5*a**5 + 14*a**3 - 8*a - 13*a**4 + 9*a**2 = 0. What is a?
-2/3, 0, 1, 2
Solve -1/2*c**3 + 0 + 0*c + 1/4*c**2 - 3/4*c**4 = 0 for c.
-1, 0, 1/3
Let p(h) be the second derivative of -h**7/420 + h**6/90 - h**5/60 - 4*h**3/3 + 7*h. Let i(l) be the second derivative of p(l). Factor i(f).
-2*f*(f - 1)**2
Let r be (-1 + (-1)/3)*(-24)/48. Suppose 2/9*k**2 + r - 8/9*k = 0. What is k?
1, 3
Let t be (-8)/36 + 29/9. Let k(d) be the second derivative of -1/4*d**4 - 1/60*d**6 - 1/4*d**2 + 2*d + 0 + 1/3*d**t + 1/10*d**5. Suppose k(g) = 0. What is g?
1
Let w(c) be the first derivative of -c**2/2 + 4. Let s(m) = -2*m + 2 - 2*m + m**2 - 1. Let i(n) = -2*s(n) + 4*w(n). Solve i(b) = 0 for b.
1
Let g(b) = b + 5. Let y be g(-5). Let d(q) be the first derivative of 0*q + y*q**2 - 1/4*q**4 + 1/3*q**3 + 2. Suppose d(x) = 0. Calculate x.
0, 1
Let f(i) be the second derivative of 1/70*i**5 + 0*i**4 - 4*i - 1/21*i**3 + 0 + 0*i**2. Factor f(s).
2*s*(s - 1)*(s + 1)/7
Let g(d) be the first derivative of d**7/21 - d**6/15 - d**5/10 + d**4/6 + 3*d - 2. Let y(t) be the first derivative of g(t). Factor y(w).
2*w**2*(w - 1)**2*(w + 1)
Let q(w) be the second derivative of -w**7/105 - w**6/75 + w**5/50 + w**4/30 + 7*w. Let q(a) = 0. What is a?
-1, 0, 1
Determine u so that -5/4*u + 3/4*u**3 + 1/2 - u**2 = 0.
-1, 1/3, 2
Let h(f) be the second derivative of 0 - 1/21*f**7 + 0*f**2 + 1/3*f**4 + 0*f**5 + 1/3*f**3 - 2/15*f**6 - 2*f. Factor h(q).
-2*q*(q - 1)*(q + 1)**3
Let m = 5 - 3. Solve 3*b - b + 7*b**2 - 23*b**m = 0.
0, 1/8
Let f(l) be the second derivative of -l + 1/80*l**5 - 1/24*l**3 + 0 + 1/4*l**2 - 1/24*l**4. Suppose f(d) = 0. Calculate d.
-1, 1, 2
Let k be ((-38)/3)/((-4)/6). Let t = -9 + k. Factor 4*b**4 - b**3 + 2*b**2 - 6*b**5 - 9*b**3 + t*b**4.
-2*b**2*(b - 1)**2*(3*b - 1)
Let c(l) = -20*l**4 + 11*l**3 + 27*l**2 - 7*l + 11. Let j(o) = 7*o**4 - 4*o**3 - 9*o**2 + 2*o - 4. Let v(d) = 4*c(d) + 11*j(d). Factor v(y).
-3*y*(y - 1)**2*(y + 2)
Suppose -5*d + 29 = 3*b - b, 2*b - 9 = -d. Suppose 2*q**2 + 0*q**2 + q**3 + d*q**3 = 0. Calculate q.
-1/3, 0
Determine x so that -11*x**4 - 7*x + 3*x**5 + 5*x - 9*x**5 - 24*x**3 - 9*x**4 - 12*x**2 = 0.
-1, -1/3, 0
Find a such that 36*a**4 + 3*a**3 + 3*a**5 - 5 - 36*a**2 + 12*a - 18*a**5 + 5 = 0.
-1, 0, 2/5, 1, 2
Factor 4/9*t**2 + 0*t + 2/9*t**4 + 0 + 2/3*t**3.
2*t**2*(t + 1)*(t + 2)/9
Let q(v) be the second derivative of v**7/42 + v**6/30 - v**5/20 - v**4/12 - 4*v. Factor q(y).
y**2*(y - 1)*(y + 1)**2
Find s such that 0*s - 2/5*s**2 + 0 = 0.
0
Let k be ((-3)/(-6))/1*8. Let w be 0/((k - 3)*2). Factor w*t**2 + 13*t**4 + 12*t**4 - 20*t**3 + 4*t**2.
t**2*(5*t - 2)**2
Let d be (-4 - (-33)/9)*-9. Let c(t) be the third derivative of 1/40*t**5 + 0 + 0*t**d + 0*t + 1/16*t**4 - 4*t**2. What is y in c(y) = 0?
-1, 0
Let z(v) be the first derivative of v**8/252 - v**7/105 + v**6/180 - v**2/2 + 3. Let s(w) be the second derivative of z(w). Determine l, given that s(l) = 0.
0, 1/2, 1
Let s(v) = -2*v - 3 - 1 + 0*v. Let l be s(-4). Let r**4 + 2*r**3 - 3*r**l - 4*r**3 = 0. Calculate r.
-1, 0
Suppose -4/7*j + 0 + 2/7*j**2 = 0. Calculate j.
0, 2
Let w(p) be the third derivative of p**6/30 + 3*p**2. Factor w(k).
4*k**3
Let y(w) be the third derivative of -w**8/2016 + w**7/420 + w**6/720 - w**5/120 - 11*w**2. What is i in y(i) = 0?
-1, 0, 1, 3
Suppose -2*l = 2*l + 40. Let f be (4/l)/((-5)/25). Factor 0 - 2 + g**3 + 2*g**2 + f*g - 3*g**3.
-2*(g - 1)**2*(g + 1)
Let c = -3/14 + 23/42. Suppose -2*i = -3*i. Solve 0 + 1/3*y**4 - c*y**2 + i*y**3 + 0*y = 0 for y.
-1, 0, 1
Let f = 204/665 - 2/95. Suppose f*j**4 + 0 - 4/7*j**2 + 0*j - 2/7*j**3 = 0. Calculate j.
-1, 0, 2
Let l(w) = 7*w**3 + 21*w**2 + 3*w - 3. Let m(j) = 8*j**3 + 20*j**2 + 4*j - 4. Let v(k) = -4*l(k) + 3*m(k). Factor v(n).
-4*n**2*(n + 6)
Suppose 0 + 2/3*q**3 - 2/3*q + 0*q**2 = 0. What is q?
-1, 0, 1
Let j be (2/120)/(2/4). Let i(n) be the second derivative of 2*n + 0 + 0*n**3 - j*n**4 + 1/5*n**2. Factor i(m).
-2*(m - 1)*(m + 1)/5
Suppose -2*t - 12 = -5*i, -3*i + 14 = 3*t - 10. Suppose t*q - 3 = 5. Suppose -d - 1/2 - 1/2*d**q = 0. What is d?
-1
Let z = 72 - 68. Determine d, given that 0 + 14/11*d**5 - 4/11*d**3 - 10/11*d**z + 0*d**2 + 0*d = 0.
-2/7, 0, 1
Let o(j) = j**2 - j + 1. Let t(k) = -10*k**2 + 5. Let y(i) = -5*o(i) - t(i). Factor y(u).
5*(u - 1)*(u + 2)
Suppose 2*a**2 - 4*a + 11 - 4*a - 3 = 0. What is a?
2
Let b(y) be the first derivative of -1/20*y**4 + 0*y + 2 - 2/15*y**3 - 1/10*y**2. Factor b(l).
-l*(l + 1)**2/5
Let h(y) be the first derivative of 0*y - 4/9*y**3 + 0*y**2 + 2 + 0*y**4 + 1/18*y**6 + 1/5*y**5. Factor h(r).
r**2*(r - 1)*(r + 2)**2/3
Let v = 293/2310 + 1/154. Let -2/15*m**2 + 4/15*m - v = 0. What is m?
1
Let g(j) be the second derivative of -j**7/28 - 7*j**6/60 + 13*j**5/60 + j**4/4 - 17*j**3/36 + j**2/4 - 12*j + 1. Solve g(d) = 0.
-3, -1, 1/3, 1
Suppose 1 = d - 1. Let v(s) be the first derivative of -1/5*s**4 - 3 - 4/15*s**3 + 2/5*s + 2/25*s**5 + 1/15*s**6 + 1/5*s**d. Factor v(j).
2*(j - 1)**2*(j + 1)**3/5
Suppose o = -2*y + 3*o - 12, -5*y - 5*o = 50. Let c be (-6)/9*(y + 5). Find f, given that 1/2 + f**4 + 1/2*f - 3/2*f**c - 1/2*f**3 = 0.
-1, -1/2, 1
Let h(n) be the first derivative of 0*n + 3/20*n**4 - 1/5*n**3 + 3 + 3/25*n**5 - 3/10*n**2. Suppose h(k) = 0. Calculate k.
-1, 0, 1
Let a(o) be the first derivative of -o**3/12 + o**2/4 + 37. Determine u so that a(u) = 0.
0, 2
Let g(w) be the second derivative of w**4/6 + 4*w**3 + 36*w**2 + 20*w. Determine l so that g(l) = 0.
-6
L