 - 1/90*p**5 + 1/36*p**4 + 0 + 0*p + 2/9*p**3. Find k such that s(k) = 0.
-1, 2
Let p(g) be the first derivative of -g**4/6 - 2*g**3/3 - g**2 - 2*g/3 - 11. Factor p(l).
-2*(l + 1)**3/3
Let h(g) be the first derivative of g**5/5 - 3*g**4/4 + g**3/3 + 3*g**2/2 - 2*g + 7. Factor h(p).
(p - 2)*(p - 1)**2*(p + 1)
Let p(j) be the second derivative of -7*j**5/15 - 10*j**4/3 - 16*j**3/9 + 11*j. Factor p(i).
-4*i*(i + 4)*(7*i + 2)/3
Factor 5/3*s**2 - 10/3 - 5*s + 5*s**3 + 5/3*s**4.
5*(s - 1)*(s + 1)**2*(s + 2)/3
Let z(d) = d**2 + 5*d + 4. Let p be z(-5). Let t = -2 + p. Factor -4/9*h**t + 2/9*h + 0 + 2/9*h**3.
2*h*(h - 1)**2/9
Let n(q) = q**3 + 2*q**2 - 1. Let h be n(1). Let u**2 + 1 + u + 2*u**h + 5 + 8*u = 0. Calculate u.
-2, -1
Let k(s) be the third derivative of s**5/60 - s**4/24 - 45*s**2. What is c in k(c) = 0?
0, 1
Suppose 8*p - 15 = 3*p. Factor 32*v**2 + v**p - 32*v**2 - v.
v*(v - 1)*(v + 1)
Let x = 89 - 89. Suppose 4*g = -l - 2, g - 4*l + 0*l = 8. Let g - 1/4*z**5 - 1/4*z**4 + 0*z**3 + x*z**2 + 0*z = 0. What is z?
-1, 0
Let l = -57/68 + 997/1088. Let q = 183/704 - l. Factor -6/11*s**2 + q*s**3 + 8/11 + 0*s.
2*(s - 2)**2*(s + 1)/11
Let g = -4 + 18. Let u be 8/14*g/4. Factor 4/7*o**u + 2/7*o**5 + 2/7*o - 2/7 - 2/7*o**4 - 4/7*o**3.
2*(o - 1)**3*(o + 1)**2/7
Let f be 0 + 2 - (1 + 3). Let t(u) = 2*u**2 + 2*u + 1. Let d be t(f). Suppose 2/7*a**4 + 2/7*a**3 - 2/7*a**2 + 0 - 2/7*a**d + 0*a = 0. Calculate a.
-1, 0, 1
Let q(r) = r**2 + 2*r - 22. Let c be q(-6). Let i(z) be the third derivative of -c*z**2 - 1/90*z**5 + 1/9*z**3 + 0 + 1/72*z**4 - 1/360*z**6 + 0*z. Factor i(m).
-(m - 1)*(m + 1)*(m + 2)/3
What is p in 0 + 1/3*p - 1/2*p**5 - 1/2*p**2 + 7/6*p**4 - 1/2*p**3 = 0?
-2/3, 0, 1
Let w(q) be the third derivative of q**6/160 - q**5/40 + q**2. Factor w(h).
3*h**2*(h - 2)/4
Let d = -13199/48 - -275. Let b(v) be the second derivative of -d*v**4 + 0 - 1/2*v**2 + 1/6*v**3 + 3*v. Factor b(o).
-(o - 2)**2/4
Let t(y) be the first derivative of -y**4/2 + 2*y**3/3 + 4*y**2 - 8*y + 52. Let t(f) = 0. What is f?
-2, 1, 2
Let h be ((-2)/3)/((-4)/18). Suppose d - 7*i + 2*i = 15, 13 = h*d + i. Suppose 18*a**4 + d*a + 37*a**3 + 3*a + 32*a**2 + 5*a**3 = 0. What is a?
-1, -2/3, 0
Let k be ((-20)/25)/((-6)/15). Let 13*n**k - 12*n**2 - 1 + 0 = 0. Calculate n.
-1, 1
Let g(k) be the third derivative of -k**7/30 - 3*k**6/40 - k**5/30 - 9*k**2. Factor g(m).
-m**2*(m + 1)*(7*m + 2)
Let r(l) be the first derivative of 1/42*l**4 - 4/21*l**3 - 1 - l + 4/7*l**2. Let t(w) be the first derivative of r(w). Find a, given that t(a) = 0.
2
Let d(c) be the first derivative of -c**5/5 - 5*c**4/8 - 2*c**3/3 - c**2/4 + 2. Factor d(j).
-j*(j + 1)**2*(2*j + 1)/2
Let l(f) be the second derivative of 1/5*f**2 + 2/15*f**3 + 1/30*f**4 + 0 - 5*f. Factor l(k).
2*(k + 1)**2/5
Let u be (-16)/(-2) + (-6)/3. Let r = u + -4. Factor 2*h**5 - 4*h**4 - 2*h + 4*h**r - h**5 + h**5.
2*h*(h - 1)**3*(h + 1)
Suppose 4*v + v = -35. Let d(a) = a**2 + 7*a + 4. Let l be d(v). Factor 4*m**3 - 5 - 2*m - 2*m**5 - 2*m**4 + 4*m**2 + 3 - m**l + m**4.
-2*(m - 1)**2*(m + 1)**3
Let o(q) = -125*q**2 - 93*q - 18. Let f(i) = 124*i**2 + 92*i + 18. Let n(m) = 3*f(m) + 4*o(m). Suppose n(y) = 0. What is y?
-3/8
Factor -13*x**3 + 4*x**4 + 32*x**3 - 15*x**3.
4*x**3*(x + 1)
Let v(t) = -9*t**4 - 20*t**3 - 25*t**2 - 14*t + 4. Let r(f) = f**4 + f - 1. Let b(w) = -4*r(w) - v(w). Factor b(n).
5*n*(n + 1)**2*(n + 2)
Let b(i) be the third derivative of i**7/280 + 3*i**6/160 + i**5/40 + 8*i**2. Factor b(w).
3*w**2*(w + 1)*(w + 2)/4
Factor 2/3*p**2 + 0*p - 2/3.
2*(p - 1)*(p + 1)/3
Let g(r) be the first derivative of 5*r**6/6 - 15*r**4/2 + 40*r**3/3 - 15*r**2/2 - 9. Let g(h) = 0. Calculate h.
-3, 0, 1
Let h(g) = -g**2 - 3*g + 2. Let s(k) = -1. Let c = -3 + 2. Let o(d) = c*h(d) - 4*s(d). Determine r, given that o(r) = 0.
-2, -1
Determine p, given that 0*p + 3/5*p**3 + 0 - 6/5*p**2 = 0.
0, 2
Suppose 0 = 2*i - 0*i. Let l be (-7)/((-21)/15) - 5. Factor l*u + i*u**3 + 2/9*u**2 - 2/9*u**4 + 0.
-2*u**2*(u - 1)*(u + 1)/9
Let t(w) be the first derivative of 125*w**6/6 - 105*w**5 + 190*w**4 - 488*w**3/3 + 72*w**2 - 16*w + 1. Factor t(u).
(u - 2)*(u - 1)*(5*u - 2)**3
Suppose 2*b + 3*b + 2*q - 40 = 0, 3*q = 5*b - 65. Let c = 15 + -10. Solve -3*n + b*n**5 + 14*n**2 - 14*n**4 - 6*n + c*n - 6*n**3 = 0 for n.
-1, 0, 2/5, 1
Let v(r) be the first derivative of 3*r**5/25 + 3*r**4/20 + 7. Find a, given that v(a) = 0.
-1, 0
Suppose -7 = -q - 4. Suppose 4*z = -z + 5*p + 50, p = -q*z + 38. Factor -32*j**2 + 0 - 14*j**2 + 60*j**3 + 1 - 25*j**4 - 2 + z*j.
-(j - 1)**2*(5*j - 1)**2
Let f(p) be the second derivative of 9*p**7/14 + 8*p**6/5 + 3*p**5/4 - p**4/2 + 22*p. Factor f(g).
3*g**2*(g + 1)**2*(9*g - 2)
Let l(d) = d**2 - 11*d + 14. Let p be l(10). Suppose 2/3*k**p + 1/3*k**5 + 0 - 2/3*k**2 - 1/3*k + 0*k**3 = 0. Calculate k.
-1, 0, 1
Let q be 0 + -3 + (1 - -4). Factor 3 - 7*n - 5 + 5*n**2 - 10*n**q.
-(n + 1)*(5*n + 2)
Let c(j) be the first derivative of -3 + 1/8*j**2 + 1/12*j**3 + 0*j. Factor c(g).
g*(g + 1)/4
Let x(a) = 2*a**2 + 2*a. Let i = 7 - 6. Suppose -2 = -j + i. Let g(k) = 2*k**2 + 3*k + 1. Let l(s) = j*x(s) - 4*g(s). Factor l(o).
-2*(o + 1)*(o + 2)
Let x(w) be the first derivative of -w**5/90 + w**3/9 - w**2 + 3. Let l(m) be the second derivative of x(m). Factor l(j).
-2*(j - 1)*(j + 1)/3
Let a(v) be the second derivative of v**4/108 + v**3/54 + 34*v. Find t, given that a(t) = 0.
-1, 0
Let d(g) be the third derivative of -g**8/3528 - g**7/441 - g**6/126 - g**5/63 - 5*g**4/252 - g**3/63 - 16*g**2. What is b in d(b) = 0?
-1
Factor 8/7*j - 24/7*j**2 - 12/7*j**4 + 2/7*j**5 + 26/7*j**3 + 0.
2*j*(j - 2)**2*(j - 1)**2/7
Let h be (-1)/(3/(-12)) - (0 - -2). Factor -1/5*k**h - 1/5 - 2/5*k.
-(k + 1)**2/5
Let q(m) be the first derivative of -m**4/2 + 32*m**3/3 - 40. Factor q(k).
-2*k**2*(k - 16)
Let f = 21 + -18. Let m be (-28)/(-8) - f*1. Solve -1/2*b**2 - 1/4 + 3/4*b**4 - 3/4*b + m*b**3 + 1/4*b**5 = 0 for b.
-1, 1
Let r(h) = 5*h**2 + 5*h**2 - h**3 - 8*h**2 - 4*h. Let g = -2 + 9. Let m(f) = -2*f**3 + 3*f**2 - 7*f. Let y(s) = g*r(s) - 4*m(s). Factor y(u).
u**2*(u + 2)
Factor -24/7 + 8/7*b + 18/7*b**2 + 2/7*b**4 - 12/7*b**3.
2*(b - 3)*(b - 2)**2*(b + 1)/7
Let -9*l**4 + 12*l**3 - 12*l - 4*l**2 - 4*l**4 + 17*l**4 = 0. Calculate l.
-3, -1, 0, 1
Factor 2/7*j**2 - 1/7*j + 1/7*j**3 - 2/7.
(j - 1)*(j + 1)*(j + 2)/7
Let t(j) be the first derivative of 2/3*j**3 + 0*j - 2/5*j**5 - 3 - 1/2*j**4 + j**2. Determine g, given that t(g) = 0.
-1, 0, 1
Let o(z) = z**2 + 2*z. Let g be o(-4). Let x be g/12 - (-2)/(-3). Factor -2*d**5 + x*d**5 + 0*d**5 + d**5 + d**3.
-d**3*(d - 1)*(d + 1)
Suppose 0 + 2/7*k**2 - 2/7*k = 0. What is k?
0, 1
Suppose 0 = 4*l - 17 + 25. Let s be 1*l - (-160)/70. Factor -s*j**4 + 0 - 1/7*j**3 + 0*j**2 + 0*j.
-j**3*(2*j + 1)/7
Let x = -18 - -23. Suppose -10 + 20 = x*d. Let 6/5*g - 4/5 - 2/5*g**d = 0. Calculate g.
1, 2
Let l(z) be the third derivative of z**5/60 + 23*z**4/120 - z**3/3 + 37*z**2. Find s, given that l(s) = 0.
-5, 2/5
Let m = 8 - 6. Suppose -m*p = 4*b, -17 = -4*p + 4*b - 5. Factor -j - 5*j**2 - j**2 - p*j**3 - j**3 - 2*j.
-3*j*(j + 1)**2
Let r = 269 + -266. Factor o**2 - 1/2*o**r + 0 - 1/2*o.
-o*(o - 1)**2/2
Suppose 34 = 4*d - 14. Let q be (d/(-8))/((-18)/16). Solve 2/3*r - 2/3*r**5 - q*r**4 + 0*r**3 + 4/3*r**2 + 0 = 0.
-1, 0, 1
Let w(z) be the first derivative of 2*z**6 + 4*z**5/5 + 23. Factor w(p).
4*p**4*(3*p + 1)
Let o(v) = -11*v**2 - 12*v + 5. Let p(s) = s**2 + 2*s. Let b(n) = -o(n) - 6*p(n). Factor b(l).
5*(l - 1)*(l + 1)
Let x(v) be the first derivative of -v**5/10 + 3*v**4/8 - v**3/2 + v**2/4 - 10. Factor x(r).
-r*(r - 1)**3/2
Suppose 4 = g + 2. Let l be (5/((-45)/(-12)))/g. Solve 0 + 2/9*z**4 + 2/3*z**2 + 2/9*z + l*z**3 = 0 for z.
-1, 0
Let r(n) be the third derivative of 0*n**4 + 1/21*n**3 + 0 + 3*n**2 + 1/735*n**7 - 1/105*n**5 + 0*n**6 + 0*n. Solve r(b) = 0.
-1, 1
Let g(m) be the first derivative of 15*m**3 - 55*m**2/2 + 10*m - 19. Solve g(q) = 0.
2/9, 1
Factor -164*n**2 + 5*n + 24*n**2 - 75 + 85.
-5*(4*n + 1)*(7*n - 2)
Let z(l) be the first derivative of 0*l**2 + 1/4*l - 1/12*l**3 + 3. Find c such that z(c) = 0.
-1, 1
Let p(k) = 2*k**2 + 7*k + 10. Let x be p(-2). Determine r so that 1/2*r**3 - 1/2*r**2 - 1/2*r + 1/2*r**x + 0 = 0.
-1, 0, 1
