Let p(w) = 4*w**2 + 11*w + 16. Let j(f) = f**2 + f. Let m(l) = k*j(l) - p(l). Suppose m(g) = 0. Calculate g.
-4
Factor 2/5*q**4 + 24/5*q**2 + 4*q + 6/5 + 12/5*q**3.
2*(q + 1)**3*(q + 3)/5
Let s(a) be the first derivative of -a**4/20 + 3*a**2/10 + 5*a + 2. Let j(b) be the first derivative of s(b). Factor j(x).
-3*(x - 1)*(x + 1)/5
Let i(k) be the second derivative of -k**6/10 + 9*k**5/10 - 3*k**4 + 4*k**3 - 3*k. Suppose i(t) = 0. Calculate t.
0, 2
Determine z so that -4*z**4 + 36 - 79 + 37 - 25*z + 15*z**3 = 0.
-1, -1/4, 2, 3
Let q be (-1 - 6/(-10))/((-12)/54). Suppose 0*z - 12/5*z**4 + 0 + 6/5*z**2 + q*z**5 - 3/5*z**3 = 0. What is z?
-2/3, 0, 1
Suppose -4*m = -2*g - 3*m + 9, -2*m = -g + 12. Factor 0*h - 11 + 3*h + 2 + 3*h - h**g.
-(h - 3)**2
Let u(s) = -s**3 + 7*s**2 + 2*s - 10. Let g be u(7). Let n be 2 - g - (-32)/14. Factor n + 0*c - 32/7*c**2.
-2*(4*c - 1)*(4*c + 1)/7
Let g(n) = n**3 - n + 1. Let c(p) = 7*p**3 - 7*p + 2. Let q(x) = c(x) - 2*g(x). Factor q(j).
5*j*(j - 1)*(j + 1)
Let c(i) be the third derivative of i**6/30 + i**5/5 + i**4/3 - 21*i**2. Factor c(f).
4*f*(f + 1)*(f + 2)
Determine d, given that -40*d**2 + 3*d**3 + 20*d**2 + 14*d**2 = 0.
0, 2
Let g be 8/(-32) - 2/(-4). Let i(k) be the first derivative of 1/8*k**4 - 1/4*k**2 + 1/20*k**5 + 0*k**3 + 1 - g*k. Determine m, given that i(m) = 0.
-1, 1
Let w(c) be the second derivative of -1/3*c**2 - c + 0 + 1/18*c**4 - 1/9*c**3 + 1/30*c**5. Find l, given that w(l) = 0.
-1, 1
Let x(n) be the first derivative of 5*n**4 + 0*n**2 + 0*n - 9 - 8/3*n**3. Factor x(m).
4*m**2*(5*m - 2)
Let q(g) = -g**3 + 26*g**2 - 32*g + 19. Let z(p) = p**3 + 2*p**2 + 1. Let v(m) = -q(m) + 3*z(m). Let v(a) = 0. Calculate a.
1, 2
Let d(z) be the second derivative of 0*z**2 + 4*z + 7/12*z**5 + 2/9*z**3 + 2/3*z**4 + 0. Let d(i) = 0. What is i?
-2/5, -2/7, 0
Let s(c) = 10*c**5 - 10*c**4 - 15*c**3 + 15*c**2 + 5*c. Let j(n) = 9*n**5 - 9*n**4 - 16*n**3 + 16*n**2 + 4*n. Let z(g) = 5*j(g) - 4*s(g). Factor z(b).
5*b**2*(b - 2)*(b - 1)*(b + 2)
Solve 8*z**3 + z**3 + 0*z**5 + 3*z**5 - 6*z**3 - 6*z**4 = 0.
0, 1
Suppose -2*u = 0, 0*n - 2*u = -5*n + 15. Factor -1/6 + l - 3/2*l**2 + 2/3*l**n.
(l - 1)**2*(4*l - 1)/6
Let u be 90/21 + (4 - 8). Find v, given that u*v**2 + 0 - 2/7*v = 0.
0, 1
Let n(f) be the third derivative of 160*f**7/189 + 68*f**6/27 + 409*f**5/135 + 17*f**4/9 + 2*f**3/3 + 26*f**2. Factor n(t).
4*(4*t + 1)**2*(5*t + 3)**2/9
Let s(n) be the third derivative of -n**5/60 - n**4/12 - n**3/6 - 7*n**2. Factor s(a).
-(a + 1)**2
Let v(h) be the second derivative of -h**7/420 + h**6/36 - 2*h**5/15 + h**4/3 - 2*h**3/3 - 3*h. Let n(x) be the second derivative of v(x). Solve n(b) = 0 for b.
1, 2
Let x(w) be the second derivative of -w**5/60 - w**4/18 + 2*w**3/9 + 4*w**2/3 - w. Factor x(i).
-(i - 2)*(i + 2)**2/3
Factor -432*l + 3*l**3 - 49*l**3 - 216*l**2 - 4*l**4 - 2*l**3 - 324.
-4*(l + 3)**4
Let w(n) be the first derivative of -n**6/6 + n**5 - 5*n**4/2 + 10*n**3/3 - 5*n**2/2 + n - 19. Factor w(d).
-(d - 1)**5
Let j = 0 + 0. Let s be 24 + -15 - (4 + 3). Factor -1/2*z**4 - 1/2*z**s + z**3 + j + 0*z.
-z**2*(z - 1)**2/2
Let j(m) be the first derivative of 0*m**2 + 0*m**3 + 0*m - 1/10*m**5 - 6 - 1/8*m**4. Find i such that j(i) = 0.
-1, 0
Let t(s) be the third derivative of -s**5/45 + s**4/18 + 13*s**2. Determine o so that t(o) = 0.
0, 1
Let t(c) be the second derivative of 3*c**5/20 - 3*c**4/2 + 9*c**3/2 - 2*c - 6. Factor t(g).
3*g*(g - 3)**2
Let h(v) be the first derivative of -v**8/3360 + v**7/1680 + v**6/720 - v**5/240 - 3*v**3 + 10. Let k(i) be the third derivative of h(i). Factor k(j).
-j*(j - 1)**2*(j + 1)/2
Suppose 4*y**5 - 12*y**2 + 9*y**4 - 3*y**5 - 4*y**5 = 0. What is y?
-1, 0, 2
Let x(o) be the first derivative of 3/8*o**4 + o + 1 - 3/4*o**2 - 1/3*o**3. Factor x(g).
(g - 1)*(g + 1)*(3*g - 2)/2
Let h be (-2)/(2 + 0)*5. Let d be 3/(1*-3) - h. Find r, given that -9*r**3 + 3*r**3 - r**4 + 5*r**d + 2*r**2 = 0.
0, 1/2, 1
Let -6 + 18*x + 0*x**5 + 9*x**5 - 4*x**4 - 36*x**3 + 2 + 9*x**5 + 8*x**2 = 0. Calculate x.
-1, 2/9, 1
Let k(v) = v**2 - 7*v + 10. Let o be k(8). Let -4*j**2 + o*j**2 + 128 + 67*j + 2*j**3 + 10*j**2 + 29*j = 0. What is j?
-4
Let n(a) be the first derivative of a**5/40 + a**4/24 - a**3/12 - a**2/4 - 2*a - 4. Let y(m) be the first derivative of n(m). Factor y(s).
(s - 1)*(s + 1)**2/2
Let q be 20/8 + (-2)/4. Suppose 0 + 0 - 6*h**q + 8*h**2 = 0. Calculate h.
0
Suppose 2*m - 7*m + 15 = 0. Let o = -6 - -8. Factor 2*r**3 + 12*r**2 - m*r + o - 7*r**3 - 6*r.
-(r - 1)**2*(5*r - 2)
Let t = -1/65 - -14/65. Let c(w) be the second derivative of 2/15*w**3 - 1/30*w**4 - t*w**2 + 0 - w. Factor c(g).
-2*(g - 1)**2/5
Let x(y) = 21*y**3 - 6*y**2 + 9*y - 9. Let a(q) = 3*q + 0*q - 1 + 2*q - 4*q. Let o(w) = -9*a(w) + x(w). Determine m so that o(m) = 0.
0, 2/7
Let o(j) = 2*j**3 + 2*j**2 + 8*j. Let t be -2 - 6 - (-2 - 0). Let g(n) = n**2 + n. Let l(q) = t*g(q) + o(q). Factor l(r).
2*r*(r - 1)**2
Let n(z) be the first derivative of 1/4*z**4 - 1 + 1/2*z**2 + 0*z + 2/3*z**3. Factor n(b).
b*(b + 1)**2
Factor -7 + 4 - 10*n**3 - 5*n**4 + 3.
-5*n**3*(n + 2)
Let h be (2 - 11)*3/(-9). Factor 1 - h*o + o**3 + o - o**2 + o.
(o - 1)**2*(o + 1)
Let o(w) be the first derivative of -2*w**3/15 + 3*w**2/5 + 7. Find l such that o(l) = 0.
0, 3
Factor -4*d + 4*d**2 - 3*d**2 + 4*d - 3 + 2*d.
(d - 1)*(d + 3)
Suppose -14/11*i**2 - 18/11*i - 4/11 = 0. Calculate i.
-1, -2/7
Find l, given that -7/4*l - 1/4*l**4 - 3/2 + 3/4*l**2 + 3/4*l**3 = 0.
-1, 2, 3
Factor -38*r**2 + 5 - 48*r**2 - 8*r + 90*r**2 - 1.
4*(r - 1)**2
Let z(m) be the third derivative of -m**6/900 + m**4/60 + 2*m**3/45 + 18*m**2. Factor z(g).
-2*(g - 2)*(g + 1)**2/15
Suppose 0 = -h - 2*z - 17 - 3, 5*h - 2*z + 76 = 0. Let i be h/(-24) + 4/6. What is a in 16/3*a**3 - 2/3 + i*a**2 - 8/3*a**5 - 8/3*a - 2/3*a**4 = 0?
-1, -1/4, 1
Suppose 0 = -7*g + 2*g. Find v, given that 4/7*v**2 + g*v + 0 - 18/7*v**3 = 0.
0, 2/9
Let h = 2/1375 - -203/49500. Let m(z) be the third derivative of 0*z + 0*z**3 + 0 - h*z**6 - 1/504*z**8 + 0*z**5 - 2/315*z**7 + 0*z**4 + 2*z**2. Factor m(t).
-2*t**3*(t + 1)**2/3
Let d be 6 + 7/(14/(-4)). Let k be (-13 + 16)*1/d. Factor k*i + 1/4*i**3 + 3/4*i**2 + 1/4.
(i + 1)**3/4
Let k be (-46)/(-8) + 9/(-12). Factor -2*w**4 - 8*w**2 + 6*w**4 + 2*w - 2*w**k + 4*w**2.
-2*w*(w - 1)**3*(w + 1)
Let d(o) be the first derivative of 2*o**6/5 - 3*o**5/20 - o**4 + o**3/2 - o - 6. Let w(g) be the first derivative of d(g). Find t, given that w(t) = 0.
-1, 0, 1/4, 1
Let z(i) = i + 10. Let b be z(-4). Factor -2*n**5 - 7*n**4 - n + 5*n - 8*n**3 + b*n**5 + 8*n**2 + 3*n**4 - 4.
4*(n - 1)**3*(n + 1)**2
Let p(j) be the second derivative of 2*j + 0 + 12/25*j**5 + 4/5*j**3 + j**4 + 3/10*j**2. Find x, given that p(x) = 0.
-1/2, -1/4
Suppose 0*q**2 - 2/5*q**3 + 2/5*q + 0 = 0. What is q?
-1, 0, 1
Let y = 79/268 + -3/67. Let l(i) be the second derivative of 0 + 1/40*i**6 + y*i**3 - 3/8*i**2 + 0*i**4 + 4*i - 3/40*i**5. Factor l(w).
3*(w - 1)**3*(w + 1)/4
Let m(v) be the first derivative of v**4/22 - 2*v**3/11 + 2*v**2/11 + 7. Determine z so that m(z) = 0.
0, 1, 2
Suppose 7 - 22 = -5*i. Suppose -5*d + 36 = -4*c, 0 = -4*d - 4*c + 2*c + 8. What is k in -k**2 - 2*k**5 - i*k**4 - 3*k**2 + 5*k**4 + 2*k + 2*k**d = 0?
-1, 0, 1
Factor 0 + 0*o + 0*o**2 - 2/3*o**4 - 2/3*o**3.
-2*o**3*(o + 1)/3
Let x be (-6)/(-3) - 4/1. Let j be 1/x - 1/(-2). Suppose j - 2/5*b - 2/5*b**2 = 0. What is b?
-1, 0
Let p(i) be the third derivative of i**6/40 - i**5/20 - i**4 + 6*i**3 + 15*i**2. Factor p(h).
3*(h - 2)**2*(h + 3)
Let t be 6*(-8)/(-18) + -2. Let j be 2/(-10) - (-40)/75. Factor 0 - j*g**3 + t*g + 1/3*g**2.
-g*(g - 2)*(g + 1)/3
Let o(m) be the first derivative of m**4/32 - m**3/12 + m**2/16 + 2. Let o(y) = 0. Calculate y.
0, 1
Let c be -4 - (-1 + 2) - 1. Let n(m) = -2*m - 7. Let l be n(c). Factor -14*v**3 + 10*v**4 + 2*v**2 + 4*v**5 - 4*v**l + 6*v**3 - 4*v**5.
-2*v**2*(v - 1)**2*(2*v - 1)
Let b = 871/5 - 174. Factor 0*i + 2/5*i**3 + 3/5*i**4 + 0 - b*i**2.
i**2*(i + 1)*(3*i - 1)/5
Let o(s) be the third derivative of s**7/280 + s**6/160 - 3*s**5/40 - s**4/8 + s**3 + s**2. Factor o(d).
3*(d - 2)*(d - 1)*(d + 2)**2/4
Suppose 3*v = 4*u + 4, 2*u - 5*v = 1 - 17. Suppose -2*k**4 + k**2 - u*k**4 + 2*k**4 + 4*k + 5*k**2 = 0. What is k?
-1, 0