= 2 + -3. Let u(w) = a*d(w) + 2*j(w). What is k in u(k) = 0?
1
Let c(n) = 5*n**2 - 1. Let a be c(-1). Let d be (a/(-12))/(3 - 38/12). Factor 0 - 1/3*b**d - 1/3*b.
-b*(b + 1)/3
Let o(h) = 9*h. Let q(v) = -v + 1. Let a be q(3). Let c(t) = -t**2 + 8*t. Let k(d) = a*o(d) + 3*c(d). Find r, given that k(r) = 0.
0, 2
Suppose 39*f = f. Let q(n) be the third derivative of f - 1/9*n**3 + 3*n**2 + 1/180*n**5 - 1/72*n**4 + 0*n. Let q(l) = 0. What is l?
-1, 2
Let z = 29 + -31. Let c be 0/((-1 - -3)/z). Factor -1/4*n**2 - 1/4*n + c.
-n*(n + 1)/4
Let m be 14/3 + 3/9. Suppose x + 5*s - 7 = 5, 8 = -x + m*s. Factor -2*r**3 + 42 - 2*r**x - 42 + 4*r.
-2*r*(r - 1)*(r + 2)
Let w = 326/3 + -108. Let x(j) be the first derivative of 2*j**2 - w*j**3 + 6*j - 2. Factor x(y).
-2*(y - 3)*(y + 1)
Solve 251*o**4 + 12*o - 248*o**4 - 21*o**2 - 3 + 3 + 6*o**3 = 0 for o.
-4, 0, 1
Let b(u) be the second derivative of 0 + 3/130*u**5 + 0*u**3 - 1/39*u**4 + 0*u**2 - 10*u - 1/195*u**6. Determine p, given that b(p) = 0.
0, 1, 2
Suppose l = -3*l + 4, 5*r = -4*l + 149. Factor -r*f**2 + 3*f - 2*f + 25*f**2.
-f*(4*f - 1)
Let y(x) be the second derivative of x**5/20 - x**4/2 - x**3/3 + 15*x**2/2 + 63*x. Let m be y(6). Solve 12/7*n**3 - 3/7 + m*n**2 + 6/7*n = 0.
-1, 1/4
Let g(s) = -5 + 4 + 4*s**5 + s - 5*s**5 - s**3. Let d(p) = -10*p**5 - 2*p**4 - 6*p**3 + 2*p**2 + 8*p - 8. Let i(j) = d(j) - 8*g(j). Factor i(c).
-2*c**2*(c - 1)*(c + 1)**2
Let x(w) be the first derivative of w**6/90 + 2*w**5/15 + w**4/2 - 16*w**3/3 - 5. Let p(c) be the third derivative of x(c). Determine y, given that p(y) = 0.
-3, -1
Let j be (-6)/(-15) - 18/(-5). Factor 2*q**3 + 17*q**4 + q**3 - 20*q**j.
-3*q**3*(q - 1)
Let x be (-6 - -2)*3/(-4). Let c = 413 - 799/2. What is a in -9/2*a**2 - 1/2*a**x - 27/2 - c*a = 0?
-3
Suppose 3*x + 5*w = 13, -2*x - 5*w + 7 = -0*w. Let s(k) be the second derivative of -1/90*k**x + 0*k**3 + 0 - 1/36*k**4 + 4*k + 1/30*k**5 + 0*k**2. Factor s(p).
-p**2*(p - 1)**2/3
Suppose -38*h + 171 = -19*h. Factor h*s - 27/2 - 3/2*s**2.
-3*(s - 3)**2/2
Let s(r) be the second derivative of 3*r**5/100 - 7*r**3/10 - 9*r**2/5 - 30*r. Determine k, given that s(k) = 0.
-2, -1, 3
Let c(w) be the second derivative of -w**4/18 - 22*w**3/3 - 363*w**2 + w + 42. Factor c(i).
-2*(i + 33)**2/3
Suppose -2*s = 4*t - 22, 5*s - 5 - 35 = -5*t. Factor -194*r**2 + 50*r**t + 403*r**2 - 60*r + 15*r**4 - 20 - 194*r**2.
5*(r - 1)*(r + 2)**2*(3*r + 1)
Let u = 27 - 30. Let y(b) = -b**3 - 3*b**2 - 3*b - 3. Let n be y(u). Suppose 0 - 6*f**2 - 3/2*f**3 - n*f = 0. What is f?
-2, 0
Suppose -118 = -4*g - 26. Suppose -19 = 2*h - g. Factor -4/3 + 2/3*a**3 - 2/3*a + 4/3*a**h.
2*(a - 1)*(a + 1)*(a + 2)/3
Let z(c) = 18*c**3 - 8*c - 8. Let d be z(-1). Let i be (-14)/(-63)*d/(-8). Determine o so that -o + i*o**2 + 1/2 = 0.
1
Let n = -43 + 46. Suppose 4*q + o - 5*o = 28, q + n*o = -9. Factor -2/5*t**2 + 0*t + 2/5*t**4 - 2/5*t**5 + 2/5*t**q + 0.
-2*t**2*(t - 1)**2*(t + 1)/5
Let f(r) be the third derivative of 1/30*r**4 + 0*r + 1/600*r**6 - 35*r**2 + 1/75*r**5 + 0 + 0*r**3. Solve f(d) = 0 for d.
-2, 0
Solve 10/7*r**5 - 10/21 - 52/3*r**3 - 148/7*r**2 - 178/21*r - 58/21*r**4 = 0 for r.
-1, -1/15, 5
Suppose -f + 4 = 2. Solve -6*o**4 - 5*o**5 - 6*o**4 + f*o**4 = 0.
-2, 0
Let f(c) = -2*c**3 + 16*c**2 + 31*c - 3. Let k(x) = -10*x**3 + 78*x**2 + 154*x - 14. Let t(j) = -28*f(j) + 6*k(j). Solve t(w) = 0.
-2, 0, 7
Suppose -19 = 3*s - 25. Factor -s + 17*b - 10*b + 2*b**2 - 2*b**2 - 3*b**2.
-(b - 2)*(3*b - 1)
Suppose 3*v + 9 = 5*r, v - 11 = -3*r - 0*r. Solve -3*z**2 - 7 - 9 - v*z**2 + 26 + 5*z = 0 for z.
-1, 2
Let b(a) be the second derivative of -a**6/1980 + a**3 + 7*a. Let o(y) be the second derivative of b(y). Determine z so that o(z) = 0.
0
Let x(s) be the first derivative of -s**4/48 + s**2/8 - 2*s - 14. Let c(g) be the first derivative of x(g). Suppose c(h) = 0. Calculate h.
-1, 1
Let r = -2187/44 + 555/11. What is z in -5/4*z**4 + 0*z - r*z**2 - 1/4*z**5 + 0 - 7/4*z**3 = 0?
-3, -1, 0
Factor 23/5*o**2 + 21/5*o - 2/5.
(o + 1)*(23*o - 2)/5
Suppose -2*n - 14 + 40 = 2*t, 0 = -2*t - 3*n + 30. Suppose 15*z - 3*z**2 - 11 + 2 - t = 0. Calculate z.
2, 3
Let t be -2 + -4 - (-45)/5. Factor 3/2*s**4 + 0*s**2 + 3*s**t - 3*s - 3/2.
3*(s - 1)*(s + 1)**3/2
Suppose -6*m = -0 - 54. Suppose 0*z**2 - 7*z**2 - 16 - m*z - 7*z + 3*z**2 = 0. What is z?
-2
Let h(l) be the second derivative of l**7/1890 - 2*l**6/45 + 8*l**5/5 - 8*l**4/3 + 13*l. Let p(z) be the third derivative of h(z). Factor p(k).
4*(k - 12)**2/3
Let g(d) be the second derivative of -3/5*d**2 - 1/2*d**3 + 0 - 1/5*d**4 - 29*d - 3/100*d**5. Find p such that g(p) = 0.
-2, -1
Let a(o) = -5*o**2 - 22*o + 121. Let s(v) = -2*v**2. Let i(m) = 5*a(m) - 15*s(m). Factor i(g).
5*(g - 11)**2
Let d(u) be the second derivative of -u**5/5 - 4*u**4/3 + 10*u**3 + 36*u**2 - 14*u - 4. Factor d(a).
-4*(a - 3)*(a + 1)*(a + 6)
Let d be 2*10/(-12)*-3. Suppose 0 = h, -d*q + h - 6*h = -15. Let -138*j + 160*j**2 + 60*j**q - 78*j - 24*j - 80 - 35*j**4 = 0. Calculate j.
-2, -2/7, 2
Factor 20/9*d - 8/3 - 4/9*d**2.
-4*(d - 3)*(d - 2)/9
Let v(x) = x**3 - 7*x**2 + 11*x - 3. Suppose 0 = -4*f + 6 + 14. Let j be v(f). Factor 0*r**2 + r**4 + 0*r**2 + 2*r**j - 6*r**3 + 7*r**2.
r**2*(r - 3)**2
Let r = 14345/33 + -4778/11. Factor 0*c**2 - 2/3 + r*c**3 - c.
(c - 2)*(c + 1)**2/3
Find o, given that -1/3*o**2 + 0 + 2/3*o - 1/3*o**3 = 0.
-2, 0, 1
Find v such that -95 + 5/3*v**2 - 280/3*v = 0.
-1, 57
Let d(i) be the second derivative of -2*i**6/15 + 37*i**5/25 + 71*i**4/15 + 22*i**3/15 - 36*i**2/5 + 2*i - 5. Let d(h) = 0. What is h?
-1, 2/5, 9
Suppose 2*h = -2*h + 8. Let t(f) = 4*f**3 - 2 + 0*f**3 - 7*f**2 - 2 - 9*f - h. Let k(o) = -o**2 - 1. Let m(b) = 4*k(b) - t(b). Factor m(a).
-(a - 2)*(a + 1)*(4*a + 1)
Let g = 31 - 12. Factor -9*n**5 - 2*n**4 + n - 11*n**5 + 2*n**2 + g*n**5.
-n*(n - 1)*(n + 1)**3
Let a(s) be the second derivative of -5*s**4/12 - 15*s**3/2 - 88*s. Factor a(t).
-5*t*(t + 9)
Let f be 32/(-12)*13/(-52). Let x(c) be the first derivative of 4 - c**4 - f*c**3 + 2*c + 2*c**2. Factor x(g).
-2*(g - 1)*(g + 1)*(2*g + 1)
Let -5*b - 968 - 37*b - 2*b**2 + 26*b - 72*b = 0. Calculate b.
-22
Factor 14*w - 6*w + w**2 + 2*w**2 - w**2.
2*w*(w + 4)
Let j(w) be the third derivative of 1/18*w**5 - 7/144*w**4 - 11/720*w**6 + 0 - 21*w**2 + 0*w - 1/18*w**3. Determine f so that j(f) = 0.
-2/11, 1
Let s(k) be the second derivative of -k**8/6720 - k**7/1260 + k**6/720 + k**5/60 - 11*k**4/3 - 11*k. Let h(t) be the third derivative of s(t). Factor h(p).
-(p - 1)*(p + 1)*(p + 2)
Suppose -123 = -5*s + c - 115, 4*s - 40 = -4*c. Factor -2/3*h**s - 66*h - 54 - 38/3*h**2.
-2*(h + 1)*(h + 9)**2/3
Let z(g) be the third derivative of -13*g**5/510 + 8*g**4/51 - 4*g**3/17 - 196*g**2 + 2. Determine w so that z(w) = 0.
6/13, 2
Let m(f) be the second derivative of -f**6/42 - 4*f**5/35 - f**4/28 + 10*f**3/21 + 2*f**2/7 + 90*f. Determine d so that m(d) = 0.
-2, -1/5, 1
Let z be 5 - (-14)/((-462)/153). Let 16/11 + 8/11*w - 2/11*w**3 - z*w**2 = 0. What is w?
-2, 2
Let y(v) be the first derivative of -v**4/18 + 238*v**3/27 - 3599*v**2/9 + 6962*v/9 + 367. Factor y(o).
-2*(o - 59)**2*(o - 1)/9
Let c(h) be the second derivative of -3/20*h**5 - h**4 - 3*h**2 + 30*h - 5/2*h**3 + 0. Suppose c(k) = 0. Calculate k.
-2, -1
Let s(k) = -12*k**3 + 54*k**2 - 102*k + 27. Let z(g) = 13*g**3 - 53*g**2 + 103*g - 27. Suppose -3*m - 4*m = -21. Let r(v) = m*z(v) + 4*s(v). Factor r(d).
-3*(d - 3)**2*(3*d - 1)
Suppose 5*b = 3*b + 30. Factor 24*o + 2*o + 3*o**3 + 21*o**2 + 18*o + b - 11*o.
3*(o + 1)**2*(o + 5)
Let m(l) be the first derivative of l**3/5 - 9*l**2/5 + 3*l + 44. Factor m(j).
3*(j - 5)*(j - 1)/5
Let y(o) be the second derivative of -o**5/3 - o**4/3 + 5*o**2 - 3*o. Let s(m) be the first derivative of y(m). Let s(i) = 0. Calculate i.
-2/5, 0
Let j(h) be the first derivative of h**5/12 + 35*h**4/6 + 490*h**3/3 + 37*h**2/2 + 5. Let v(r) be the second derivative of j(r). Solve v(o) = 0.
-14
Let y(n) be the second derivative of -8*n - 1/60*n**5 + 0 + 0*n**3 + 0*n**2 - 1/36*n**4. Determine f, given that y(f) = 0.
-1, 0
Let c(d) be the second derivative of -1/36*d**4 + 0*d**3 + 0*d**2 + 0 + 4*d. Factor c(p).
-p**2/3
Let u(p) be the first derivative of -p**8/1848 + 2*p**7/1155 - p**6/660 + 5*p**2/