hat is k?
0, 11
Let m = 16295 + -32589/2. Let 3/4 - m*r - 1/4*r**2 = 0. What is r?
-3, 1
Let k(t) be the second derivative of -t**5/150 + t**3/45 - 189*t. Factor k(c).
-2*c*(c - 1)*(c + 1)/15
Let s(v) be the first derivative of 2*v**2 - 2/3*v**3 + 6*v - 5. Factor s(n).
-2*(n - 3)*(n + 1)
Factor -1/4*i**2 + 9/4*i - 2.
-(i - 8)*(i - 1)/4
Suppose 11*l + 14*l = -2*l. Let z(u) be the third derivative of l*u**3 + 1/8*u**4 - 1/40*u**6 - 1/70*u**7 + 1/20*u**5 + 0*u + 0 + 2*u**2. Factor z(s).
-3*s*(s - 1)*(s + 1)**2
Suppose 0 = -u + 2*c + 9, -4*u - u = -2*c - 21. Suppose -u*h - 9 = -27. Factor -2/3*o**2 - 4*o - h.
-2*(o + 3)**2/3
Let z be (-16)/168 - (-470)/525. Find k, given that 1/5*k**3 + 4/5*k**2 + 0 + z*k = 0.
-2, 0
Let s(y) be the second derivative of -y**6/105 - y**5/7 - 8*y**4/21 - 15*y + 1. Factor s(j).
-2*j**2*(j + 2)*(j + 8)/7
Let x(d) = d**2 + 12*d + 13. Let l be x(-11). Let y be 13*(1 - 2)*-1. Find j such that -8*j**4 - 28*j**3 - 5*j - j - y*j - 4 - j - 36*j**l = 0.
-1, -1/2
Let k(o) = -5*o + 50. Let w be k(0). Suppose -3*u + 2 + w*u**2 - 3*u - 2*u**3 - 44*u**2 = 0. What is u?
1
Let z(j) = -3*j - 17. Let i be z(-7). Factor -2*o**2 + 2*o**2 + 4*o**2 + 4*o**3 + i*o + 4*o**2.
4*o*(o + 1)**2
Let z(s) be the second derivative of s**4/24 + s**3/2 + 9*s**2/4 + 14*s + 2. Factor z(r).
(r + 3)**2/2
Let o = 14/25 + 8/75. Factor 1/6 - o*x + 1/6*x**4 + x**2 - 2/3*x**3.
(x - 1)**4/6
Suppose -48*f + 45*f - 33 = 0. Let d be f/((-44)/48)*1/26. Solve -2/13*n**3 + 0 + 4/13*n + d*n**2 - 6/13*n**4 - 2/13*n**5 = 0.
-2, -1, 0, 1
Let a(k) be the second derivative of -k**4/54 + k**3/27 + 2*k**2/9 - 4*k - 7. Solve a(u) = 0 for u.
-1, 2
Factor 29/2*i**2 + 27/2*i - 1/2*i**4 - 27/2*i**3 - 14.
-(i - 1)**2*(i + 1)*(i + 28)/2
Let d(o) be the second derivative of 5*o**4/8 - o**3/4 - 3*o**2 + 112*o + 2. Factor d(w).
3*(w - 1)*(5*w + 4)/2
Let i(r) be the second derivative of -32*r**7/105 - 32*r**6/15 - 127*r**5/25 - 59*r**4/15 + 16*r**3/15 + 8*r**2/5 + 186*r. Solve i(s) = 0 for s.
-2, -1, -1/4, 1/4
Let q(k) = 29*k**2 - k - 1. Let c be q(-1). Let m = -53/2 + c. Factor 3/2*s**4 - m*s**3 + 0 + s**2 + 0*s.
s**2*(s - 1)*(3*s - 2)/2
Suppose -288 + 97*j**2 - 2*j**5 - 49*j**2 + 42*j**4 - 816*j - 770*j**2 - 150*j**3 = 0. Calculate j.
-1, 12
Let j(o) be the second derivative of o**7/77 + 2*o**6/33 - 27*o**5/110 - 5*o**4/33 + 12*o + 9. Suppose j(p) = 0. What is p?
-5, -1/3, 0, 2
Let s(q) = -q - 8. Let i be s(-8). Let u(r) be the second derivative of 3*r + 0*r**2 + 0 + 1/30*r**6 + 0*r**3 - 1/20*r**5 + i*r**4. Factor u(x).
x**3*(x - 1)
Suppose 2 = -n - 3*v, 19*v - 16*v + 22 = 4*n. Let k(r) be the second derivative of 0*r**2 - 1/4*r**n + r**3 + 0 - 4*r. Factor k(j).
-3*j*(j - 2)
Let z(g) = 8*g**4 + 12*g**3 - 90*g**2 + 23*g + 123. Let v(m) = 9*m**4 + 11*m**3 - 90*m**2 + 24*m + 124. Let d(t) = 3*v(t) - 4*z(t). Factor d(k).
-5*(k - 2)**2*(k + 1)*(k + 6)
Let y(s) be the third derivative of -s**7/385 - 7*s**6/660 + 37*s**5/330 - 17*s**4/132 - 10*s**3/33 + 30*s**2 - 3*s. Suppose y(i) = 0. Calculate i.
-5, -1/3, 1, 2
Let v = -112 + 451/4. Let j be ((-30)/(-45))/((-8)/39) + 4. Factor -3/2*t**2 + j*t**4 + 0*t + v + 0*t**3.
3*(t - 1)**2*(t + 1)**2/4
Factor -80*n + 354*n**3 + 30*n**2 + 352*n**3 - 701*n**3.
5*n*(n - 2)*(n + 8)
Factor 25*l**4 - 140*l + 60 - 5*l**2 - 135*l**3 - 65*l + 75*l**2 + 185*l**2.
5*(l - 1)**3*(5*l - 12)
Let q(a) = -10*a**3 + 55*a**2 - 110*a + 50. Let o(f) = -f**3 - 3*f + 1. Let b(r) = -5*o(r) + q(r). Solve b(t) = 0.
1, 9
Let q(z) be the second derivative of z**6/80 - 51*z**5/160 - z**4/32 + 17*z**3/16 + 3*z + 14. Factor q(r).
3*r*(r - 17)*(r - 1)*(r + 1)/8
Let c(u) be the second derivative of -u**7/105 + 2*u**6/25 - 2*u**5/25 - 3*u**4/5 + u**3/3 + 12*u**2/5 - 131*u. Solve c(l) = 0 for l.
-1, 1, 3, 4
Let i(g) be the first derivative of 1/2*g**4 + 10 + 1/120*g**6 + 0*g + 0*g**2 - 1/10*g**5 - 4/3*g**3. Let x(o) be the third derivative of i(o). Solve x(m) = 0.
2
Let i = 863/936 + -64/117. Factor 3/2 + i*k**3 + 15/8*k**2 + 3*k.
3*(k + 1)*(k + 2)**2/8
Let k be 40/9*(-1)/(96/(-72)). Find y, given that -2/3*y**3 + 0 - 8/3*y - k*y**2 = 0.
-4, -1, 0
Let s = -376/189 - 8/27. Let z = 94/35 + s. Suppose -2/5*u**2 + 4/5*u - z = 0. What is u?
1
Let b(z) be the third derivative of 0 + 3/50*z**5 + 0*z + 0*z**3 + 11/525*z**7 + 1/280*z**8 + 11*z**2 + 1/20*z**6 + 1/30*z**4. Suppose b(t) = 0. What is t?
-1, -2/3, 0
Let p be -10 + 15 + (-17)/(-1). Determine a so that -13*a**4 - 30*a**2 - 27*a**4 + 41*a**3 + 5*a**5 - p*a**3 + 46*a**3 = 0.
0, 1, 6
Let q(c) be the second derivative of -c**6/45 - 4*c**5/45 + c**4/18 + 4*c**3/9 - 4*c**2/9 - 3*c - 12. Let q(u) = 0. Calculate u.
-2, 1/3, 1
Suppose -4*q - j + 19 = 0, -q - 4*j + j = 9. Solve 220*t**2 - 93*t**5 - 126*t + 250*t**3 + 148*t**4 - 763*t**4 + q*t + 318*t**5 = 0 for t.
-3/5, 0, 2/3, 2
Let f(i) be the first derivative of i**5/5 + 27*i**4/2 + 160*i**3/3 + 82*i**2 - 4*i + 33. Let w(t) = t**4 - t**3 - t + 1. Let c(n) = f(n) + 4*w(n). Factor c(b).
5*b*(b + 2)*(b + 4)**2
Let m(d) = 4*d + 59. Let j be m(-14). Let v(b) be the first derivative of 0*b**j + 9/2*b**2 - 6*b - 11 - 3/4*b**4. Solve v(s) = 0.
-2, 1
Let w = 1409/32 + -44. Let j = 55/288 + w. Suppose j*u**3 + 0*u**2 - 2/9*u + 0 = 0. What is u?
-1, 0, 1
Let c be 1/((-1)/10*-1). Let t be 1/(-5) + 22/c. Factor v - v**2 - t*v**3 + v**5 + 1 - 2*v**2 + v**4 + v**2.
(v - 1)**2*(v + 1)**3
Let s(l) = -l**3 + l + 2. Let g(o) = 28*o**3 + 12*o**2 - 40*o - 48. Let p(b) = g(b) + 24*s(b). Determine n so that p(n) = 0.
-4, 0, 1
Let m = 24893/2985 + -6/995. Determine x, given that -5/3*x**2 - 20/3*x + m = 0.
-5, 1
Let s(o) be the second derivative of o**4/30 - 2*o**3/3 + 5*o**2 + 12*o + 17. What is x in s(x) = 0?
5
Let n(p) be the second derivative of 9*p**5/80 - p**4/2 + 7*p**3/8 - 3*p**2/4 + 3*p - 9. Factor n(c).
3*(c - 1)**2*(3*c - 2)/4
Let r(p) = -26*p**3 - 128*p**2 - 163 + 12*p**3 - 114*p - 294*p + 19. Let x(c) = 27*c**3 + 255*c**2 + 816*c + 288. Let h(y) = -7*r(y) - 4*x(y). Factor h(i).
-2*(i + 6)**2*(5*i + 2)
Let g(f) be the third derivative of f**7/735 - f**6/105 - f**5/35 + f**4/21 + 5*f**3/21 + 775*f**2. Solve g(r) = 0.
-1, 1, 5
Let l(x) = -x**2 + 2. Let a(c) = -c**2 - 2*c - 4. Let o(d) = -a(d) + 2*l(d). Factor o(v).
-(v - 4)*(v + 2)
Let t(y) be the first derivative of 4*y**5/5 - 7*y**4 - 52*y**3 - 106*y**2 - 88*y - 44. Suppose t(q) = 0. Calculate q.
-2, -1, 11
Let p(r) be the third derivative of 0*r + 1/60*r**5 + 2/15*r**3 + 3/40*r**4 - 22*r**2 + 0. Solve p(x) = 0 for x.
-1, -4/5
Let t(g) be the third derivative of -g**8/504 + g**6/60 + g**5/45 - 9*g**2. Factor t(x).
-2*x**2*(x - 2)*(x + 1)**2/3
Let b be 18/(-10)*2620/(-2358). Factor c + 2*c**b - 3/2 - c**3 - 1/2*c**4.
-(c - 1)**2*(c + 1)*(c + 3)/2
Factor 20808/5 + 408/5*t + 2/5*t**2.
2*(t + 102)**2/5
Let m(b) be the first derivative of -b**3/3 + 11*b**2/2 + 12*b + 137. Factor m(s).
-(s - 12)*(s + 1)
Let a(o) be the second derivative of o**4/36 - 25*o**3/9 - 17*o**2/2 + o + 14. Let a(f) = 0. What is f?
-1, 51
Let u(y) be the third derivative of y**7/315 - 11*y**6/180 + 7*y**5/18 - 25*y**4/36 + 165*y**2. Factor u(g).
2*g*(g - 5)**2*(g - 1)/3
Let h(r) be the first derivative of -r**6/24 + 7*r**5/12 - 5*r**4/3 - 40*r**3/3 + 7*r**2/2 + 19. Let t(q) be the second derivative of h(q). Factor t(j).
-5*(j - 4)**2*(j + 1)
Let y(j) be the third derivative of 44*j**7/315 + 17*j**6/36 - 14*j**5/9 + 5*j**4/36 + 2*j**3/3 + 647*j**2. Find k, given that y(k) = 0.
-3, -2/11, 1/4, 1
Let u = -83/31 + 539/155. Determine t, given that -2/5*t**2 - u - 6/5*t = 0.
-2, -1
Let h be (-1)/(-5*(2 + -1)). Let o(p) be the first derivative of 2/25*p**5 + 5 + 2/15*p**3 + 0*p - h*p**4 + 0*p**2. Factor o(l).
2*l**2*(l - 1)**2/5
Suppose 146*d = 136*d + 90. Suppose 13*y = d*y + 32. Find p, given that 0 + y*p**2 + 8/3*p + 10/3*p**3 = 0.
-2, -2/5, 0
Let x = 204 + -186. Let g = 200/11 - x. Factor -g*b**2 - 6/11*b - 4/11.
-2*(b + 1)*(b + 2)/11
Let o(h) = 10*h - 257. Let p be o(26). Suppose -2/5*m**5 + 2/5*m + 0*m**p - 4/5*m**2 + 0 + 4/5*m**4 = 0. Calculate m.
-1, 0, 1
Factor 2/15*p**2 - 2/15 - 2/15*p**3 + 2/15*p.
-2*(p - 1)**2*(p + 1)/15
Let i(f) = -2*f**4 + 8*f**2 + 2*f. Let w(v) = -6*v**4 + 25*v**2 + 5*v. Let s(d) = 7*i(d) - 2*w(d). Factor s(j).
-2*j*(j - 2)*(j + 1)**2
Let a(l) be the seco