k**2 + 20*k**3 - 7*k**4 + 3*k**4 - 2*k**4 + 8*k**4.
4*k*(k - 2)*(k + 1)*(k + 6)
Let i(w) be the first derivative of -w**5/10 - 23*w**4/8 - 10*w**3 + w**2 + 40*w + 10. Factor i(y).
-(y - 1)*(y + 2)**2*(y + 20)/2
Let a = 553/12 - 183/4. Factor 4/3 + 1/3*i**3 - a*i**2 - 4/3*i.
(i - 2)*(i - 1)*(i + 2)/3
Let g(w) be the second derivative of 0 - 24*w + 1/6*w**4 - 1/15*w**6 - 2/5*w**5 + 0*w**2 + 4/3*w**3. Factor g(z).
-2*z*(z - 1)*(z + 1)*(z + 4)
Let 0 + 0*q**2 + 0*q + 16/3*q**4 - 4/3*q**5 - 4*q**3 = 0. Calculate q.
0, 1, 3
Let f be (-3 - -4)/((-5)/(-15)). Factor 0 + 0*y + 4/11*y**f + 2/11*y**4 + 2/11*y**2.
2*y**2*(y + 1)**2/11
Let v(g) be the third derivative of g**6/120 - g**5/40 - g**4/4 - 4*g**3/3 - 3*g**2. Let f(n) be the first derivative of v(n). Factor f(j).
3*(j - 2)*(j + 1)
Factor 15/4*g**3 - 549/4*g**2 - 117 - 348*g.
3*(g - 39)*(g + 2)*(5*g + 2)/4
Let t(x) be the second derivative of -x**5/20 + 11*x**4/12 - 13*x**3/2 + 45*x**2/2 + 8*x + 5. Factor t(y).
-(y - 5)*(y - 3)**2
Let m be 3 + -1 + 4 - 6. Let j(z) be the second derivative of 1/8*z**4 - 8*z + 1/4*z**3 + m*z**2 + 0. Let j(s) = 0. Calculate s.
-1, 0
Solve 3*o**4 + 69*o**3 + 189*o - 28*o**3 - 141*o**2 - 14*o**3 - 78 = 0 for o.
-13, 1, 2
Factor -2/11*b**3 - 34/11*b + 0 - 36/11*b**2.
-2*b*(b + 1)*(b + 17)/11
Suppose 2*x + 16*x = 36. Let u = 1/7 - -11/21. Factor 1/3 - 1/6*s**3 + u*s**x - 5/6*s.
-(s - 2)*(s - 1)**2/6
Let x(c) be the first derivative of c**3/3 + 11*c**2 + 121*c + 114. Solve x(f) = 0 for f.
-11
Suppose -136 = -29*n + 38. Factor -a**3 + 10*a + 7/2*a**2 - 1/2*a**4 + n.
-(a - 3)*(a + 1)*(a + 2)**2/2
Factor 243/2*r**4 + 783*r**3 + 2847/2*r**2 + 522*r + 54.
3*(r + 3)**2*(9*r + 2)**2/2
Let x(c) = -5*c + 83. Let b be x(15). Let w(m) be the second derivative of b*m**2 + 0 + 2*m - 8/3*m**3 + 1/3*m**4. Find k, given that w(k) = 0.
2
Let u(w) be the third derivative of -1/40*w**4 + 1/600*w**6 + 0*w**3 + 0 + 5*w + 1/150*w**5 + w**2. Suppose u(t) = 0. Calculate t.
-3, 0, 1
Suppose -1/3*d**3 + 1/3*d + 1/3*d**4 - 1/3*d**2 + 0 = 0. Calculate d.
-1, 0, 1
Suppose 64 = 4*r + 52. What is v in -3*v**2 + 7*v**2 - r*v**2 - 2 + 7 - 6*v = 0?
1, 5
Let x(f) be the first derivative of f**4/4 - 31*f**3/3 - f**2 + 62*f - 16. Let h be x(31). Factor -3/8*y - 1/4*y**2 + 1/8*y**3 + h.
y*(y - 3)*(y + 1)/8
Suppose 5*s + 10 = 2*w, -4*s + 46 = 3*w - w. Let t = 17 - w. Determine v, given that 26*v**2 - 3*v**3 - 6*v**t - 11*v**2 - 9*v + 3 = 0.
1
Suppose -s = -66 + 21. Determine n so that -30*n + 37*n**3 + 2*n**4 + 0*n**4 + 40*n**2 + 3*n**4 - s - 7*n**3 = 0.
-3, -1, 1
Let g be (-1)/2 + 28/8. Factor -15*t**2 - 7*t**4 + 5*t**2 + 2*t**4 - 2*t**g - 13*t**3.
-5*t**2*(t + 1)*(t + 2)
Let c be 4/(-16) + 17/4. Suppose 5*x = -c*z - 20, 5*z - 4*x - x - 20 = 0. What is i in 2*i - 4*i - 3*i**2 + z*i - i = 0?
-1, 0
Let u(a) be the second derivative of a**8/3360 - a**6/90 + 13*a**4/12 + 21*a. Let h(o) be the third derivative of u(o). Suppose h(b) = 0. What is b?
-2, 0, 2
Let s(k) be the second derivative of k**6/24 + k**5/2 + 15*k**4/8 + 10*k**3/3 + 25*k**2/8 - 272*k. Factor s(l).
5*(l + 1)**3*(l + 5)/4
Suppose -13 - 2 = -5*t. Suppose t*p**2 + 13*p**2 + 15 - 3 + 10*p**3 - 12*p**3 - 26*p = 0. What is p?
1, 6
Factor 0 + 27*i - 882*i**2 + 0 + 885*i**2.
3*i*(i + 9)
Let p be 19/(-6)*(183 + -185). Find v, given that p*v**3 + 25/3*v**2 + 4/3 + 7/3*v**4 + 1/3*v**5 + 16/3*v = 0.
-2, -1
Let s(g) be the third derivative of g**6/300 + g**5/25 + 3*g**4/20 + 4*g**3/15 + 112*g**2. Determine y so that s(y) = 0.
-4, -1
Factor -90/7 - 87/7*s + 3/7*s**2.
3*(s - 30)*(s + 1)/7
Let y(l) be the second derivative of -l**10/12096 + l**8/2688 + 5*l**4/3 + 20*l. Let h(j) be the third derivative of y(j). Determine k so that h(k) = 0.
-1, 0, 1
Let o(i) be the third derivative of 5/6*i**4 - 1/6*i**6 + 0 + 1/42*i**7 + 1/6*i**5 - 44*i**2 + 0*i - 5/2*i**3. Factor o(g).
5*(g - 3)*(g - 1)**2*(g + 1)
Let f be (0 + 2 - 3)*-3. Let w be 8/(-16) + ((-2023)/70)/(-17). Factor w*t**2 + 3/5*t**f - 3/5*t**4 + 0 + 0*t.
-3*t**2*(t - 2)*(t + 1)/5
Let b(c) be the third derivative of 0*c + 1/80*c**5 + 0*c**4 + 0 + 0*c**3 + 10*c**2. Determine l so that b(l) = 0.
0
Suppose -75*x = 243*x - 1590. Find z, given that -458/3*z**3 - 392/3*z**x + 16/3 + 40/3*z + 1078/3*z**4 - 284/3*z**2 = 0.
-2/7, -1/4, 2/7, 1, 2
Suppose -43*s + 395 = -38*s. Factor o**2 + 3 - 42*o - 41*o + s*o.
(o - 3)*(o - 1)
Let a be -3*(-58)/594 + (-210)/(-55) + -4. Find v, given that 1/9 + 2/9*v + a*v**2 = 0.
-1
Solve -6 + 13/4*y**2 + 5/2*y + 1/4*y**3 = 0 for y.
-12, -2, 1
Let b(d) be the third derivative of d**5/30 - d**4/4 - 4*d**3/3 + 239*d**2. Factor b(q).
2*(q - 4)*(q + 1)
Let i(o) = 12*o - 492. Let d be i(41). Let l(m) be the first derivative of -1/27*m**3 + 1/15*m**5 + 0*m**4 + 1/27*m**6 - 3 + d*m + 0*m**2. Factor l(s).
s**2*(s + 1)**2*(2*s - 1)/9
Let k = 114 - 114. Let s(m) be the third derivative of k*m - 1/2*m**4 + m**2 - 1/5*m**5 + 0*m**3 + 0 - 1/40*m**6. Solve s(o) = 0 for o.
-2, 0
Suppose 6*v**4 - 6*v**2 - 21/8*v**5 + 9/8*v**3 + 3/2*v + 0 = 0. What is v?
-1, 0, 2/7, 1, 2
Factor -1 - 11/2*w + 11/2*w**3 + w**2.
(w - 1)*(w + 1)*(11*w + 2)/2
Factor -q**4 + 58*q**2 + 3*q**4 + 0*q**4 - 60*q**2.
2*q**2*(q - 1)*(q + 1)
Determine w, given that 48 + 6*w**2 + 4 - 7 - 19*w**2 - 2*w**2 - 130*w = 0.
-9, 1/3
Let -121 - 69*o + 20 - 9*o + 3*o**2 - 67 = 0. What is o?
-2, 28
Let t(r) be the first derivative of r**5/25 + 2*r**4/5 + 16*r**3/15 - 17*r - 2. Let u(f) be the first derivative of t(f). Determine k so that u(k) = 0.
-4, -2, 0
Let v(z) = -4*z**2 - 48*z. Let d(b) = -20*b**2 - 238*b. Let i(g) = -2*d(g) + 11*v(g). Factor i(w).
-4*w*(w + 13)
Let c = 153 - 149. Factor 9*s**2 + c*s + s + 3*s**4 - 312*s**3 - 2*s + 321*s**3.
3*s*(s + 1)**3
Suppose -58*a = -55*a - 9. Factor 20*j**2 - 3*j**a - 2*j**3 - 82 + 82.
-5*j**2*(j - 4)
Suppose l - 6 = -3*d, -173*d = -171*d - 5*l + 30. Find q such that d*q + 1/2 - 1/2*q**2 = 0.
-1, 1
Suppose 0 + 176/7*w**4 + 40/7*w**2 + 0*w - 188/7*w**3 - 4*w**5 = 0. Calculate w.
0, 2/7, 1, 5
Let 4/3*r + 26/5 - 2/15*r**2 = 0. What is r?
-3, 13
Let i = -500 - -1001/2. Solve s**2 + 0 - 1/2*s**5 + i*s + 0*s**3 - s**4 = 0 for s.
-1, 0, 1
Let t(l) be the second derivative of l**7/210 - 7*l**6/150 + 19*l**5/100 - 5*l**4/12 + 8*l**3/15 - 2*l**2/5 - 16*l + 5. Factor t(h).
(h - 2)**2*(h - 1)**3/5
Let y(s) be the third derivative of -1/24*s**4 + 0 + 5*s**2 + 0*s + 1/480*s**6 + 0*s**5 + 0*s**3. Factor y(k).
k*(k - 2)*(k + 2)/4
Let b(k) = -k**5 - k**4 + 2*k**3 - k**2 + k. Let x(m) = 38*m**4 - 36*m**3 - 34*m**2 + 32*m. Let z(n) = 4*b(n) + 2*x(n). Let z(a) = 0. Calculate a.
-1, 0, 1, 17
Let y(n) be the third derivative of 2/525*n**7 + 0*n + 0 + 0*n**4 + 1/300*n**6 + 7*n**2 - 1/840*n**8 - 1/75*n**5 + 0*n**3. What is j in y(j) = 0?
-1, 0, 1, 2
Let i(p) be the third derivative of -p**8/6720 + p**6/720 + 5*p**4/24 - 2*p**2. Let n(m) be the second derivative of i(m). Find x such that n(x) = 0.
-1, 0, 1
Let -28 + 0*f**4 - 10*f + 12*f**3 + 3*f**3 + 10*f**3 + 30*f**2 - 15*f**3 - 2*f**4 = 0. What is f?
-2, -1, 1, 7
Suppose -b - 4*g - 2 - 11 = 0, 5*g + 11 = 4*b. Let h = b + 4. Suppose -4/3*y**5 - 8/3*y**2 + 2/3*y + 1/3 + 7/3*y**4 + 2/3*y**h = 0. Calculate y.
-1, -1/4, 1
Let z = -52 + 54. What is q in 4*q**3 + 2*q**2 + 305*q - 273*q + 18*q**z + 16 = 0?
-2, -1
Let o = -54197/18 - -3011. Let w(s) be the second derivative of o*s**2 + 1/180*s**5 + 1/18*s**3 + 7*s + 0 + 1/36*s**4. Factor w(n).
(n + 1)**3/9
Suppose -11*m + 4*m = 840. Let o be (-110)/(-56) + (m/32)/15. Suppose -o*x**2 - 2/7 - 2/7*x**4 - 8/7*x**3 - 8/7*x = 0. What is x?
-1
Determine b so that 239/2*b + 1/2*b**3 - 121/2*b**2 - 119/2 = 0.
1, 119
Let w be (-3 + 3 - -3)/((-3)/(-2)). Let t(h) be the second derivative of 0 - w*h - 1/21*h**4 + 2/7*h**2 + 0*h**3. Factor t(g).
-4*(g - 1)*(g + 1)/7
Let i(a) = a**4 - a**3 + a**2 - a + 1. Let b(k) = 3*k**5 + 13*k**4 - 13*k**3 - 29*k**2 - 22*k + 4. Let d(u) = b(u) - 4*i(u). Factor d(w).
3*w*(w - 2)*(w + 1)**2*(w + 3)
Let l(k) be the first derivative of -25*k**4/14 - 10*k**3 - 99*k**2/7 - 54*k/7 + 699. Factor l(n).
-2*(n + 3)*(5*n + 3)**2/7
Let t(k) be the first derivative of -4*k + 1/3*k**3 + 8 + 0*k**2. Solve t(r) = 0 for r.
-2, 2
Suppose 5 - 17 = -3*d. Let n be (-2)/(3 + (-14)/d). Let 7*s**3 + 9*s**n - 6*s**2 + 8*s**3 + 3*s*