30. What is w in 0*w**v + 0*w - 1/2*w**3 + 1/4*w**5 + 0 + 1/4*w**4 = 0?
-2, 0, 1
Let m(t) be the first derivative of -t**4/66 + t**3/33 - 6*t - 3. Let b(u) be the first derivative of m(u). Factor b(g).
-2*g*(g - 1)/11
Let v(c) be the first derivative of 0*c**4 + 6/5*c**5 - 2*c**3 - 3/2*c**2 + 12 + 0*c + 1/2*c**6. What is f in v(f) = 0?
-1, 0, 1
Let n(u) be the third derivative of 0*u**3 + 0*u + 0 - 27/10*u**5 - 1/112*u**8 + 10*u**2 - 1/7*u**7 - 27/8*u**4 - 9/10*u**6. Determine y, given that n(y) = 0.
-3, -1, 0
Let j be (-10)/85 - (-18)/153. Let x(l) be the first derivative of 0*l**3 + 2/3*l**6 - l**4 + j*l**2 + 0*l**5 - 3 + 0*l. Factor x(u).
4*u**3*(u - 1)*(u + 1)
Let g(s) = -s**2 - 9*s - 2. Let n be g(-8). Find a such that 9*a**2 + a**3 - 4*a**3 + n*a**2 + 2*a**3 + 49 - 63*a = 0.
1, 7
Let q(m) = m**3 - 5 + m**4 - 3*m - 65*m**2 + 2 + 66*m**2. Let r(x) = 2*x**2 - 2*x - 2. Let v(o) = 2*q(o) - 3*r(o). Factor v(n).
2*n**2*(n - 1)*(n + 2)
Let r(q) be the first derivative of -8*q**5 + 33*q**4 - 632*q**3/15 + 24*q**2 - 32*q/5 - 121. Let r(s) = 0. Calculate s.
2/5, 1/2, 2
Let a(r) = r**3 + 6*r**2 + 8*r + 2. Let v be a(-4). Factor -3*z**2 + z**2 + 7*z**v - z**3 + 6*z**3.
5*z**2*(z + 1)
Factor 2/11*v**2 - 80/11*v + 78/11.
2*(v - 39)*(v - 1)/11
Let t(i) be the third derivative of 1/2*i**3 + 0*i + 1/540*i**6 - 3*i**2 + 0 + 0*i**4 + 1/180*i**5. Let k(v) be the first derivative of t(v). Factor k(j).
2*j*(j + 1)/3
Factor -16/3*s**2 + 0*s**4 - 4*s**3 + 2/3*s**5 - 2*s + 0.
2*s*(s - 3)*(s + 1)**3/3
Let p(n) be the second derivative of 98*n**6/15 + 84*n**5/5 - 9*n**4 + 4*n**3/3 - 2*n - 32. Factor p(z).
4*z*(z + 2)*(7*z - 1)**2
Let z(k) be the first derivative of 2*k**3/3 - 9*k**2 + 16*k - 454. Factor z(g).
2*(g - 8)*(g - 1)
Suppose -4*y = -9*y, -k + y = 0. Suppose -3*t = -4*g - k*t + 15, 25 = 3*g - 5*t. Let 1/5*f**4 + 1/5*f**3 + 0*f**2 + g + 0*f = 0. Calculate f.
-1, 0
Let f be 0*((-119)/(-21))/(-17). Factor 0*z + 5/2*z**5 + 15/2*z**4 + 5*z**3 + f + 0*z**2.
5*z**3*(z + 1)*(z + 2)/2
Let o(z) be the third derivative of -z**5/240 + 3*z**4/32 - 3*z**3/4 + z**2 - 16. What is x in o(x) = 0?
3, 6
Let p(v) be the third derivative of v**6/1020 - 4*v**5/17 + 400*v**4/17 - 64000*v**3/51 - 98*v**2 + 1. Factor p(d).
2*(d - 40)**3/17
Let k(l) be the first derivative of -l**5/20 - l**4/4 - 5*l**3/12 - l**2/4 - 227. What is p in k(p) = 0?
-2, -1, 0
Let m(g) be the first derivative of 4*g**3/3 - 38*g**2 - 264*g - 359. Factor m(t).
4*(t - 22)*(t + 3)
Let k = 376 + -373. Let p(x) be the second derivative of 2*x + 1/2*x**k - 1/24*x**4 + 0 - 9/4*x**2. Let p(f) = 0. What is f?
3
Let r(f) = f**3 - 9*f**2 + 5. Let i be r(9). Factor 2*v**4 + v - 13*v**3 + 3*v**i - 3*v**2 + 9*v**3 + v**2.
v*(v - 1)*(v + 1)**2*(3*v - 1)
Let n(c) = 5*c**3 + 4*c**2 - 92*c + 47. Let s(i) = 2*i**3 + 4*i**2 - 46*i + 24. Let f(a) = -4*n(a) + 9*s(a). Solve f(z) = 0 for z.
1, 2, 7
Let f(j) be the first derivative of -33*j**5/20 + 351*j**4/32 - 33*j**3/8 - 15*j**2/8 - 425. Let f(x) = 0. Calculate x.
-2/11, 0, 1/2, 5
Let a(p) = -2*p**2 - p + 1. Let h(t) = -52*t**2 - 192*t - 1740. Let r(b) = 24*a(b) - h(b). Solve r(u) = 0 for u.
-21
Let w be 8/(-20) - 1/(20/147). Let l = w + 9. Factor 1/2 + 1/4*r**5 - r**4 - l*r + r**3 + 1/2*r**2.
(r - 2)*(r - 1)**3*(r + 1)/4
Let w(v) be the first derivative of -4*v**3/3 - 22*v**2 - 48. Factor w(y).
-4*y*(y + 11)
Let i(s) = -s + 1. Let f(u) = 5*u**5 + 140*u**4 - 5*u**3 - 140*u**2 - 25*u + 25. Let m(b) = -f(b) + 25*i(b). What is d in m(d) = 0?
-28, -1, 0, 1
Solve 0 - 16/9*n - 4/9*n**3 + 16/9*n**2 = 0 for n.
0, 2
Let c be (-616)/(-165) - (-91)/(-65). Determine n so that 1/3*n**3 + 11/3*n - c*n**2 - 5/3 = 0.
1, 5
Let v(n) be the third derivative of n**9/120960 - n**8/40320 - 3*n**5/10 - 2*n**2. Let l(k) be the third derivative of v(k). Factor l(t).
t**2*(t - 1)/2
Suppose 0 = 91*c + 89*c - 360. Factor 2/13*h**c + 8/13 - 8/13*h.
2*(h - 2)**2/13
Suppose 5*o - 47 = -3*k, 3*o = -2*k - o + 34. Determine y, given that k*y**4 - 16*y**3 - 2*y + 2*y**4 - 4*y**4 - 1435*y**2 + 1446*y**2 = 0.
0, 2/7, 1
Let f(h) be the second derivative of h**4/15 - 16*h**3/5 + 46*h**2/5 - 162*h. Solve f(p) = 0.
1, 23
Let m(i) be the second derivative of -4*i**7/63 + 11*i**6/15 + 37*i**5/30 - 13*i. What is u in m(u) = 0?
-1, 0, 37/4
Let r(y) be the third derivative of y**5/12 + 5*y**4/12 - y**2 + 2*y. Factor r(k).
5*k*(k + 2)
Suppose 2 - 5/2*f**2 - f + f**4 + 1/4*f**3 + 1/4*f**5 = 0. What is f?
-2, 1
Determine w, given that -6*w**3 + 25 - 36*w - 15*w**2 - 15*w + 17*w - 43*w**2 - 7 = 0.
-9, -1, 1/3
Let i(x) be the second derivative of x**4/4 + 5*x**3/2 + 9*x**2 - 74*x - 1. Factor i(s).
3*(s + 2)*(s + 3)
Let j(v) = v**3 - v**2 + v. Let k = 29 + -25. Let m(t) = -2*t**3 - 50*t**2 + 482*t - 1458. Let z(f) = k*j(f) + m(f). What is u in z(u) = 0?
9
Let f(t) = -10*t - 9*t - 3*t - 2*t**2 + 3 + 20*t. Let b(d) = -d**2 - d + 1. Suppose -s - 3 = 5*p, -3*p - 2*s + 5 = 2*s. Let o(z) = p*f(z) + 3*b(z). Factor o(n).
-n*(n + 1)
Let v(w) = 6*w**2 + w**2 - w**2 - 15*w - 3*w**3 + 3*w**2. Let z = -25 - -20. Let q(d) = 6*d**3 - 19*d**2 + 29*d. Let x(a) = z*v(a) - 3*q(a). Factor x(o).
-3*o*(o - 2)**2
Let y(u) be the first derivative of -15 + 0*u - 8/5*u**2 - 2/15*u**3. Solve y(h) = 0 for h.
-8, 0
Let q(k) be the second derivative of 9*k**5/4 + 485*k**4/12 + 350*k**3/3 - 90*k**2 - 71*k + 2. Let q(i) = 0. Calculate i.
-9, -2, 2/9
Let h(i) be the first derivative of 4 - 1/5*i**2 + 1/5*i**3 + 1/50*i**5 - 1/10*i**4 - 5*i. Let l(m) be the first derivative of h(m). Factor l(y).
2*(y - 1)**3/5
Solve 2/15*a + 2/15*a**2 - 4/5 = 0.
-3, 2
Let w(x) be the third derivative of -x**5/90 - 31*x**4/18 - 961*x**3/9 - 107*x**2. Factor w(f).
-2*(f + 31)**2/3
Let a(n) be the second derivative of -n**5/10 - 7*n**4/6 - 16*n**3/3 - 12*n**2 + n - 88. Suppose a(q) = 0. What is q?
-3, -2
Let f = -4115/14 - -643/2. Let b = f - 27. Let 4/7 - 4/7*c**2 - 4/7*c + b*c**3 = 0. What is c?
-1, 1
Suppose -17 = 5*d + 15 - 52. Suppose 0*u + 128/7 - 4/7*u**d + 36/7*u**3 - 88/7*u**2 = 0. What is u?
-1, 2, 4
Determine j so that 12/7*j**2 - 48/7 - 16/7*j + 4/7*j**3 = 0.
-3, -2, 2
Let r be 7/(-28)*1 + 1/4. Let n(o) be the first derivative of 4/15*o**3 - 2/5*o - 5 + 0*o**4 + r*o**2 - 2/25*o**5. Determine m, given that n(m) = 0.
-1, 1
Let s(k) be the first derivative of 5*k**2 + 0*k - 32 - 75/4*k**4 + 5/3*k**3. Factor s(t).
-5*t*(3*t + 1)*(5*t - 2)
Let v = -21 - -29. Suppose v = 3*b - 10. Determine k, given that -k**3 - 4*k**4 - b*k**2 - 2*k**3 - k - 4*k**3 - 2*k**3 = 0.
-1, -1/4, 0
Let t(d) be the third derivative of -d**6/60 - d**5/5 - 2*d**4/3 + 51*d**2. Determine c, given that t(c) = 0.
-4, -2, 0
Let y(q) = 2*q - 12. Let p be y(6). Let s = 18 + -11. What is z in -8 + 2 - 4*z**3 + s*z**3 + p - 9*z = 0?
-1, 2
Let i(n) = 29*n**2 - 14*n - 2. Let q be i(2). Factor 43*f**2 - 4 + 2*f - q*f**2 + 45*f**2.
2*(f - 1)*(f + 2)
Let w = 262/53 - 1728/371. Factor 4/7 - 6/7*g + w*g**2.
2*(g - 2)*(g - 1)/7
Let c be ((-3)/(-9))/(2/(-12)). Let v(t) = -7*t**2 - 4*t - 2. Let m(r) = -3*r**2 - 2*r - 1. Let j(p) = c*v(p) + 5*m(p). Factor j(w).
-(w + 1)**2
Factor -49 - 2*d**2 + 1 + 38*d - 14 + 26 - 32.
-2*(d - 17)*(d - 2)
Let v(k) be the third derivative of -k**8/294 + 2*k**7/245 + k**6/30 - k**5/35 - 5*k**4/42 - 104*k**2. Find n such that v(n) = 0.
-1, 0, 1, 5/2
Suppose -5*z + 3*z = 0. Let m be z + -3*(-2 - -1). Determine j, given that 3*j + 8*j**m + 0*j**2 + 9*j**2 - 2*j**3 = 0.
-1, -1/2, 0
Let k be (31/10 - 3)/((-33)/(-55)). Let f(b) be the third derivative of 0*b - 5*b**2 + 0 - k*b**4 - 1/3*b**3 - 1/30*b**5. Factor f(s).
-2*(s + 1)**2
Let r be ((-6)/(-4))/(-18 - 185/(-10)). Let -2/3 - 1/6*i**2 + 1/6*i**5 + 1/6*i**4 + 4/3*i - 5/6*i**r = 0. What is i?
-2, 1
Let t(j) be the second derivative of -j**2 + 1/2*j**4 + 1/2*j**5 - 1/3*j**3 + 0 + 2/15*j**6 + 20*j. Suppose t(v) = 0. Calculate v.
-1, 1/2
Let p(h) be the first derivative of h**5/20 - 87*h**4/4 + 7569*h**3/2 - 658503*h**2/2 + 57289761*h/4 - 504. Suppose p(i) = 0. What is i?
87
Let u(l) be the third derivative of l**8/6720 - 19*l**7/5040 - 7*l**6/360 - 2*l**5/5 + 26*l**2. Let h(t) be the third derivative of u(t). Factor h(d).
(d - 7)*(3*d + 2)
Let h = -558 - -560. Let q(s) be the third derivative of 0*s**3 + 0*s**5 + 0*s**4 + 0*s + 0 - 1/1176*s**8