1). Find w, given that w**2 - 7/4*w - y = 0.
-1/4, 2
Let v(a) = -a**3 + 11*a**2 + 101*a - 4. Let k be v(-6). Determine y so that -21/5*y**3 - 6/5*y**4 + 9/5*y**5 + 0*y + 0 - 6/5*y**k = 0.
-1, -1/3, 0, 2
Factor -33750/7*m - 2/7*m**3 - 843750/7 - 450/7*m**2.
-2*(m + 75)**3/7
Let z = -33 - -37. Suppose 7*f**3 + 10*f - 22*f**3 - 5 + f**2 + z*f**2 + 5*f = 0. What is f?
-1, 1/3, 1
Let r(v) be the second derivative of v**4/4 + 11*v**3 + 363*v**2/2 + 207*v. Let r(u) = 0. What is u?
-11
Let n(g) be the third derivative of g**7/140 + 21*g**6/80 + 29*g**5/8 + 375*g**4/16 + 125*g**3/2 + 505*g**2. Suppose n(u) = 0. Calculate u.
-10, -5, -1
Let y = 10/59 - -442/177. Suppose -10 + 4 = d + 2*a, -a = -d + 6. Factor y + 2/3*t**3 - 2*t**d + 0*t.
2*(t - 2)**2*(t + 1)/3
Suppose 0 = -7*a - 27 - 15. Let k(x) = 5*x**3 - 19*x**2 + 46*x - 26. Let d(y) = -y**2 - y + 1. Let z(s) = a*d(s) - k(s). Factor z(w).
-5*(w - 2)**2*(w - 1)
Let k(f) = f**2 + 2*f + 1. Let y be k(-3). Suppose 2*v = -16*v + 54. Suppose -2/13*p + 20/13*p**2 + 10/13*p**5 - 4/13 - 16/13*p**y - 8/13*p**v = 0. What is p?
-1, -2/5, 1
Let i(z) = -16*z**3 + 3*z - 6*z**2 + 9 + 12*z + z**3 + 5*z**4 + z**4. Let t(d) = 3*d**4 - 8*d**3 - 3*d**2 + 8*d + 5. Let l(a) = -5*i(a) + 9*t(a). Factor l(v).
-3*v*(v - 1)**2*(v + 1)
Let w(z) be the third derivative of z**6/480 - z**5/80 + z**4/48 + 2*z**2 + 64. Suppose w(d) = 0. What is d?
0, 1, 2
What is h in 7*h**4 + 150*h**2 - 305*h**3 - 97*h**5 + 182*h**5 - 90*h**5 + 153*h**4 = 0?
0, 1, 30
Let q(c) = c**3 - 26*c**2 + 190*c - 292. Let z(h) = h + 2. Let n(l) = q(l) + 2*z(l). Suppose n(p) = 0. Calculate p.
2, 12
Factor 10/9*d + 8/9 + 2/9*d**2.
2*(d + 1)*(d + 4)/9
What is a in -4/3 - a - 1/6*a**2 = 0?
-4, -2
Let x(v) be the third derivative of 7/24*v**4 + 1/15*v**7 + 1/10*v**5 + 0 - 16*v**2 - 1/3*v**3 - 5/24*v**6 + 0*v. Determine l so that x(l) = 0.
-1/2, 2/7, 1
Let s(d) be the first derivative of -4/7*d**2 - 12/35*d**5 + 13 - 1/21*d**6 - 8/7*d**3 + 0*d - 13/14*d**4. Factor s(m).
-2*m*(m + 1)**2*(m + 2)**2/7
Let z(t) be the third derivative of t**6/30 - t**5/30 + 2*t**2 - 9. Factor z(j).
2*j**2*(2*j - 1)
Let r(c) be the second derivative of -c**4/48 + 7*c**3/4 - 441*c**2/8 + c + 151. Factor r(z).
-(z - 21)**2/4
Factor -18/5*a**2 + 60 + 9*a - 3/5*a**3.
-3*(a - 4)*(a + 5)**2/5
Let m = -549 + 549. Let o(a) be the first derivative of 2 - 1/4*a**4 + 0*a**3 + m*a**2 + 0*a. Solve o(b) = 0 for b.
0
Let p(j) be the second derivative of j**7/13860 + j**6/660 + 3*j**5/220 - j**4 + j. Let w(y) be the third derivative of p(y). Factor w(d).
2*(d + 3)**2/11
Let f(x) be the third derivative of 23/15*x**6 + 3*x**2 + 2*x**5 + 0 + 2/3*x**3 + 3/28*x**8 + 0*x + 3/2*x**4 + 22/35*x**7. Solve f(t) = 0.
-1, -1/3
Solve -1631*f**4 - 1075*f + 3952*f**4 - 175821*f**2 - 750 + 11155*f**3 + 181291*f**2 + 4359*f**4 + 1200*f**5 = 0 for f.
-3, -5/4, -2/5, 1/3
Suppose 420 = 3*j - 6*j. Let v be j/30*-3*2. Factor -3*r - 25*r**3 + v*r**3 + 7*r**4 - 4*r**4 - 3*r**2.
3*r*(r - 1)*(r + 1)**2
Let r(l) be the first derivative of -l**6/120 - l**5/20 - 5*l**4/48 - l**3/12 + 6*l - 7. Let p(o) be the first derivative of r(o). Let p(k) = 0. What is k?
-2, -1, 0
Let i(w) be the first derivative of -w**6/57 - 2*w**5/19 - 4*w**4/19 - 8*w**3/57 + 247. Determine d, given that i(d) = 0.
-2, -1, 0
Suppose 2*m = -m + 27. Suppose d + 1 - 4 = v, -3*d - 4*v = -m. Suppose -6*o**4 - 25*o**d - 3*o**5 + 11*o**3 + 11*o**3 = 0. Calculate o.
-1, 0
Let i(g) be the third derivative of -g**7/420 + g**6/48 + 13*g**5/120 + 7*g**4/48 - 84*g**2. Solve i(b) = 0.
-1, 0, 7
Solve 0*m + 4*m - 24*m**2 - 7*m + 23*m**2 = 0 for m.
-3, 0
Let w(v) = -55*v**2 + 125*v + 155. Let h(n) = 9*n**2 - 21*n - 26. Let c = -104 + 79. Let x(b) = c*h(b) - 4*w(b). Determine q so that x(q) = 0.
-1, 6
Let r(w) = -4*w - 3. Let b be r(-2). Let p(t) = -16*t**3 - 2*t**2 + 1. Let m be p(-1). Suppose 16 + b*z**2 - m*z - 5*z - z**2 + 4*z = 0. Calculate z.
2
Let f be -2*(-777)/(-252) + 1 + 7. Suppose 11/6*c**2 - 1/3*c - 7/6*c**3 + 0 + 3/2*c**5 - f*c**4 = 0. What is c?
-1, 0, 2/9, 1
Let x(k) = 65*k**3 - 990*k**2 + 1650*k + 2750. Let u(d) = 3*d**3 - 45*d**2 + 75*d + 125. Let h(j) = -45*u(j) + 2*x(j). Determine l so that h(l) = 0.
-1, 5
Let a(i) = -i + 9. Let b be a(7). Suppose b*f + 15 = 3*r, f = 4*r - 11 - 9. Factor r*u + 3*u**2 + 3*u + 3*u - 5*u.
3*u*(u + 2)
Let d(p) be the first derivative of p**3 - 39*p**2/2 - 100. Let d(u) = 0. Calculate u.
0, 13
Let n(v) be the first derivative of -2*v**7/105 - v**6/30 + v**5/15 + v**4/6 - 4*v**2 + 9. Let x(z) be the second derivative of n(z). Factor x(k).
-4*k*(k - 1)*(k + 1)**2
Let j(y) be the third derivative of y**5/90 + y**4/9 - 32*y**3/9 + 88*y**2. Factor j(k).
2*(k - 4)*(k + 8)/3
Let k be 16/6 + 6/(-9). Suppose -3*p + c + 72 = 0, -20*p + 13*p - 2*c = -168. Solve -12*h + 3/2 + p*h**k = 0 for h.
1/4
Let m be ((-18)/(-16))/(-42*15/(-420)). Let -m*a**2 - 1/4*a**3 - 3/4*a - 1/4 = 0. Calculate a.
-1
Let z(i) be the first derivative of 1/2*i**4 + 0*i - 16/15*i**3 - 2/25*i**5 - 14 + 4/5*i**2. Factor z(l).
-2*l*(l - 2)**2*(l - 1)/5
Let 48*g**2 + 616016*g**4 + g**3 - 5*g**5 - 616028*g**4 + 36 - 19*g**3 + 8*g**5 + 87*g = 0. What is g?
-1, 3, 4
Let v(g) be the second derivative of -1/15*g**6 - 7*g + 1/6*g**4 + 0*g**2 + 0 - 1/10*g**5 + 1/3*g**3. Factor v(s).
-2*s*(s - 1)*(s + 1)**2
Let k(j) = 24*j + 12*j**2 + 14*j - 2 - 93*j**2. Let x(s) = -s - 1. Let b(o) = 2*k(o) + 4*x(o). What is p in b(p) = 0?
2/9
Let f = 43 - 46. Let d be (273/77 - 0) + f. Factor 4/11*y - 2/11*y**2 + d.
-2*(y - 3)*(y + 1)/11
Let n be 51/(-9) + 6 - 16/(-6). Determine c, given that -10*c - 4 + 2*c + 7*c**2 - 7*c**4 + 14*c**2 + 8*c**3 - 10*c**n = 0.
-2, -2/7, 1
Let o = -89327/3 - -30202. Let h = o - 421. Determine u so that 32/3*u**2 + h*u + 2/3 = 0.
-1/4
Let f(j) be the second derivative of 2*j - 17/66*j**4 + 14/33*j**3 - 1/22*j**5 + 8/11*j**2 + 0. Find b such that f(b) = 0.
-4, -2/5, 1
Factor 264*y**3 + 1878*y**4 + 388*y**4 - 88*y**4 + 8*y**2.
2*y**2*(33*y + 2)**2
Let h = -97 - -197. Let v = h + -690/7. Suppose -4/7 - 4/7*k**2 - v*k = 0. Calculate k.
-2, -1/2
Let t(g) = -g**3 + 3*g**2 + 4*g - 3. Let d(y) = -4*y**3 + 11*y**2 + 15*y - 11. Let v = -38 - -60. Let b(o) = v*t(o) - 6*d(o). Suppose b(w) = 0. Calculate w.
-1, 0, 1
Let m(c) be the second derivative of c**8/840 + c**7/420 - c**6/45 - c**5/15 + 16*c**3/3 + 38*c. Let b(n) be the second derivative of m(n). Factor b(s).
2*s*(s - 2)*(s + 1)*(s + 2)
Let t(d) = -d**3 + 5*d + 4. Let k be t(-1). Let n(c) be the third derivative of 1/390*c**5 + 5*c**2 + 0*c**4 + 0*c**3 + 0 + k*c. Factor n(o).
2*o**2/13
Let o = 4 - 1. Suppose -o*n + 20 = n. Determine b so that -2*b**4 + 3*b**5 - 2*b**5 - 2*b**5 + 2*b**n + b**3 = 0.
0, 1
Let f(j) be the first derivative of j**6/12 - 33*j**5/10 + 359*j**4/8 - 1199*j**3/6 - 363*j**2 + 2662*j - 248. Solve f(t) = 0 for t.
-2, 2, 11
Let y(b) be the second derivative of b**4/6 + 43*b**3/3 + 82*b**2 + 2*b - 378. Find t, given that y(t) = 0.
-41, -2
Factor 13/8*t + 1/8*t**2 - 15/4.
(t - 2)*(t + 15)/8
Suppose 296 = h - k, -k - 3*k - 16 = 0. Suppose 0 = -6*g + 86 + h. Factor -8*p + g*p**2 - 68*p**2 + 10*p + 8*p.
-5*p*(p - 2)
Let b be 47/2*-1 - (-17)/(-34). Let m be (-2*(1 + 1)/b)/1. Factor m*y**2 - 1/3*y + 1/6.
(y - 1)**2/6
Let m(q) be the third derivative of q**5/80 + 3*q**4/8 - 7*q**2 + 6. Factor m(x).
3*x*(x + 12)/4
Factor -43/2*j**2 + 0 - 3/4*j**3 + 29/4*j.
-j*(j + 29)*(3*j - 1)/4
Let t(u) be the second derivative of u**7/8820 - u**6/630 + u**5/140 - 7*u**4/3 - 21*u. Let o(f) be the third derivative of t(f). Factor o(y).
2*(y - 3)*(y - 1)/7
Suppose 32 = -3*m + 104. Let d be -3*1*6/(-9). Factor 3 - 3*y**2 - 32 - 17 + m*y - d.
-3*(y - 4)**2
Let k(z) = z**2 - 20*z + 53. Let t be k(17). Solve 3/2*h**4 + 6 + 9*h**3 + 18*h + 39/2*h**t = 0.
-2, -1
Let w = 40 + -44. Let r be 27/18 + w + 3. Factor -r*p**4 - 1/2 + 2*p + 2*p**3 - 3*p**2.
-(p - 1)**4/2
Let r = -53 + 61. Suppose -3*w - 16 = -5*d, 4*w + 4 + r = 2*d. Factor 3/5*l**d + 0 - 3/5*l.
3*l*(l - 1)/5
Suppose 4*u - 10 = 78. Suppose u = 2*o - 14. Factor -5*x**3 + 3*x**5 + 44*x**3 + x**5 + o*x**4 + 12*x + 36*x**2 - x**5.
3*x*(x + 1)**2*(x + 2)**2
Let q(z) = -5*z - 68. Let i be q(-14). Determine s so that -2*s**3 + i*s - 7*s + 11*s + 4 = 0.
-1, 2
Let -16*b**3 - 23*b*