e first derivative of 1/24*v**6 + u*v**5 + 3 + 0*v**3 - 1/8*v**4 + 1/8*v**2 + 0*v. Factor z(y).
y*(y - 1)**2*(y + 1)**2/4
Suppose 0 = -4*n + 28 + 32. Let m = 19 - n. Factor r**3 - 2*r**m + 2*r**4 + 3*r**4 - 4*r**4 + r**2 - r.
-r*(r - 1)**2*(r + 1)
Suppose 0 = h - d - 3*d + 2, -3*h + d = -5. Suppose -2*f = 2*l - 4, h*f + 5*l = 6*f - 26. Factor -2/3*t**2 + 2/3*t**f - 2/3*t**3 + 2/3*t + 0.
2*t*(t - 1)**2*(t + 1)/3
Let g be (-2)/(-7) + (-198)/(-42). Factor g*q**3 + 40 - 20*q - 12*q**4 + 9*q**4 - 30*q**2 + 8*q**4.
5*(q - 2)*(q - 1)*(q + 2)**2
Factor -60/7 - 2/7*m**2 - 22/7*m.
-2*(m + 5)*(m + 6)/7
What is q in 0 - 1/3*q**4 - 2*q - 2*q**3 - 11/3*q**2 = 0?
-3, -2, -1, 0
Let z(b) be the second derivative of -3*b**5/20 - 29*b**4/4 - 39*b**3 - 216*b. Factor z(a).
-3*a*(a + 3)*(a + 26)
Let u be 15/(-180)*24/(-27). Let t(z) be the first derivative of u*z**3 + 0*z - 2 + 0*z**2. Factor t(w).
2*w**2/9
Let m(y) be the third derivative of y**5/12 - 415*y**4/24 + 205*y**3/3 - 623*y**2. Factor m(q).
5*(q - 82)*(q - 1)
Factor 4*l**2 + 25/3*l + 2/3.
(l + 2)*(12*l + 1)/3
Factor -3/4*n**2 + 0 - 1/2*n - 1/4*n**3.
-n*(n + 1)*(n + 2)/4
Let y be (16/10)/((-115)/25 - -5). Suppose -f = -q + 2, 0 = -4*q - 8*f + y*f + 16. Factor -3/2*c**2 + 3/2*c**4 - 3/2*c**5 + 0 + 0*c + 3/2*c**q.
-3*c**2*(c - 1)**2*(c + 1)/2
Let d = 5 + -5. Let t = d - -2. What is j in -108*j**5 - 68*j**3 + 59*j - 63*j - 216*j**4 - 40*j**t - 76*j**3 = 0?
-1, -1/3, 0
Let r(b) be the third derivative of 1/60*b**5 + 1/3*b**3 + 0*b + 0 - 10*b**2 + 1/8*b**4. Determine w, given that r(w) = 0.
-2, -1
Let 3*t**4 - 12*t - 13*t**3 + 10*t**3 - 12*t**3 + 5*t**2 + 22*t**2 - 3*t**2 = 0. Calculate t.
0, 1, 2
Let u(h) = 4*h + 13. Let p be u(3). Determine g so that 51*g**2 - p*g**2 + 5 - 31*g**2 = 0.
-1, 1
Let w = 12063 + -60313/5. Find y, given that -w*y**2 + 0 - 8/5*y = 0.
-4, 0
Suppose 3*u - 5*t - 11 = 0, -3*t = u - t. Suppose -6*w + 2*w**u + 27 + 7*w**3 - 22*w - 35 = 0. What is w?
-2, -2/7, 2
Factor 60*y**2 - 2304 - 4/3*y**3 - 576*y.
-4*(y - 24)**2*(y + 3)/3
Let a(m) be the third derivative of m**7/420 - m**6/180 + m**3/6 - 15*m**2. Let x(i) be the first derivative of a(i). Factor x(o).
2*o**2*(o - 1)
Suppose 0 = 4*t - u - 17, 13 + 9 = -t - 5*u. Find r such that t*r**4 + r**4 - 24*r**5 - 5*r**3 - 2*r**2 + 23*r**5 + 4*r**2 = 0.
0, 1, 2
Let v = -15 + 30. Find j, given that v*j**2 + 12 + 8*j + 17*j + 3*j**3 - j = 0.
-2, -1
Let o(s) be the third derivative of -s**7/630 + s**6/360 + s**5/15 - 7*s**4/18 + 8*s**3/9 + 186*s**2. Let o(u) = 0. Calculate u.
-4, 1, 2
Let w(t) be the first derivative of -8/13*t**4 + 16/13*t**2 - 1/39*t**6 + 32/13*t - 16/39*t**3 - 14/65*t**5 + 36. Factor w(b).
-2*(b - 1)*(b + 2)**4/13
Let v(h) = 9*h**2 - 11*h - 9. Let d(m) = -5*m**2 + 6*m + 5. Let t(g) = 11*d(g) + 6*v(g). Let w(f) = -16*f + 4. Let q(p) = 12*t(p) + w(p). Factor q(a).
-4*(a + 2)*(3*a - 2)
Suppose 3*a - 3*h + 4 = 91, -a + 3*h = -27. Suppose x - 6 = -2*x, z = -3*x + a. Find v such that 4*v**3 - 5*v**4 - 2*v - z*v**3 + 11*v**3 - 7*v**2 - v**5 = 0.
-2, -1, 0
Let g(k) = 136*k + 274. Let a be g(-2). Factor 2/3*f**a + 2 + 8/3*f.
2*(f + 1)*(f + 3)/3
Factor -3/8*p**2 - 15/2 - 6*p + 3/8*p**3.
3*(p - 5)*(p + 2)**2/8
Let k(q) be the first derivative of -8/7*q**2 - 8/7*q**3 - 2/35*q**5 - 56 + 0*q - 3/7*q**4. Find b, given that k(b) = 0.
-2, 0
Let q(c) be the third derivative of -5*c**4/24 - c**3/6 + 8*c**2. Let g be q(-1). Factor 10*n**3 - n + 3*n**5 - 2*n + 6*n + 12*n**g + 8*n**3 + 12*n**2.
3*n*(n + 1)**4
Let y = 179/417 - -33/139. Let 1/3*t**2 - 1/3*t**3 + y*t + 0 = 0. Calculate t.
-1, 0, 2
Let n(h) be the second derivative of 1/84*h**4 + 3*h + 0*h**3 + 0*h**5 - 1/420*h**6 + 0 - 1/2*h**2. Let s(y) be the first derivative of n(y). Solve s(u) = 0.
-1, 0, 1
Suppose -4*c + 0*c - f - 4 = 0, 4*f = -2*c - 16. Solve -3*l**2 + 15 + c - 1 - 2 = 0.
-2, 2
Let i(k) = -11*k**2 - 49*k + 60. Let p(g) = -g**2 + 16. Let u be p(5). Let n(x) = -3*x**2 - 12*x + 15. Let q(t) = u*n(t) + 2*i(t). Factor q(f).
5*(f - 1)*(f + 3)
Let p = 2/4085 + 673/294120. Let o(g) be the third derivative of 3*g**2 + 0*g + 0*g**4 + 1/180*g**5 + 0 + 0*g**3 + p*g**6. Solve o(l) = 0 for l.
-1, 0
Let d be (-70)/(-100)*8/14. Let r be 4*(18/60)/3. Determine q, given that -r*q**3 + 0 + d*q + 0*q**2 = 0.
-1, 0, 1
Let j(f) = -f**2 - 2*f. Let c(q) = 16*q**2 - 68*q - 96. Let y(b) = c(b) + 12*j(b). Factor y(a).
4*(a - 24)*(a + 1)
Let k(q) = q**3 - 4*q**2 - q - 3. Let u be k(5). Let w = u - 15. Factor 6*p**2 - 10*p**w + 4*p**3 + 2 - p**4 - 2.
-p**2*(p - 2)**2
Let b(v) be the first derivative of -v**5/3 - 5*v**4/4 + 5*v**3/9 + 5*v**2/2 + 115. Suppose b(r) = 0. What is r?
-3, -1, 0, 1
Suppose 440*k - 360*k - 52*k**2 + 2*k**2 + 16*k**3 - 11*k**3 = 0. Calculate k.
0, 2, 8
Solve -2*c**3 - 6*c**2 - 2*c**5 - 98*c + 102*c + 0*c**4 + 6*c**4 = 0 for c.
-1, 0, 1, 2
Let g(d) be the second derivative of 5*d**7/84 + 43*d**6/36 + 53*d**5/24 - 3715*d**4/72 + 100*d**3 + 135*d**2 + 2*d + 41. Suppose g(f) = 0. Calculate f.
-9, -1/3, 2
Let m(i) be the third derivative of i**5/12 + 5*i**4/8 + 5*i**3/3 - 96*i**2. Factor m(w).
5*(w + 1)*(w + 2)
Suppose -26881 = -13*r - 26855. Determine j so that 0 - 6/5*j + 3/5*j**r = 0.
0, 2
Let a(z) = 32*z**5 + 48*z**4 - 68*z**3 - 228*z**2 - 12*z. Let f(t) = -13*t**5 - 19*t**4 + 27*t**3 + 91*t**2 + 5*t. Let i(x) = 5*a(x) + 12*f(x). Factor i(c).
4*c**2*(c - 2)*(c + 2)*(c + 3)
Factor 52/3*j**2 + 14/3*j**3 + 16 - 184/3*j.
2*(j - 2)*(j + 6)*(7*j - 2)/3
Let f(x) be the second derivative of 2 + 2/15*x**3 + x + 0*x**2 - 3/25*x**6 + 2/5*x**5 - 13/30*x**4. Find g, given that f(g) = 0.
0, 2/9, 1
Solve 40*u - 1/2*u**4 + 9*u**3 - 93/2*u**2 + 96 = 0.
-1, 3, 8
Let b be (-4)/15 + (-3)/(-9). Let m(t) be the third derivative of -1/150*t**5 + 0 - 3*t**2 + b*t**3 + 0*t**4 + 0*t. Determine y, given that m(y) = 0.
-1, 1
Solve -3*q**2 + 15/7*q**3 + 6/7*q + 0 = 0.
0, 2/5, 1
Let v = -297/2 + 149. Factor 1/10*p - v*p**2 + 1/2 - 1/10*p**3.
-(p - 1)*(p + 1)*(p + 5)/10
Suppose 2/7*m**2 + 2738/7 + 148/7*m = 0. Calculate m.
-37
Let g(o) be the first derivative of o**5/60 - o**4/18 + o**3/18 + 2*o + 10. Let p(b) be the first derivative of g(b). Find a such that p(a) = 0.
0, 1
Suppose -2*k + 36 = 4*k. Let a(s) = -s**3 + 6*s**2 + s - 4. Let q be a(k). Factor 2*t**2 + 2*t**2 - 6*t**q + 2.
-2*(t - 1)*(t + 1)
Factor -24 + 3/5*q**2 - 117/5*q.
3*(q - 40)*(q + 1)/5
Suppose 3*q = -2*b + 12 + 11, 4*q = -3*b + 32. Factor 2*y**5 + 4*y**b - 10*y - 4*y**2 - 4*y + 12*y.
2*y*(y - 1)*(y + 1)**3
Let a(w) be the second derivative of -w**3/2 - 2*w**2 - 21*w. Let f be a(-2). Factor 5/4*s**f - 1/4*s**4 + 0 + 1/4*s**5 - 1/2*s - 3/4*s**3.
s*(s - 1)**3*(s + 2)/4
Factor -48/7 + 44/7*w + 4/7*w**2.
4*(w - 1)*(w + 12)/7
Let m be (-250)/(-75) - (-4)/6. Suppose j - 11 = -3*z, -z + 3 + 8 = m*j. Factor 0*y - 4/15*y**z + 0 - 2/15*y**4 - 2/15*y**2.
-2*y**2*(y + 1)**2/15
Let r be -23 + 9 + 57/4. Factor -r*v**3 + 1/4*v - 3/4 + 3/4*v**2.
-(v - 3)*(v - 1)*(v + 1)/4
Let b(g) = 4*g + 39. Let m be ((-162)/(-72))/(1/(-8)*2). Let i be b(m). Determine o, given that 0*o**i + 0 + 2/3*o**4 + 0*o**2 + 0*o + 2/3*o**5 = 0.
-1, 0
Let -40/11*g**2 + 1/11*g**5 + 0*g**3 + 7/11*g**4 - 16/11*g + 48/11 = 0. What is g?
-6, -2, 1, 2
Factor -296 - 46*u + 10*u**2 + 85*u**3 - 39*u + 286.
5*(u - 1)*(u + 1)*(17*u + 2)
Suppose -3*r + 87 = -k, -4*r + k - 137 = -9*r. Factor -73*l**2 + 146*l**3 + 9*l**5 - 61*l**2 - 60*l**4 + 87*l - r*l**2 - 2*l**3 - 18.
3*(l - 3)*(l - 1)**3*(3*l - 2)
Let h(t) be the third derivative of t**8/336 + t**7/70 - 23*t**2 + 2. Let h(d) = 0. Calculate d.
-3, 0
Let m(t) be the second derivative of 0 + 0*t**2 - 1/3*t**4 + 9*t + 2/15*t**6 + 0*t**5 + 0*t**3. Factor m(l).
4*l**2*(l - 1)*(l + 1)
Let i(c) = 4*c - 27. Let q be i(8). Find t, given that -5*t**5 - 3*t**5 - 2*t**q + 11*t**5 + 2*t**4 = 0.
-2, 0
Let q = -678 - -2035/3. Let v(u) be the second derivative of -3/20*u**6 + 2/3*u**3 + 2*u + 11/24*u**5 + 0 - 53/72*u**4 + 5/252*u**7 - q*u**2. Solve v(i) = 0.
2/5, 1, 2
Let b be -6 + (18/(42/7) - -6). Let c(t) be the second derivative of 5*t + 1/8*t**b + 0 + 1/48*t**4 + 1/4*t**2. Factor c(y).
(y + 1)*(y + 2)/4
Let o(w) be the first derivative of 12*w**5/5 - 13*w**4 + 24*w**3 - 16*w**2 + 152. Factor o(v).
4*v*(v - 2)*(v - 1)*(3*v - 4)
Let j(v) be the second derivat