. Let s be h/(-3)*-3 - (3 + -51). Factor a**2 + s*a + 4*a**2 - 45*a.
5*a*(a + 1)
Let q(f) be the second derivative of -3*f**5/10 + 2941*f**4/6 - 721280*f**3/3 + 240100*f**2 - 1947*f. Factor q(h).
-2*(h - 490)**2*(3*h - 1)
Let i(n) be the second derivative of -4/3*n**4 + 1/42*n**7 + 0 + 29/6*n**3 - 264*n - 6*n**2 - 3/10*n**5 + 2/15*n**6. Factor i(u).
(u - 1)**3*(u + 3)*(u + 4)
Let m(v) be the first derivative of 3*v**4/4 - 582*v**3 + 126144*v**2 + 511584*v + 7675. Factor m(l).
3*(l - 292)**2*(l + 2)
Let y(q) be the first derivative of -3*q**5/25 + q**4/4 - q**3/15 - q**2/10 - 5238. Factor y(r).
-r*(r - 1)**2*(3*r + 1)/5
Let g(k) = 1. Let y(u) = -3*u**2 + 3 + 42*u + 5*u - 104*u. Let j(t) = 3*g(t) - y(t). Find l, given that j(l) = 0.
-19, 0
Let r(x) = -961*x**3 - 968*x**2 + 1897*x + 5. Let i(q) = 1924*q**3 + 1937*q**2 - 3793*q - 5. Let y(h) = -3*i(h) - 7*r(h). Factor y(o).
5*(o - 1)*(o + 2)*(191*o + 2)
Let x(p) be the second derivative of p**6/15 + 31*p**5/6 - 26*p**4/9 + 603*p. Determine y so that x(y) = 0.
-52, 0, 1/3
Solve -5*v**2 + 4*v**3 + 3*v + 39*v**3 - 41*v**3 - 2*v**2 = 0 for v.
0, 1/2, 3
Let r be (2 - (-52904)/(-8826))*(-22)/286. Let x = r + 2/4413. Suppose 6/13*f + x + 2/13*f**2 = 0. What is f?
-2, -1
Suppose 6*g + 4*r = g + 50, 5*r + 25 = 0. Let x be (-1)/(g/4) - (-46)/63. Solve -52/9*j**3 + 16/3*j**2 + 0 - 16/9*j - x*j**5 + 8/3*j**4 = 0.
0, 1, 2
Let x(y) be the second derivative of y**5/30 + 133*y**4/6 + 13333*y**3/3 + 39601*y**2/3 - 298*y + 1. What is g in x(g) = 0?
-199, -1
Let b(m) = -m**2 + 4820*m + 2. Let j be b(0). Let -2*o + 7/5*o**4 + 0 + 9/5*o**3 + 1/5*o**5 - 7/5*o**j = 0. What is o?
-5, -2, -1, 0, 1
Let j(g) = 66*g + 3. Let w be j(0). Let x(u) be the first derivative of 8 - 1/8*u**2 + 1/12*u**w + 0*u. Factor x(d).
d*(d - 1)/4
Let i(b) = 12*b**5 + 19*b**4 - 17*b**3 - 7*b + 7. Let f(w) = -7*w**5 - 10*w**4 + 9*w**3 + 4*w - 4. Let o(m) = 14*f(m) + 8*i(m). Let o(z) = 0. Calculate z.
0, 1, 5
Let r(y) be the second derivative of y**5/4 - 25*y**4/2 + 215*y**3/2 - 250*y**2 + 1457*y. Factor r(b).
5*(b - 25)*(b - 4)*(b - 1)
Let o = 129770 + -129770. Factor 0 + o*t**3 - 8/9*t**2 + 0*t + 2/9*t**4.
2*t**2*(t - 2)*(t + 2)/9
Let i be (350/360 - 2/9)*8. Let q(f) be the third derivative of 1/6*f**5 + 0*f + 0*f**3 - 1/3*f**4 + 9*f**2 + 0 - 1/60*f**i. Factor q(c).
-2*c*(c - 4)*(c - 1)
Let d be (135/144)/(427/976). Solve -3/7*n - 15/7*n**2 + d*n**4 + 12/7*n**5 - 9/7*n**3 + 0 = 0 for n.
-1, -1/4, 0, 1
Let l = 1067/6 - 7451/42. Let p(k) be the second derivative of 5/14*k**4 + 2*k - 27/7*k**2 + l*k**3 + 0 + 3/70*k**5. Factor p(m).
6*(m - 1)*(m + 3)**2/7
Let b(g) be the third derivative of -1/40*g**6 + 2401/2*g**3 - 284*g**2 + 0*g - 97/20*g**5 + 0 - 2303/8*g**4. Factor b(a).
-3*(a - 1)*(a + 49)**2
Let i(s) be the third derivative of -s**10/105840 + s**9/8820 - s**8/4704 + 55*s**4/12 + 21*s**2 + 3. Let r(c) be the second derivative of i(c). Factor r(q).
-2*q**3*(q - 5)*(q - 1)/7
Factor -56/9 + 58/9*u - 2/9*u**2.
-2*(u - 28)*(u - 1)/9
What is w in -80*w + 146 + 574 + 40*w**3 - 5*w**5 + 467*w**4 - 422*w**4 - 360*w**2 = 0?
-2, 2, 9
Factor -129/4*c**3 - 45/2*c**2 - 21/2*c**4 + 0 + 0*c.
-3*c**2*(c + 2)*(14*c + 15)/4
Let p be (-3)/14*716/(-358). Suppose 2*v + 7 = -o + 5*v, 7 = 5*o - v. Solve 36/7 - 24/7*f + p*f**o = 0.
2, 6
Let j(f) be the second derivative of 2/3*f**3 + 1/6*f**4 + 6*f + 10 + f**2. Factor j(l).
2*(l + 1)**2
Let y = 149 + -443/3. Let g be ((-1)/7)/(15 + 3195/(-210)). Determine w, given that g*w**2 + 2/3*w - y = 0.
-2, 1
Let m(t) be the first derivative of 13*t**6/60 - t**5/20 + 72*t - 132. Let r(z) be the first derivative of m(z). Let r(i) = 0. What is i?
0, 2/13
Let g(s) be the third derivative of 0*s + 0*s**5 + s**2 + 19 + 1/720*s**6 + 0*s**3 - 1/144*s**4. Find j, given that g(j) = 0.
-1, 0, 1
Factor -14/3*o**2 - 34/3 - 49/3*o + 1/3*o**3.
(o - 17)*(o + 1)*(o + 2)/3
Suppose 27*y - 16*y = 66. Suppose 61 - 15 + y*v**4 + 16*v**3 - 46 - v**5 = 0. What is v?
-2, 0, 8
Let j = 126179 - 126176. Factor 0*o + 1/3*o**j + 0 + 2/3*o**2.
o**2*(o + 2)/3
Let t(z) be the first derivative of 3*z**4/8 - 5*z**3/12 - z**2 + 7*z/4 - 105. Factor t(r).
(r - 1)**2*(6*r + 7)/4
Solve -17*v**5 + 77*v**2 + 23*v**5 - 77*v**2 + v**3 - 3*v**4 - 10*v**5 = 0.
-1, 0, 1/4
Factor 336*v - 152*v**4 + 75*v**4 - 41 + 81*v**4 + 16*v**3 + 41 - 356*v**2.
4*v*(v - 7)*(v - 1)*(v + 12)
Let f = 9452 + -9448. Let n(p) be the third derivative of 1/6*p**f + 1/15*p**6 - 4/3*p**3 + 1/3*p**5 + p**2 + 0*p + 7. Factor n(m).
4*(m + 1)*(m + 2)*(2*m - 1)
Let k be (-7 + -3)*((-67996)/4450 + (1 - -13)). Factor -k - 68/5*c - 4/5*c**2.
-4*(c + 1)*(c + 16)/5
Let t(z) = 2*z + 2. Let d(b) = b**2 - b - 2. Let r(s) = -d(s) + 2*t(s). Let g(c) = -16*c - 2*c**2 + 5*c**2 - 18 + 2*c. Let h(l) = 4*g(l) + 11*r(l). Factor h(k).
(k - 3)*(k + 2)
Let c(i) be the first derivative of -64 + 1/35*i**5 - 1/14*i**4 - 1/7*i**3 + 0*i + 0*i**2. Suppose c(l) = 0. What is l?
-1, 0, 3
Let k be -3*44/(-33) + 0 + -12. Let n be 10 + 1392/(-84) - k. What is i in -2/7*i**2 - 12/7*i - n = 0?
-5, -1
Solve 60 + 0*q + 34*q + 7*q**2 + 10*q**2 - 12*q**2 - 3*q**2 = 0.
-15, -2
Suppose -51*u + 545 = 33*u + 25*u. Let f(y) be the second derivative of -2/5*y**u - 1/6*y**4 + 0 + 0*y**2 + 17*y - 1/15*y**6 + 2*y**3. Factor f(v).
-2*v*(v - 1)*(v + 2)*(v + 3)
Let f(i) = i**2 + 9*i + 23. Let y be f(-4). Let g = 0 + y. Determine z so that 48*z**g + 138*z**5 - 17*z**5 - 4*z**2 - 320*z**4 + 155*z**4 = 0.
0, 2/11, 1
Determine j, given that -2*j**4 - 450*j**2 + 32*j**3 + 5160*j + 28*j**3 - 5160*j = 0.
0, 15
Let m(x) be the first derivative of -x**5/20 - 83*x**4/16 + 85*x**3/4 - 257*x**2/8 + 43*x/2 + 21. Factor m(l).
-(l - 1)**3*(l + 86)/4
Solve -31*s**3 + 64*s - 7*s**3 - 2*s**3 - 23*s**3 + 16*s**4 - s**5 - 16*s**2 = 0.
-1, 0, 1, 8
Let j be -22 - -12 - (4 + -16). Let o(r) = -r**3 + 7*r**2 + 8*r + 3. Let b be o(8). Factor -2*i**2 + 14*i**j - 18 - i**3 - 8*i + 4*i**b + 11*i.
3*(i - 1)*(i + 2)*(i + 3)
Factor 5*l**4 - 17*l**4 - 4*l + 2*l**4 - 5*l**2 + 17*l**2 + 3*l**3 + 3*l**5.
l*(l - 2)**2*(l + 1)*(3*l - 1)
Solve -6/7*d**4 + 432/7 + 62/7*d**3 - 540/7*d + 54/7*d**2 - 2/7*d**5 = 0 for d.
-6, -4, 1, 3
Find c, given that -321/4*c + 477/2 + 1/4*c**2 = 0.
3, 318
Let m(f) be the first derivative of -f**3/5 - 81*f**2/5 - 1599*f/5 + 291. Factor m(t).
-3*(t + 13)*(t + 41)/5
Let k(b) = b + 26. Let j be k(-12). Suppose -d = 4*t, -4*d = -0*t + 2*t - j. Suppose -9*u**3 + 11*u - 8*u - u**5 + 3*u**2 - 3*u**d + 7*u**5 = 0. Calculate u.
-1, -1/2, 0, 1
Let f(y) be the third derivative of 1/120*y**6 + 1/168*y**8 - 1/12*y**3 + 12*y**2 - 1/15*y**5 + 3/140*y**7 - 1/8*y**4 + 0 + 0*y. Factor f(t).
(t - 1)*(t + 1)**3*(4*t + 1)/2
Suppose 3038*t - 802*t - 4285 - 187 = 0. Factor -54*r**3 + 348*r**t + 16 - 440/3*r.
-2*(r - 6)*(9*r - 2)**2/3
Let u(f) be the second derivative of 2*f**6/105 + 17*f**5/140 - 17*f**3/42 - 2*f**2/7 - 198*f. Let u(b) = 0. Calculate b.
-4, -1, -1/4, 1
Let m be 6/(-15) - 2/(-5). Factor -5*r**3 + 2*r**3 + m*r**2 + 148 - r**3 - 28*r**2 + 20*r + 152.
-4*(r - 3)*(r + 5)**2
Let o(x) = 5*x**5 + x**4 + 63*x**3 + 35*x**2 + 22*x - 6. Let j(m) = 6*m**5 - m**4 + 66*m**3 + 33*m**2 + 23*m - 7. Let v(t) = -6*j(t) + 7*o(t). Factor v(s).
-s*(s - 16)*(s + 1)**3
Factor -19/5*b + 14 + 1/5*b**2.
(b - 14)*(b - 5)/5
Suppose 7*h - 633 + 2201 = 0. Let w = 224 + h. Factor 2/3*s**2 - 2/3*s**5 - 2*s**3 + 0 + w*s + 2*s**4.
-2*s**2*(s - 1)**3/3
Let s(g) be the first derivative of -15*g**4/2 - 19*g**3 - 12*g**2 + 3*g - 1110. Factor s(c).
-3*(c + 1)**2*(10*c - 1)
Suppose -5 = -f - m, 5 = 2*f - 5*m + 2. Suppose -2*v - 4 = -4*j, v + 2 + f = 4*j. Find t, given that t - 26*t**2 - 15*t + j*t + 10*t**2 - 4*t**3 = 0.
-3, -1, 0
Let l(d) be the third derivative of -d**5/25 + 57*d**4/40 - 7*d**3/5 + 19*d**2 + 63. Factor l(y).
-3*(y - 14)*(4*y - 1)/5
Let j(b) be the first derivative of b**4/4 + 11*b**3/3 - b**2/2 - 11*b + 3113. Suppose j(h) = 0. Calculate h.
-11, -1, 1
Let b(x) be the first derivative of 10*x - 7/6*x**4 + 0*x**2 - x**3 + 7. Let q(d) be the first derivative of b(d). What is o in q(o) = 0?
-3/7, 0
Let u(o) be the third derivative of -2/5*o**6 - 1/70*o**7 + 7*o**2 - 16/5*o**5 + 12 + 0*o**4 + 0*o + 0*o**3. Let u(n) = 0. What is n?
-8, 0
Suppose 2*k + 717 - 709 = 0. Let a be (-1)/3 + (-16)