41*b**4/12 - 22*b**3/3 + 3*b**2/2 - 2*b - 9. Factor p(f).
(f - 1)*(41*f - 3)
Let o(k) = k**3 + 10*k**2 + 7*k - 18. Let h be o(-9). Let 4*z**2 + h*z**2 - z**3 - 4*z**2 - 2*z**2 - z = 0. What is z?
-1, 0
Factor 8*i**4 + 7929*i**2 + 2*i**5 - 8*i - 7937*i**2 + 0*i + 6*i**3.
2*i*(i - 1)*(i + 1)*(i + 2)**2
Suppose -6/5*v**3 + 0 + 2/5*v**2 + 0*v - 2/5*v**5 + 6/5*v**4 = 0. What is v?
0, 1
Let t(r) be the second derivative of -r**6/270 + r**5/15 - 7*r**4/18 + 10*r**3/27 + 25*r**2/6 + 6*r - 33. Factor t(p).
-(p - 5)**2*(p - 3)*(p + 1)/9
Suppose 3*x + x - 12 = 0. Let s be 10/(-15) + (-7)/(-6). Factor 9/4*p**2 + 5/4*p**4 + 3*p**x + 0 + s*p.
p*(p + 1)**2*(5*p + 2)/4
Let h(c) be the third derivative of -841*c**5/4 + 29*c**4/2 - 2*c**3/5 - 41*c**2 + 1. Factor h(m).
-3*(145*m - 2)**2/5
Let i(v) be the first derivative of -6/5*v - 19/10*v**2 - 24 + 1/4*v**4 - 8/15*v**3. What is x in i(x) = 0?
-1, -2/5, 3
Let u(s) be the first derivative of -2/21*s**3 + 0*s - 2/7*s**2 - 2. What is d in u(d) = 0?
-2, 0
Let j(m) be the first derivative of 0*m**2 + 0*m**3 - 21 + 0*m - 1/4*m**5 + 5/8*m**4. Factor j(u).
-5*u**3*(u - 2)/4
Suppose -13*f - 8 = -17*f. Factor -13*y - 7*y + 40 + 5*y**4 - 80*y**2 + 5*y**3 + 50*y**f.
5*(y - 2)*(y - 1)*(y + 2)**2
Suppose 0*g - 24/5*g**3 - 4/5*g**4 - 4*g**2 + 0 = 0. Calculate g.
-5, -1, 0
Let m(d) be the second derivative of -d**6/30 + 29*d**5/20 - 27*d**4/2 - 352*d**3/3 - 256*d**2 - 456*d. Factor m(i).
-(i - 16)**2*(i + 1)*(i + 2)
Suppose 0 = -3*v + 4*v. Suppose k = -v*k + 2. Factor 12*r**4 + 3 - 6*r**4 - 6*r**k - 3*r**4.
3*(r - 1)**2*(r + 1)**2
Factor -7*h - 10*h**2 + 11*h**2 - 3*h - 5 - 6*h**2.
-5*(h + 1)**2
Let n(g) be the first derivative of -14/5*g**5 + 19/2*g**4 - 50/3*g**3 + 1/3*g**6 - 14 + 16*g**2 - 8*g. Factor n(i).
2*(i - 2)**2*(i - 1)**3
Determine p so that -66*p**2 + 265*p**5 - 144*p**3 - 5*p - 50*p**4 - 78*p**2 + 96 + 37*p - 271*p**5 = 0.
-3, -2, 2/3
Let x be 8/(96/126)*2/(-3). Let o(c) = -c**3 - 5*c**2 + 14*c. Let n be o(x). Factor -2/5*d + 6/5*d**2 - 4/5*d**3 + n.
-2*d*(d - 1)*(2*d - 1)/5
Let t(q) be the second derivative of -q**5/10 + 17*q**4/6 - 55*q**3/3 + 39*q**2 + 580*q. Solve t(y) = 0 for y.
1, 3, 13
Let u(q) be the second derivative of -1/120*q**5 - 3*q - 1/3*q**3 + 0 - 1/12*q**4 - 3/2*q**2. Let n(a) be the first derivative of u(a). Factor n(t).
-(t + 2)**2/2
Suppose -5*m + 12 = -m. Factor 4*p**2 + 2*p**5 + 3*p**3 - 9*p**m + 0*p**2.
2*p**2*(p - 1)**2*(p + 2)
Suppose -10*x**2 - 286/5*x - 2/5*x**3 + 338/5 = 0. Calculate x.
-13, 1
Let c(a) be the second derivative of a**4/36 - a**3/2 + 4*a**2/3 - 74*a. Factor c(h).
(h - 8)*(h - 1)/3
Suppose 3*u = -5*n - 5 + 30, 0 = -2*n + 3*u - 11. Factor 0*p + 0 + 2/7*p**3 - 6/7*p**n.
2*p**2*(p - 3)/7
Let k(y) be the third derivative of y**9/45360 + y**8/15120 + 23*y**5/60 - 26*y**2. Let a(z) be the third derivative of k(z). Determine l, given that a(l) = 0.
-1, 0
Determine h so that 30/17*h + 2/17*h**3 + 14/17*h**2 + 18/17 = 0.
-3, -1
Let s = -62 + 89. Let g(h) = -3*h + 81. Let r be g(s). Factor r*a**3 - 2/5 - 2/5*a**4 + 0*a + 4/5*a**2.
-2*(a - 1)**2*(a + 1)**2/5
Factor -6/11*x - 10/11*x**2 + 0 - 2/11*x**3 + 2/11*x**4.
2*x*(x - 3)*(x + 1)**2/11
Let a(b) be the third derivative of 0 + 0*b + 3/40*b**4 - 5*b**2 - 1/100*b**5 + 0*b**3. Solve a(d) = 0.
0, 3
Suppose 0 = 3*b - 2*c + c - 5, 4*b - 5*c - 3 = 0. Factor -13*u + 2*u**4 + 5*u + 10*u**3 - b*u**3 + 2*u**4 - 4.
4*(u - 1)*(u + 1)**3
Let w(r) be the third derivative of -r**8/84 + 2*r**7/105 + 3*r**6/10 - 3*r**5/5 + 33*r**2. Solve w(s) = 0 for s.
-3, 0, 1, 3
Factor 1/4*w**2 - 5/2*w - 6.
(w - 12)*(w + 2)/4
Let w(z) be the third derivative of 3/40*z**6 + 0*z + 3*z**2 + 0 - 1/12*z**4 + 0*z**3 + 13/210*z**7 + 5/336*z**8 - 1/60*z**5. Let w(n) = 0. Calculate n.
-1, 0, 2/5
Let t = -2656/22227 + 8/239. Let x = t - -168/31. Factor -8/3*g - 1/3*g**2 - x.
-(g + 4)**2/3
Let s(i) be the third derivative of i**10/120960 + i**9/60480 - i**8/13440 + 31*i**4/24 + 31*i**2. Let p(w) be the second derivative of s(w). Factor p(o).
o**3*(o - 1)*(o + 2)/4
Let d be 42/2*(0 - 4)/(-4). Factor 12*z**4 + 39*z**3 + 49*z**2 + 16*z**2 - 20*z**2 + 2 + d*z + 1.
3*(z + 1)**3*(4*z + 1)
Let a(g) = g**5 - g**4 - g**3 - 2*g**2 - g + 1. Let l(f) = 4*f**5 + 2*f**4 - 12*f**3 - 12*f**2 - 6*f + 6. Let i(k) = -12*a(k) + 2*l(k). Factor i(w).
-4*w**3*(w - 3)*(w - 1)
Let j be (-10)/6 + (-10)/(-5). Suppose -k + 3 = 1. Factor j*m**k + 2/3 + m.
(m + 1)*(m + 2)/3
Suppose 2*q - 109 = -5*a, 4*q + 5*a = 6*q - 99. Factor 80*p**5 + 800*p**4 + q + 1000*p**2 + 325*p - 33 + 1400*p**3 + 21.
5*(p + 8)*(2*p + 1)**4
Suppose 19*o + 49 = 49. Let h(y) be the third derivative of 1/10*y**5 - 7/16*y**4 + o*y - 1/2*y**3 + 0 + 4*y**2. Factor h(q).
3*(q - 2)*(4*q + 1)/2
Let q(s) be the third derivative of -s**7/42 - s**6/4 - 5*s**5/12 + 5*s**4/2 + 269*s**2. Factor q(d).
-5*d*(d - 1)*(d + 3)*(d + 4)
Let o = -1369 - -1371. Find s such that 2/5*s + 0 - 1/5*s**o = 0.
0, 2
Let o be 7/(-7) + 7 + (-18)/4. Solve -o*x - 3 + 3*x**2 + 3/2*x**3 = 0 for x.
-2, -1, 1
Suppose 6*y = -8 + 140. Let v(w) = 70*w**3 - w**2 - 59*w - 21. Let s(o) = 14*o**3 - 12*o - 4. Let k(z) = y*s(z) - 4*v(z). Factor k(n).
4*(n - 1)*(n + 1)*(7*n + 1)
Let x(l) be the second derivative of 5*l**4/36 + 20*l**3/9 + 40*l**2/3 + 46*l. What is c in x(c) = 0?
-4
Let s(p) be the second derivative of 0*p**2 + 1/21*p**3 + 0 + 1/42*p**4 - 36*p. Let s(a) = 0. What is a?
-1, 0
Suppose 13 = -l - 0. Let d(n) = n**2 + 14*n + 16. Let r be d(l). Let -m**4 + 2*m**3 - r*m**5 - m**5 - 7*m**4 + 6*m**4 = 0. Calculate m.
-1, 0, 1/2
Let b(o) be the second derivative of -o**4/4 - 15*o**3/2 + 51*o**2 + 32*o + 3. Factor b(q).
-3*(q - 2)*(q + 17)
Suppose 0 = -3*z - 3*x + 597, -5*z = -2*x + x - 989. Factor -11*l**2 + 80 - z*l + 23*l**2 - 5*l**3 + 78*l + 33*l**2.
-5*(l - 4)**2*(l - 1)
Let w(o) be the third derivative of -o**5/140 - 5*o**4/28 - 5*o**2 + 1. Factor w(s).
-3*s*(s + 10)/7
Let x(f) be the first derivative of 30 - 10*f**3 - 5/6*f**6 + 0*f - 5*f**4 + 6*f**5 + 25/2*f**2. What is s in x(s) = 0?
-1, 0, 1, 5
Let m(v) be the first derivative of v**4/10 - 16*v**3/15 + 13*v**2/5 - 12*v/5 + 21. Let m(b) = 0. Calculate b.
1, 6
Let z(o) = 16*o**4 - 42*o**3 + 32*o**2 - 6*o - 6. Let b(w) = 46*w**4 - 125*w**3 + 96*w**2 - 17*w - 17. Let r(u) = 6*b(u) - 17*z(u). Suppose r(i) = 0. What is i?
0, 1, 8
Let s(u) be the third derivative of -u**7/105 + u**6/12 + 2*u**5/15 - 5*u**4/3 - 98*u**2. Factor s(q).
-2*q*(q - 5)*(q - 2)*(q + 2)
Factor -38/9 - 4*d + 2/9*d**2.
2*(d - 19)*(d + 1)/9
Let g = -69/7 - -359/35. Suppose -9 = -7*s + 4*s. Factor 2/5*z**5 - 2/5 - g*z**4 + 2/5*z + 4/5*z**2 - 4/5*z**s.
2*(z - 1)**3*(z + 1)**2/5
Let -48*t**3 + 67*t**2 + 9*t**3 - 81*t + 6*t**4 + 27 - 41*t**2 + 61*t**2 = 0. Calculate t.
1, 3/2, 3
Let v(b) be the third derivative of b**7/630 + b**6/45 + 11*b**5/90 + b**4/3 + b**3/2 - 3*b**2 - 8*b. Find h, given that v(h) = 0.
-3, -1
Let v(z) be the first derivative of -3*z**4/4 + z**3 + 9*z**2 + 1. Factor v(g).
-3*g*(g - 3)*(g + 2)
Let r(p) be the first derivative of -p**4/2 + 2*p**3 + 10*p**2 + 121. Solve r(l) = 0.
-2, 0, 5
Determine d, given that -8/3 - 7*d**2 + 34/3*d = 0.
2/7, 4/3
Let b(z) be the first derivative of -z**8/6720 - z**7/3360 + 7*z**3 + 3. Let a(k) be the third derivative of b(k). Factor a(u).
-u**3*(u + 1)/4
Let m(i) be the third derivative of i**5/240 + i**4/6 - 6*i**2 - 8*i. Find k such that m(k) = 0.
-16, 0
Let y(s) = -5*s**3 - s + 2. Let h = -8 - -10. Let u(j) = 0*j**2 + j + j**h + 0*j**2 - 4 + 11*j**3. Let x(c) = 4*u(c) + 9*y(c). Suppose x(v) = 0. Calculate v.
1, 2
Suppose 5*g + 2*i - 132 = 0, g - 5*i - 11 - 10 = 0. Let u be (-4)/10 - (g/(-10) - -2). Factor -2/5 - u*z**2 + 3/5*z.
-(z - 2)*(z - 1)/5
Let g = 2 - -5. Suppose g*x - 2*x + 14 = c, -3*c - 4*x = -4. Let -13*n**4 + 9*n**5 + 4*n**3 + n**4 - 2*n**c + 2*n**4 = 0. Calculate n.
0, 2/3
Let k(u) be the first derivative of u**6/6 - 3*u**5/5 - 3*u**4/2 + 26*u**3/3 - 27*u**2/2 + 9*u - 84. Suppose k(w) = 0. Calculate w.
-3, 1, 3
Factor -200/9 + 40/3*t - 2/9*t**4 - 4/3*t**3 + 22/9*t**2.
-2*(t - 2)**2*(t + 5)**2/9
Let f = 9 + -11. Let z be 19/2 - f/(-4). Find u, given that -4*u**2 + 9*u**5 - u**2 + 2 + z*u + 2*u**4 - 18*u**3 + u**2 = 0.
-1, -2/9, 1
Let k(h) be the third derivative of -h**5/60 - h**4