ermine q so that d(q) = 0.
0, 2/7
Let y(r) = 7*r**2 + 7*r + 4. Let i(q) = 8*q**2 + 8*q + 5. Let a(o) = 4*i(o) - 5*y(o). Suppose a(v) = 0. What is v?
-1, 0
Let v(b) be the third derivative of b**7/945 + 11*b**6/540 + 7*b**5/54 + 25*b**4/108 + 21*b**2. Factor v(i).
2*i*(i + 1)*(i + 5)**2/9
Let b = 2221/20 - 111. Let n(i) be the third derivative of -1/40*i**6 - b*i**5 + 0*i - 1/24*i**4 - 1/210*i**7 + 2*i**2 + 0 + 0*i**3. Factor n(d).
-d*(d + 1)**3
Let x(u) be the third derivative of -u**5/20 - u**4/2 + 22*u**2. Suppose x(i) = 0. What is i?
-4, 0
Solve 2/11*z - 3/11 + 1/11*z**2 = 0 for z.
-3, 1
Let k = 25 - 25. Find h such that 0*h + 1/4*h**3 + k + 1/4*h**2 = 0.
-1, 0
Factor -20*c - 8 + 4*c**5 + 0*c**3 + 16*c**4 + 11*c**3 + 5*c**3 - 8*c**2.
4*(c - 1)*(c + 1)**3*(c + 2)
Let a(k) be the first derivative of -35*k**6/6 - 5*k**5 + 45*k**4/4 + 25*k**3/3 - 5*k**2 + 10. Find b such that a(b) = 0.
-1, 0, 2/7, 1
Let c be 3/(-2) - 187/(-22). Let d = -7 + c. What is p in 1/2*p**4 + 1/2*p**2 + 0 + d*p - p**3 = 0?
0, 1
Let f(o) be the third derivative of -2/35*o**7 + 16/15*o**5 + 0*o - 1/84*o**8 + 0 + 0*o**4 - 32/3*o**3 + 2/15*o**6 + 4*o**2. What is i in f(i) = 0?
-2, 1, 2
Let t = 13 - 10. Suppose 3*g + 5*v + t = -g, -3*v = 3*g. Factor 2/9*m - 8/9*m**2 + 0 + 2/9*m**5 + 4/3*m**g - 8/9*m**4.
2*m*(m - 1)**4/9
Let k be 12/45 + 10/25. Solve -1/3*w + 0 - k*w**2 = 0 for w.
-1/2, 0
Let o(k) be the second derivative of 2*k**7/21 - 2*k**6/15 - k**5/5 + k**4/3 - 9*k. Factor o(q).
4*q**2*(q - 1)**2*(q + 1)
Let j(t) be the first derivative of 2*t**3/69 + 3*t**2/23 - 8*t/23 + 32. Determine l so that j(l) = 0.
-4, 1
Let x = -4 + 6. Let c be x/(-2) - 20/(-12). Factor 0*m**2 + 1/3*m**5 + 0*m**4 + 0 + 1/3*m - c*m**3.
m*(m - 1)**2*(m + 1)**2/3
Let l(w) be the first derivative of -8 + 1/5*w**2 - 1/5*w - 1/10*w**4 + 1/25*w**5 + 0*w**3. Solve l(o) = 0 for o.
-1, 1
Suppose -y = -39 + 17. Determine j, given that -y*j**2 + 6*j**2 - 19*j**3 - 4*j**4 + 3*j**3 = 0.
-2, 0
Let n(l) be the third derivative of -l**5/30 + l**4/6 + 8*l**2. Factor n(s).
-2*s*(s - 2)
Let x(q) be the second derivative of -q**4/8 + 3*q**3/2 - 5*q. Factor x(p).
-3*p*(p - 6)/2
Let k be 26/(-430) + 7/35. Let a = k - -154/129. Factor -a*g - 2/3*g**2 - 2/3.
-2*(g + 1)**2/3
Let o = -5 - -7. Let w(a) be the third derivative of 0 - 1/24*a**3 + o*a**2 - 1/240*a**5 + 0*a + 1/48*a**4. Factor w(l).
-(l - 1)**2/4
Determine p, given that -2*p**4 + p**3 - p - p**2 + 9*p**4 - 3*p**4 - 3*p**4 = 0.
-1, 0, 1
Let x be (-29)/(-58) - (0 + (-3)/2). Factor -6 - 3/2*d**x + 6*d.
-3*(d - 2)**2/2
Let j(o) = o**2 + 3*o + 2. Let d be j(-3). Suppose -5*x + 10*l - 7*l + 27 = 0, -25 = -4*x - l. Factor -2*p - 3*p**3 - x*p - 9*p**d - 2 - p - 1.
-3*(p + 1)**3
Let o = -8555/4 + 2177. Let z = o - 38. Let 0 + z*n**2 + 1/4*n = 0. What is n?
-1, 0
Let r(m) be the second derivative of -3*m**5/80 + 7*m**3/8 + 9*m**2/4 - 46*m. Factor r(f).
-3*(f - 3)*(f + 1)*(f + 2)/4
Suppose 2*y + 6 = -y + 3*c, -4*c + 8 = 2*y. Solve 0 - 4/5*b**3 + 2/5*b**2 + 2/5*b**4 + y*b = 0.
0, 1
Let o be 1*(-20)/(-10) - 20/11. Factor 18/11 + o*y**2 + 12/11*y.
2*(y + 3)**2/11
Factor 0 + 2*k**3 - k - 7/2*k**2.
k*(k - 2)*(4*k + 1)/2
Let i(t) be the second derivative of t**6/70 + 3*t**5/70 + t**4/28 + 5*t. Factor i(s).
3*s**2*(s + 1)**2/7
Let n = -345 - -205. Let g = n + 424/3. Find a such that 2/3*a**2 - g*a + 2/3 = 0.
1
Suppose j + j - 5*u - 31 = 0, 3*u = -15. Let w(g) be the second derivative of -1/48*g**4 + 1/80*g**5 + 0 - 1/24*g**j + 2*g + 1/8*g**2. Factor w(x).
(x - 1)**2*(x + 1)/4
Let c be (48/(-25) + 2)/((-4)/(-5)). Let r(o) be the third derivative of 0 + 3*o**2 + 1/105*o**7 + 0*o**6 - c*o**5 + 0*o + 0*o**3 + 1/6*o**4. Factor r(k).
2*k*(k - 1)**2*(k + 2)
Let s(t) be the third derivative of t**5/270 + t**4/36 + 2*t**3/27 + 5*t**2. Factor s(o).
2*(o + 1)*(o + 2)/9
Suppose -26 + 12 = -7*j. Find q, given that 0*q - 2/3*q**j + 1/3*q**3 + 0 = 0.
0, 2
Let j(v) = -2*v - 10. Let s be j(-7). Let i = s + 0. Find l such that 4*l**i - l - 2*l**2 + 0*l**4 + l**5 - 2*l**4 = 0.
-1, 0, 1
Let c(o) = 4*o**4 + 4*o**3 - 9*o. Let l(q) = q**3 - 2*q + 7*q**4 + 0*q**4 - 6*q**4. Let x be 36/(-10) + 2/(-5). Let t(u) = x*c(u) + 18*l(u). Factor t(r).
2*r**3*(r + 1)
Solve -17*n**3 + 3*n**4 - 9*n**4 + 9*n**3 + 8*n**2 = 0 for n.
-2, 0, 2/3
Let w(o) be the second derivative of -o**8/33600 + o**7/6300 - o**6/3600 - 5*o**4/12 - 2*o. Let b(p) be the third derivative of w(p). Factor b(i).
-i*(i - 1)**2/5
Let u = 203/1507 - -455459/1507. Let b = -302 + u. Factor 2/11*m**2 + 2/11 + b*m.
2*(m + 1)**2/11
Suppose 40 = 13*u - 25. Let z(i) be the second derivative of 4*i**2 + i + 1/15*i**6 - 1/2*i**4 + 1/5*i**u - 4/3*i**3 + 0. Factor z(m).
2*(m - 1)**2*(m + 2)**2
Suppose -2 = 18*q - 2. Factor 0 - 3/7*n**3 - 3/7*n**4 + q*n + 0*n**2.
-3*n**3*(n + 1)/7
Let d(b) be the first derivative of -1/11*b**6 - 8/11*b**3 + 14/55*b**5 - 8/11*b**2 + 3/11*b**4 - 4 + 0*b. Find p such that d(p) = 0.
-1, -2/3, 0, 2
Factor -1/2 + 1/2*y**4 - y**3 + 0*y**2 + y.
(y - 1)**3*(y + 1)/2
Let d(u) be the second derivative of -u**5/250 + u**4/50 - 2*u**3/75 + 3*u. Let d(c) = 0. Calculate c.
0, 1, 2
Let -60/11*o**4 - 4/11 + 100/11*o**3 - 80/11*o**2 + 14/11*o**5 + 30/11*o = 0. What is o?
2/7, 1
Let g(m) be the second derivative of -m**7/14 - m**6/10 + 9*m**5/20 + m**4/4 - m**3 - 3*m. Solve g(b) = 0.
-2, -1, 0, 1
Let y(m) be the first derivative of -m**7/210 - m**6/15 - 2*m**5/5 - 4*m**4/3 - 8*m**3/3 + 9*m**2/2 + 9. Let b(r) be the second derivative of y(r). Factor b(z).
-(z + 2)**4
Let l = 266 - 793/3. Suppose -2/3 - 1/3*u**4 - 7/3*u - 3*u**2 - l*u**3 = 0. What is u?
-2, -1
Suppose 8 = 9*b - 5*b. Let 0*i + 2/3*i**b + 4/3*i**3 + 0 + 2/3*i**4 = 0. Calculate i.
-1, 0
Suppose -2*y + 3 = -y. Suppose y*p**4 - 3*p**3 - 5*p**2 + 2*p**4 + 4*p**5 + p - 2*p = 0. Calculate p.
-1, -1/4, 0, 1
Let x = 1 + 2. Determine w, given that -2 + w + 2*w - w + 2*w**2 - 2*w**x + 0*w = 0.
-1, 1
Let n be (-1 + 0)/(2/(-4)). Let m be ((-2)/(-135))/((-4)/12)*-20. Solve 2/9 + m*o**n - 10/9*o = 0 for o.
1/4, 1
Suppose -3*q + 90 = -5*a, 2*q - 91 = a - 38. Suppose 0 = d - 6*d + l + 45, 5*d + 3*l = q. Factor d*o + 4*o**3 + 2*o**2 - 8*o + 2*o**4.
2*o**2*(o + 1)**2
Let b(h) be the first derivative of -h**3/6 - h**2/4 + 3*h - 18. Find q, given that b(q) = 0.
-3, 2
Let r(c) = 3*c**3 + 5*c**2 - c - 18. Let w(d) = d**3 + 3*d**2 - d - 9. Let p(k) = 2*r(k) - 5*w(k). Factor p(l).
(l - 3)**2*(l + 1)
Suppose 0 = s - 3*g + 5*g - 8, 5*s + g = 13. Find m such that -1 + m**2 + s*m**4 - 3*m**4 + m**2 = 0.
-1, 1
Let w(r) be the second derivative of -2/3*r**3 - 3/2*r**2 + 1/30*r**6 + 1/6*r**4 + 5*r + 1/5*r**5 + 0. Determine a so that w(a) = 0.
-3, -1, 1
Factor p**2 - 2*p**2 + 46*p - 2*p**2 - 61*p.
-3*p*(p + 5)
Factor 1/5 - 1/5*n**2 + 1/5*n - 1/5*n**3.
-(n - 1)*(n + 1)**2/5
Let i = 41/90 - 1/18. Let m(x) be the first derivative of -x**4 + 4/3*x**3 + 1/3*x**6 + x**2 - 1 - 2*x - i*x**5. Factor m(y).
2*(y - 1)**3*(y + 1)**2
Let d(r) be the second derivative of -r**5/10 + 13*r. Suppose d(v) = 0. What is v?
0
Let m(i) be the first derivative of -i**6/6 + 2*i**5/5 - 2*i**3/3 + i**2/2 - 5. Factor m(h).
-h*(h - 1)**3*(h + 1)
Factor 6/7*x**4 + 0*x + 0 + 9/7*x**3 - 3/7*x**5 + 0*x**2.
-3*x**3*(x - 3)*(x + 1)/7
Let z(n) = -8*n**2 - 32*n + 10. Let f(u) = -20*u**2 - 80*u + 24. Let t(y) = 5*f(y) - 12*z(y). Solve t(r) = 0.
-4, 0
Let i(c) be the second derivative of -2*c**7/105 + c**6/24 - c**5/60 - c**2 + 2*c. Let k(w) be the first derivative of i(w). Factor k(l).
-l**2*(l - 1)*(4*l - 1)
Let r(m) = m**4 + m**3 + m**2 - m + 1. Let u(l) = -7*l**4 + 5*l**4 - 5*l**2 - 2 - l**5 - l**3 + 0 + 2*l. Let f(x) = 3*r(x) + u(x). What is g in f(g) = 0?
-1, 1
Let r(v) be the first derivative of v**6/360 + v**5/30 + v**4/6 + 4*v**3/9 - 3*v**2 + 5. Let b(c) be the second derivative of r(c). Factor b(w).
(w + 2)**3/3
Let o(u) be the second derivative of 0*u**2 - 2*u + 2/9*u**3 + 0 + 1/60*u**5 - 1/9*u**4. What is x in o(x) = 0?
0, 2
Factor 10/9*v**3 + 2*v**2 + 2/9*v**4 + 14/9*v + 4/9.
2*(v + 1)**3*(v + 2)/9
Let h(j) be the third derivative of j**8/10080 - j**7/1890 + j**6/1080 + j**4/24 + 3*j**2. Let k(m) be the second derivative of h(m). Factor k(q).
2*q*(q - 1)**2/3
Suppose -2*y + 16 = 3*b, 16 = 5*b - 2*y - 0*y. Let w = 250/159 + 5/53. Sup