r = 2 - 2. Factor -i**2 - 4*i + r*i + i**n + 3*i + 1.
(i - 1)**2*(i + 1)
Let p be (-26)/45 - 4/(-5). Let 2/9*f**3 + 0 + p*f**4 - 2/9*f - 2/9*f**2 = 0. What is f?
-1, 0, 1
Let t(u) be the second derivative of -u**7/3780 - u**6/810 + u**5/540 + u**4/54 + u**3/3 - 3*u. Let s(h) be the second derivative of t(h). Factor s(n).
-2*(n - 1)*(n + 1)*(n + 2)/9
Let c be -15 - (1 + -2 + 2). Let t = c + 16. Find h such that 1/5*h**2 - 1/5*h + t = 0.
0, 1
Let m(s) = 5*s**2 + 3. Let k(v) = v**2 + 1. Let c(z) = -6*k(z) + 2*m(z). Factor c(t).
4*t**2
Let 7/4*p**2 + 2 + 15/2*p = 0. Calculate p.
-4, -2/7
Find w, given that -112/3*w - 2*w**2 + 4*w**3 - 32 + 2/3*w**4 = 0.
-4, -1, 3
Let c(q) be the first derivative of -5*q**4/4 + 25*q**3 - 375*q**2/2 + 625*q - 15. Suppose c(k) = 0. What is k?
5
Let d(k) = 2*k**2 - 8*k - 2. Let b(t) = -21 - t + 21. Let l(r) = 8*b(r) - d(r). Factor l(a).
-2*(a - 1)*(a + 1)
Let y(l) = 25*l**3 + 60*l**2 + 48*l + 13. Let w(q) = 50*q**3 + 120*q**2 + 97*q + 27. Let k(a) = -3*w(a) + 7*y(a). Factor k(m).
5*(m + 1)**2*(5*m + 2)
Let v be 0 - (64/(-180))/8. Let j(d) be the first derivative of -2/9*d**4 - 4/9*d**2 - 2 - v*d**5 - 2/9*d - 4/9*d**3. Solve j(k) = 0.
-1
Let r(p) = p + 10. Suppose 0 = -y - 2*t + 2, y + 0*y + 3*t - 7 = 0. Let i be r(y). Factor -4 - s**2 - 7*s**2 - i*s - 16*s.
-2*(s + 2)*(4*s + 1)
Let n(v) = v**2 + v. Let j be n(0). Suppose j = 5*h + 15, -2*h = -a - 0*h + 8. Let 0 + r**a - 1 + 0 + 0 = 0. What is r?
-1, 1
Let x(k) be the second derivative of k**6/1440 - k**4/96 + k**3/2 - 2*k. Let d(f) be the second derivative of x(f). Solve d(g) = 0.
-1, 1
Let n(v) = -3*v**2 + 7*v + 4. Let g(j) = j + 1. Suppose -p - p - 4 = 0. Let u(q) = p*g(q) + n(q). Let u(k) = 0. Calculate k.
-1/3, 2
Let q(x) be the second derivative of x**5/90 + 5*x**4/54 - 37*x. Factor q(j).
2*j**2*(j + 5)/9
Suppose 0*z = 4*z + 2*a + 592, 586 = -4*z + a. Let q = z - -591/4. Suppose -q*r**4 + 1/2*r**2 + 1/4 - 1/2*r**3 - 1/4*r**5 + 3/4*r = 0. What is r?
-1, 1
Let p = 25 - 17. Let g(h) = h - 2. Let x be g(4). What is v in p*v**3 + 8 - 8*v**2 - 3*v**3 + 12*v - 10*v**x = 0?
-2/5, 2
Let x = -123 + 127. Let b(a) be the third derivative of -1/240*a**6 + 0 + 0*a**3 + 0*a - 1/24*a**4 + x*a**2 - 1/40*a**5. Factor b(h).
-h*(h + 1)*(h + 2)/2
What is o in -o**2 - 6 - 10 - 4*o**3 + 7*o**2 - 2*o**2 + 16*o = 0?
-2, 1, 2
Let k(x) be the third derivative of x**8/504 - 4*x**7/315 + x**6/30 - 2*x**5/45 + x**4/36 + 5*x**2. Factor k(j).
2*j*(j - 1)**4/3
Let z be 4/(-9)*(-12)/16. Factor 1/3*y**5 + 0 + 0*y**2 - z*y**4 + 0*y + 0*y**3.
y**4*(y - 1)/3
Let t(g) be the first derivative of 1/2*g**4 - 2 - 4*g - g**2 + 4/3*g**3. Find j such that t(j) = 0.
-2, -1, 1
Let q = 14 - 27/2. Suppose 0 - q*i + 1/2*i**2 + i**3 = 0. What is i?
-1, 0, 1/2
Let a(p) be the third derivative of -p**7/1260 + p**6/540 + p**5/90 - p**3/6 + 3*p**2. Let g(r) be the first derivative of a(r). Find m, given that g(m) = 0.
-1, 0, 2
Factor 3*l**3 - 3*l**2 - 12*l - 15*l + 27*l.
3*l**2*(l - 1)
Let w(d) = 4 - 2 + 0*d**2 - 2*d**2 + 6*d**3 + 2. Let c(n) = n**5 - n**4 + n**3 + n**2 + n + 1. Let m(f) = -2*c(f) + w(f). Determine k, given that m(k) = 0.
-1, 1
Let m(s) be the third derivative of s**9/60480 + s**8/80640 - s**7/5040 - s**6/2880 + s**5/20 + 3*s**2. Let n(q) be the third derivative of m(q). Factor n(f).
(f - 1)*(f + 1)*(4*f + 1)/4
Let i(x) be the second derivative of x**3/6 + 4*x**2 - x. Let o be i(-6). Determine q, given that 2*q**3 - 2*q + q**2 + q**o + 0 - 2 = 0.
-1, 1
Let f = -287 - -863/3. Factor -4/3*o**2 - 2/3*o + 2/3*o**4 + 2/3 - f*o**5 + 4/3*o**3.
-2*(o - 1)**3*(o + 1)**2/3
Let s(i) = -2*i - 4. Let v be s(-3). Determine g so that -6 + v + 4 + 3*g**2 + 3*g**3 = 0.
-1, 0
Let c be (-3)/(-2) + 44 + -45. Factor 1/2*j**2 - c*j + 0.
j*(j - 1)/2
Let w(l) = 3 + l + 5*l**2 + 9*l - 2*l**2 - 4*l. Let m(g) = -g**2 - g - 1. Let y(f) = 12*m(f) + 3*w(f). Solve y(a) = 0.
1
Let d(c) = c**2 - 6*c - 3. Let v be d(7). Let f = 6 - 4. What is i in -i**3 + f*i**5 + i**3 - 4*i**v - 2*i + 4*i**2 = 0?
-1, 0, 1
Factor 1/2*r - 1/2*r**3 - 1/4 + 1/4*r**4 + 0*r**2.
(r - 1)**3*(r + 1)/4
Let x(b) = -4*b**5 + 24*b**4 - 10*b**3 + 4*b**2 - 14*b + 14. Let d(m) = m**5 - 5*m**4 + 2*m**3 - m**2 + 3*m - 3. Let p(z) = 28*d(z) + 6*x(z). Factor p(j).
4*j**2*(j - 1)*(j + 1)**2
Find r such that 0*r + 40*r**2 - 40 - 5/2*r**5 - 15/2*r**4 + 10*r**3 = 0.
-2, 1, 2
Let n be ((-11)/22)/(2/4)*-3. Factor -1/3*b**n + 0 + b**2 - 2/3*b.
-b*(b - 2)*(b - 1)/3
Factor 0*j + 0*j**3 + 2/5*j**5 + 6/5*j**4 - 8/5*j**2 + 0.
2*j**2*(j - 1)*(j + 2)**2/5
Find c such that 10*c**2 + 37*c**3 + 10 + 5*c**5 + 16*c**3 - 20*c**4 - 33*c**3 - 25*c = 0.
-1, 1, 2
Let s(m) = 5*m**5 + 6*m**4 + m**3. Suppose 0 = 3*w - 2 - 4. Let f(g) = 16*g**5 + 17*g**4 + 2*g**3 + g**2. Let y(q) = w*f(q) - 7*s(q). What is j in y(j) = 0?
-2, -1, 0, 1/3
Let z(i) be the third derivative of 0*i**3 + 0 + 0*i**5 + 0*i + 0*i**4 + 1/660*i**6 + 2*i**2. Factor z(h).
2*h**3/11
Let w(s) be the second derivative of 3*s**2 + 0 + 13/2*s**3 - 21/5*s**5 + s + 13/4*s**4. What is l in w(l) = 0?
-2/7, -1/4, 1
Factor -2/3*d**2 + 0 + 0*d + 10/3*d**4 - 8/3*d**3.
2*d**2*(d - 1)*(5*d + 1)/3
Let b(w) be the second derivative of w**5/20 + 3*w**4/2 - w**3/6 - 9*w**2 + 2*w. Let j be b(-18). Factor j*r**2 + 3*r - 3/2*r**4 - 3*r**3 + 3/2.
-3*(r - 1)*(r + 1)**3/2
Let k(x) be the third derivative of -x**7/630 - x**6/360 + x**5/180 + x**4/72 + 17*x**2. Solve k(v) = 0.
-1, 0, 1
Let p(b) be the second derivative of -b**5/40 + 7*b**4/24 - 2*b**3/3 - 4*b**2 - b - 7. Factor p(g).
-(g - 4)**2*(g + 1)/2
Let w(f) be the first derivative of 15*f**4/4 + 13*f**3 + 6*f**2 - 12*f - 10. Solve w(n) = 0 for n.
-2, -1, 2/5
Let f = -6 + 3. Let t be (f/21)/(2/(-7)). Find s such that 0 - 1/2*s - t*s**3 - s**2 = 0.
-1, 0
Suppose 4/3*u - 8/3 - 1/6*u**2 = 0. What is u?
4
Suppose -15 = -p - 2*f, -5*f = -4 + 19. Find h, given that 6*h - p*h + 15*h - 6 + 11*h - 3*h**2 = 0.
2/3, 3
Suppose 0*c + 4*c + 6 = 5*r, 0 = r + 4*c - 6. Suppose 5*z = k - 17, 6*k - 3*k = -r*z. Factor 1 + 1/2*u**k - 3/2*u.
(u - 2)*(u - 1)/2
Factor 2/7*s**4 - 72/7*s**3 - 3456/7*s + 0 + 864/7*s**2.
2*s*(s - 12)**3/7
Let f(r) = -r**2 - 6*r - 6. Let v be f(-4). Factor -5*h**2 + 2*h**2 + h**v.
-2*h**2
Factor -7/2*k**3 + 1 - k**2 + 7/2*k.
-(k - 1)*(k + 1)*(7*k + 2)/2
Let t(s) be the third derivative of 7*s**5/15 + 11*s**4/2 - 20*s**3/3 - 13*s**2. Factor t(u).
4*(u + 5)*(7*u - 2)
Determine p, given that 216*p + 9*p**3 - 204 + 15*p**3 - 4*p**4 - 108*p**2 + 2*p**4 + 42 = 0.
3
Suppose -2*h = -3*t + 12, -h = -5*t + 3*t + 7. Factor 0*x + 1/4*x**5 + 5/4*x**4 + 0 + x**2 + t*x**3.
x**2*(x + 1)*(x + 2)**2/4
Let m = 1555 + -867. Let p = m + -6182/9. Factor -2/9*u**4 - p*u**3 - 4/9 - 14/9*u - 2*u**2.
-2*(u + 1)**3*(u + 2)/9
Let c(j) be the third derivative of -j**8/448 - 3*j**7/280 + 3*j**6/80 + j**5/8 - 21*j**4/32 + 9*j**3/8 + 5*j**2. Solve c(b) = 0.
-3, 1
Determine x so that 4/7*x - 2/7*x**3 + 2/7*x**2 + 0 = 0.
-1, 0, 2
Let n(k) be the second derivative of k**7/840 - k**6/480 - k**5/480 - k**3/3 + 4*k. Let f(d) be the second derivative of n(d). What is g in f(g) = 0?
-1/4, 0, 1
Factor -4/5*b**2 + 2/5*b**3 - 2/5*b + 1/5*b**4 + 3/5.
(b - 1)**2*(b + 1)*(b + 3)/5
Let 0 + 0*g**2 - 2/7*g**3 - 2/7*g**4 + 0*g = 0. What is g?
-1, 0
Suppose 0 = 67*n - 62*n - 15. Let k(b) be the second derivative of -1/18*b**n + 0*b**2 + 1/36*b**4 + 2*b + 0. Solve k(a) = 0 for a.
0, 1
Let z(o) be the third derivative of -o**6/240 + o**5/40 - o**4/16 + o**3/12 + 20*o**2. Factor z(a).
-(a - 1)**3/2
Let m(q) = -3*q**3 - 2*q**2 + q + 20. Let z(n) = 7*n**3 + 3*n**2 - n - 41. Let y(v) = 5*m(v) + 2*z(v). Factor y(i).
-(i - 2)*(i + 3)**2
Let w = 48 - 43. Let k(l) be the third derivative of 0*l**3 - 3*l**2 + 1/54*l**4 + 0 + 0*l + 1/90*l**w. What is q in k(q) = 0?
-2/3, 0
Let s(m) be the first derivative of 32/13*m + 2/39*m**3 - 8/13*m**2 + 1. What is w in s(w) = 0?
4
Let x be (213/(-99) - -3)*-3. Let d = -101/44 - x. Factor d*t**2 - 1/2 - 1/4*t.
(t - 2)*(t + 1)/4
Let f = -179 - -1977/11. Find s such that 6/11*s**2 - 8/11 - f*s = 0.
-2/3, 2
Let d(g) be the first derivative of 2*g**5/25 + g**4/10 - 16*g**3/15 - 12*g**2/5 - 17. Factor d(w).
2*w*(w - 3)*(w + 2)**2/5
Factor 0*y + 2/3*y**5 + 0*y**2 + 2*y**4 + 4/3*y**3 + 0.
2*y**3*(y + 1)*(y + 2)/3
Suppose