 q**5/45 - 5*q**4/72 + q**3/9 + 3*q**2. Determine i, given that r(i) = 0.
1, 2
Let f = 1068 + -9598/9. Determine a so that 4/9 + f*a - 14/9*a**3 - 4/9*a**2 = 0.
-1, -2/7, 1
Suppose -32*q + 28*q = -12. Let t(s) be the first derivative of q - 1/6*s**3 + 1/4*s**2 + 0*s + 1/10*s**5 - 1/8*s**4. Determine l so that t(l) = 0.
-1, 0, 1
Determine v so that 3/7*v**3 - 12/7*v**2 + 18/7 + 3/7*v = 0.
-1, 2, 3
Determine n, given that 2/5 + 3/5*n + 1/5*n**2 = 0.
-2, -1
Factor -3*i - 32*i**2 + 4*i + i + 33*i**2 - 3.
(i - 1)*(i + 3)
Let w(i) be the third derivative of -i**6/780 + i**4/156 - i**2. Factor w(j).
-2*j*(j - 1)*(j + 1)/13
Factor -1/4*m**2 - 64 - 8*m.
-(m + 16)**2/4
Let c(v) = 29*v**3 + 69*v**2 - 29*v - 42. Let g(r) = 7*r**3 + 17*r**2 - 7*r - 11. Let d(n) = -2*c(n) + 9*g(n). What is w in d(w) = 0?
-3, -1, 1
Let x(c) = -c**5 - 6*c**4 - 6*c**3 - 2*c**2 - 3*c - 2. Let j(o) = o**4 - o**2 + o + 1. Let d(k) = -2*j(k) - x(k). Factor d(s).
s*(s + 1)**4
Let m(h) be the first derivative of h**4 - 4*h**3/3 - 10. Determine o so that m(o) = 0.
0, 1
Let v = 1022/771 - -2/257. Factor v*l + 2/3*l**2 + 2/3.
2*(l + 1)**2/3
Factor -8/7*h**3 + 0*h**2 + 4/7*h**5 + 4/7*h + 0*h**4 + 0.
4*h*(h - 1)**2*(h + 1)**2/7
Let b = 18 + -305/17. Let x = b + 25/153. Factor x*o**2 + 4/9*o + 2/9.
2*(o + 1)**2/9
Let d(w) = -w**3 + 7*w**2 - 7*w + 9. Let a be d(6). Let k be (-10)/(-6) + a + -4. Factor 2/3*s**2 - k*s**4 - 1/3*s + 0 + 1/3*s**5 + 0*s**3.
s*(s - 1)**3*(s + 1)/3
Let u(s) be the third derivative of -s**7/945 + s**6/135 - s**5/45 + s**4/27 - s**3/27 - 9*s**2. What is r in u(r) = 0?
1
Let v(d) be the first derivative of -4*d**3/27 + 11*d**2/9 + 4*d/3 - 20. Factor v(m).
-2*(m - 6)*(2*m + 1)/9
Suppose -1 = 5*h - 21. Let r(z) be the second derivative of 0 - 1/9*z**3 + 2*z - 2/3*z**2 + 1/18*z**h. Factor r(a).
2*(a - 2)*(a + 1)/3
Let z(b) be the third derivative of b**5/100 - b**4/20 - 3*b**3/10 + 55*b**2. Factor z(t).
3*(t - 3)*(t + 1)/5
Let v = -377/28 + 96/7. Determine r, given that 3/4*r**2 + 1/4*r**3 + v + 3/4*r = 0.
-1
Let a = -739/3 + 249. Let g(u) = -5*u - 6. Let b be g(-2). Let 2/3*x**4 - 8/3*x + 2/3 + b*x**2 - a*x**3 = 0. What is x?
1
Let s(y) be the first derivative of -3*y**4/7 - 4*y**3/21 + 16*y**2/7 - 16*y/7 + 18. Factor s(z).
-4*(z - 1)*(z + 2)*(3*z - 2)/7
Let l(q) be the second derivative of -q**5/25 - q**4/15 + 8*q**3/15 + 8*q**2/5 + 21*q. Let l(g) = 0. Calculate g.
-2, -1, 2
Let z(y) be the first derivative of -y**9/108 + 3*y**8/140 - y**7/105 + 2*y**3 + 7. Let c(l) be the third derivative of z(l). Factor c(q).
-4*q**3*(q - 1)*(7*q - 2)
Solve 3 - 2 - 5*r**2 + 6*r**2 + 2*r = 0.
-1
Determine g so that 0*g**4 - 1/3*g**3 + 0*g**2 + 0*g + 1/3*g**5 + 0 = 0.
-1, 0, 1
Let g(f) = -15*f**4 + 5*f**3 - 85*f**2 + 35*f. Let o(i) = i**4 + i**3 + i**2. Let p(x) = -g(x) - 20*o(x). Determine c so that p(c) = 0.
-7, 0, 1
Suppose -a = 2*a - 12. Factor 5*m**2 - a*m**2 + 2*m - m.
m*(m + 1)
Let k(u) be the second derivative of 1/30*u**6 - 1/12*u**4 + 0*u**2 + 0 + 0*u**3 + 0*u**5 + u. Factor k(g).
g**2*(g - 1)*(g + 1)
Let x(j) = -4*j + 1. Let k = -2 + 1. Let o be x(k). Suppose n + 2 - o*n**3 - 4 + 2*n**3 + 4*n**2 = 0. What is n?
-2/3, 1
Let p(d) be the second derivative of d**7/98 + d**6/70 - 3*d**5/70 + 2*d + 31. Factor p(c).
3*c**3*(c - 1)*(c + 2)/7
Let g(t) be the first derivative of -8*t**3/33 - 5*t**2/11 - 2*t/11 - 21. Factor g(k).
-2*(k + 1)*(4*k + 1)/11
Suppose 12/7*d - 3/7*d**2 + 15/7 = 0. Calculate d.
-1, 5
Let o(b) = b**3 - 5*b**2 + 5*b. Let z be o(4). Suppose -z*n - 3 = -11. Factor 1 + 0*p + n*p + 0 + p**2.
(p + 1)**2
Let a(m) = 2*m**4 + 26*m**3 - 34*m**2 + 6*m. Let p(y) = y**4 + 27*y**3 - 33*y**2 + 5*y. Let q(w) = 5*a(w) - 6*p(w). Factor q(g).
4*g**2*(g - 7)*(g - 1)
Find v, given that 0 + 0*v**2 - 2/15*v**4 + 0*v + 2/15*v**3 = 0.
0, 1
Let x = 116/153 + -16/51. Let v(a) be the first derivative of x*a**3 + 8/15*a**5 + 1/3*a**2 - 7/6*a**4 + 0*a - 3. Solve v(u) = 0 for u.
-1/4, 0, 1
Suppose 7*u - 3*u + 4*j = 0, -u = 2*j + 2. Factor 3/2*z**2 - u*z + 1/2.
(z - 1)*(3*z - 1)/2
Let t(u) = -28*u**2 - 44*u - 16. Let r(n) = n + 1. Let d = 31 - 23. Let o(y) = d*r(y) + t(y). Factor o(p).
-4*(p + 1)*(7*p + 2)
Let x(h) be the second derivative of 3*h + 0*h**2 + 0 - 1/30*h**4 - 1/15*h**3. What is j in x(j) = 0?
-1, 0
Let q(z) be the second derivative of 1/30*z**6 + 0 - 1/10*z**5 + 1/3*z**3 - 1/2*z**2 - 3*z + 0*z**4. Factor q(u).
(u - 1)**3*(u + 1)
Let i(v) be the first derivative of 3 + 0*v + 1/3*v**3 - 1/3*v**2. Factor i(n).
n*(3*n - 2)/3
Let l(p) = p**3 + 16*p**2 + 16*p + 19. Let f be l(-15). Suppose 0 = -4*u + k + 4, 20 = u + u + f*k. Suppose 1/2 + x - 7/2*x**2 + u*x**3 = 0. Calculate x.
-1/4, 1
Let t(w) be the first derivative of -24*w**5/25 - 9*w**4/10 + 7*w**3/5 + 9*w**2/5 + 3*w/5 - 11. Suppose t(i) = 0. What is i?
-1, -1/2, -1/4, 1
Let u(o) = 5*o**2 - 3*o + 1. Suppose 5*f + 5 = -0*f. Let n(p) = -p**3 - p**2 - p - 1. Let j(k) = f*u(k) - n(k). Let j(x) = 0. What is x?
0, 2
Let x(d) be the first derivative of -d**5/100 + d**4/20 - d**3/10 + d**2/10 + 4*d + 3. Let w(r) be the first derivative of x(r). Factor w(n).
-(n - 1)**3/5
Determine m so that 0*m + 2/7*m**5 + 0*m**4 - 2/7*m**3 + 0 + 0*m**2 = 0.
-1, 0, 1
Let y = 27876/77 - 362. Let h = 69/308 + y. Factor -1/2*d + 1/2*d**3 + h + 0*d**2 - 1/4*d**4.
-(d - 1)**3*(d + 1)/4
Let z(d) be the first derivative of 3*d**3 - 3 - 3/2*d**2 + 3/4*d**4 - 3*d - 6/5*d**5. Find i, given that z(i) = 0.
-1, -1/2, 1
Suppose 5*u = k + 13, -2*u - 3*k = 6 - 1. Let h(f) = -f**3 + 2*f**2 + 3*f + 2. Let p be h(3). Factor 0*w - 4*w + 0 - p*w**2 - u.
-2*(w + 1)**2
Suppose h + 4 - 1 = 0. Let v = h + 5. Solve -v*s**2 - 2*s + 0*s**2 + s**2 + s**3 = 0 for s.
-1, 0, 2
Let k(m) be the first derivative of m**3/5 - 9*m**2/10 + 12. Factor k(n).
3*n*(n - 3)/5
Let h(d) be the second derivative of d**5/40 - d**4/12 - d**3/12 + d**2/2 - 43*d - 2. Factor h(o).
(o - 2)*(o - 1)*(o + 1)/2
Let o(n) be the third derivative of n**8/168 - n**7/105 - n**6/30 + n**5/15 + n**4/12 - n**3/3 + 12*n**2. Factor o(y).
2*(y - 1)**3*(y + 1)**2
Let t(i) be the first derivative of 2*i**3/9 - i**2 + 4*i/3 + 6. Factor t(f).
2*(f - 2)*(f - 1)/3
Let n(o) be the second derivative of 0 + 1/21*o**3 + 0*o**2 - 1/42*o**4 + o. Factor n(u).
-2*u*(u - 1)/7
Suppose 4*s = 4, 5*r - 3*s - 14 = -7. Let u be (-1)/r*(4 + -7). Factor -3/2*j + 0 + 9/2*j**2 - 9/2*j**3 + u*j**4.
3*j*(j - 1)**3/2
Let v(z) be the third derivative of 1/3*z**3 + 0*z + 0 - 1/105*z**7 + 1/30*z**6 - 1/6*z**4 + 0*z**5 + 2*z**2. Factor v(h).
-2*(h - 1)**3*(h + 1)
Let g(w) be the second derivative of w**6/40 + 3*w**5/40 - w**3/4 - 3*w**2/8 - 15*w. Factor g(p).
3*(p - 1)*(p + 1)**3/4
Let g(h) be the first derivative of -h**4/30 + h**2/5 - 4*h - 6. Let t(r) be the first derivative of g(r). Factor t(n).
-2*(n - 1)*(n + 1)/5
Let s be (1/2)/((-7)/56). Let t be 2/2*(-2)/s. Solve -t*p**4 + 0*p**2 + 0*p + 0 + 0*p**3 = 0 for p.
0
Let j(y) be the second derivative of -1/70*y**6 - 9/140*y**5 + 5*y - 1/14*y**3 + 0 - 3/28*y**4 + 0*y**2. Factor j(b).
-3*b*(b + 1)**3/7
Factor 3/8*x**3 - 3/8 + 3/8*x**2 - 3/8*x.
3*(x - 1)*(x + 1)**2/8
Factor t**2 + 2*t**2 + 0*t**3 - t**2 - 2*t**3.
-2*t**2*(t - 1)
Suppose 3*a - 5 = 1. Suppose -162 = q - a*q. Factor 56*c - 4 + q*c**4 + 1 - 60*c**3 - 192*c**3 + 11 + 26*c**2.
2*(c - 1)**2*(9*c + 2)**2
Let y(a) be the first derivative of 4*a**7/105 + a**6/10 - a**4/6 - 2*a**2 - 9. Let h(g) be the second derivative of y(g). Factor h(o).
4*o*(o + 1)**2*(2*o - 1)
Suppose 0 = 4*p - 2*p - 8. Suppose 3*m - 5*m - 4*w + p = 0, -3*m + 6 = w. Let l**2 + m*l - 2*l - 1 = 0. What is l?
-1, 1
Let q(i) = 3*i**3 + 17*i**2 - 8*i. Let w(g) = g**3 + 6*g**2 - 3*g. Let u(m) = m - 1. Let x be u(-2). Let h(n) = x*q(n) + 8*w(n). Factor h(k).
-k**2*(k + 3)
Let i = 55 - 160/3. Let 0 + 0*h + i*h**3 - 2*h**4 + 2/3*h**2 - 3*h**5 = 0. What is h?
-1, -1/3, 0, 2/3
Let v = 2/137 + 133/274. Factor -1/2*l**2 + 0 + 1/2*l**4 + 0*l - v*l**5 + 1/2*l**3.
-l**2*(l - 1)**2*(l + 1)/2
Let w be 1/2*((-96)/27 - -4). Find f, given that -2/3*f**2 - w*f**3 + 0 - 4/9*f = 0.
-2, -1, 0
Let s(f) = -f**4 + f**3 + f**2. Let p(m) = -m**4 + 16*m**3 + 16*m**2. Let g(o) = -p(o) + 4*s(o). Factor g(d).
-3*d**2*(d + 2)**2
Let v(l) = 2*l**2 - 3*l + 1. Let y be v(2). Factor -5*i**4 + 0*i**y + i**4 