 207*c**2 - 336*c + 63. Let m(u) = 13*u**2 - 21*u + 4. Let o(h) = 2*j(h) - 33*m(h). Suppose o(b) = 0. What is b?
2/5, 1
Let m(q) be the second derivative of 27*q**5/140 - 15*q**4/14 + 2*q**3 - 12*q**2/7 + 5*q. Determine w so that m(w) = 0.
2/3, 2
Factor 24/7 - 2/7*m**2 - 16/7*m + 2/7*m**3.
2*(m - 2)**2*(m + 3)/7
Let i = 113907/845 + 304/169. Let t = 137 - i. Solve 4/5 - 6/5*x + t*x**2 = 0 for x.
1, 2
Let u(y) be the second derivative of -y**7/3360 - y**6/720 - y**5/480 - y**3/2 + y. Let b(r) be the second derivative of u(r). Factor b(w).
-w*(w + 1)**2/4
Let m(d) = 2*d**3 - d**2 - d + 3. Let s be m(0). Solve -1/5*r**s + 1/5 - 3/5*r + 3/5*r**2 = 0 for r.
1
Let q(o) be the first derivative of -o**4/12 + 4*o**3/9 - 5*o**2/6 + 2*o/3 + 11. Suppose q(f) = 0. Calculate f.
1, 2
Suppose 5*c = 4 + 16. Let j(w) be the second derivative of -4*w + 2*w**2 - 10/3*w**3 + 3/10*w**6 + 13/12*w**c + 3/2*w**5 + 0. Determine b so that j(b) = 0.
-2, 1/3
Factor -2/3*p**3 - 4/3*p + 1/3 + 5/3*p**2.
-(p - 1)**2*(2*p - 1)/3
Let l(p) be the first derivative of -p**4/4 + 23. Factor l(r).
-r**3
Let n = 27 + -18. Factor -n + 2*c - c**3 + c**2 + 9.
-c*(c - 2)*(c + 1)
Let q(h) = 7*h + 17. Let a be q(-2). Factor 2/11*w**4 + 18/11*w**2 + 4/11 + 10/11*w**a + 14/11*w.
2*(w + 1)**3*(w + 2)/11
Let h be (-15)/(-35) - 47/(-21). Factor 8/3 - h*y - 2*y**2.
-2*(y + 2)*(3*y - 2)/3
Let l(t) be the first derivative of 3*t**4/16 - t**3/2 - 9*t**2/8 - 15. Let l(y) = 0. Calculate y.
-1, 0, 3
Let r(g) be the second derivative of -g**7/105 - g**6/15 - g**5/5 - g**4/3 - g**3/3 - g**2/5 - 14*g. Determine b, given that r(b) = 0.
-1
Let l = -12/151 + 338/453. Factor -l*f**3 + 0 + 2/3*f**2 - 2/9*f + 2/9*f**4.
2*f*(f - 1)**3/9
Let y(b) be the third derivative of -1/24*b**4 - b**2 + 0 - 1/180*b**5 + 0*b**3 + 0*b. Suppose y(m) = 0. Calculate m.
-3, 0
Let j(d) be the second derivative of d**4/96 - 2*d. Factor j(v).
v**2/8
Let x = 5 - 3. Suppose -2*j - 2 = c, 3*j = -5 + x. Factor c*b**3 + 2 + 0*b - 2*b**2 - b + b**3.
(b - 2)*(b - 1)*(b + 1)
Let w(l) be the second derivative of l**4/30 - 2*l**3/15 - 3*l**2/5 - 12*l. Find u such that w(u) = 0.
-1, 3
Let u be 217/(-155)*(-4)/14. Let h = 39/85 + -1/17. Factor -2/5*z**5 + 2/5*z**2 + 0 + 0*z + u*z**3 - h*z**4.
-2*z**2*(z - 1)*(z + 1)**2/5
Let q(w) = -2*w**3 - 3*w**2. Let j be q(-2). Let t be j/(-15) - 14/(-21). Suppose 0 + t*r**2 + 0*r - 2/5*r**3 = 0. What is r?
0, 1
Factor 8/3*g**2 - 10/3*g + 2/3*g**3 + 0.
2*g*(g - 1)*(g + 5)/3
Let c(i) be the first derivative of 3/20*i**4 - 9/25*i**5 - 3/10*i**2 - 6 + 0*i + 3/5*i**3. Solve c(l) = 0 for l.
-1, 0, 1/3, 1
Factor 3/8*n - 3/8*n**5 - 3/4*n**4 + 0*n**3 + 0 + 3/4*n**2.
-3*n*(n - 1)*(n + 1)**3/8
Let q(n) be the second derivative of -n**6/135 - n**5/90 + n**4/54 + n**3/27 + 4*n. Let q(h) = 0. What is h?
-1, 0, 1
Suppose -m - 24 = -7*m. Let d = 3/86 + 157/430. Factor -4/5*b**m + d*b**5 + 4/5*b**2 - 2/5*b + 0*b**3 + 0.
2*b*(b - 1)**3*(b + 1)/5
Let m(a) be the third derivative of -a**6/60 + 3*a**5/110 + a**4/66 + 5*a**2. Determine t, given that m(t) = 0.
-2/11, 0, 1
Suppose -28/5*t**4 - 2/5*t + 6/5*t**5 - 24/5*t**2 + 44/5*t**3 + 4/5 = 0. What is t?
-1/3, 1, 2
Let p be (-45)/(-40) - 3/(-8). Let d(u) be the first derivative of 8/5*u**2 - 22/15*u**3 + 8/5*u - p*u**4 - 4. Solve d(k) = 0 for k.
-1, -2/5, 2/3
Let k(o) be the second derivative of -2*o**7/15 - 38*o**6/75 + 13*o**5/25 + 19*o**4/15 - 4*o**3/5 + 13*o. Solve k(w) = 0.
-3, -1, 0, 2/7, 1
Factor 0*z**2 + 5/3*z**4 + 0 + 0*z + 0*z**3 - 5/3*z**5.
-5*z**4*(z - 1)/3
Let m(n) = 4*n**3 - 8*n**2 - 4*n + 8. Let s(f) = 4*f**3 - 8*f**2 - 4*f + 8. Let b(p) = 2*m(p) - 3*s(p). Find x, given that b(x) = 0.
-1, 1, 2
Suppose -6*t + 2*t = 0. Let f = -10 + 14. Let -6/7*a**f + t + 0*a**2 + 0*a - 4/7*a**3 + 10/7*a**5 = 0. What is a?
-2/5, 0, 1
Let j be (-144)/(-96)*(-20)/(-9). Find b such that 3*b + 2/3 + j*b**2 = 0.
-1/2, -2/5
Suppose 0 = -4*z + z + 12. Let o(b) = -8*b**2 + 8*b + 11. Let u(g) = -3*g**2 + 3*g + 4. Let s(v) = z*o(v) - 11*u(v). Factor s(k).
k*(k - 1)
Let p(i) be the second derivative of 0 - 1/168*i**7 - 1/12*i**4 + 1/40*i**6 + 0*i**5 - i + 0*i**3 + 0*i**2. Factor p(y).
-y**2*(y - 2)**2*(y + 1)/4
Find m, given that -24*m**2 + 7*m**2 + m**3 + 13*m**2 = 0.
0, 4
Let h(d) = -9*d**5 - 19*d**4 - 47*d**3 - 48*d**2 - 16*d. Let v(g) = -8*g**5 - 20*g**4 - 48*g**3 - 48*g**2 - 16*g. Let j(l) = 4*h(l) - 5*v(l). Factor j(k).
4*k*(k + 1)**2*(k + 2)**2
Suppose 22 = 18*f - 7*f. Let c(o) be the third derivative of -1/36*o**3 - 1/144*o**4 + 1/720*o**6 + 0 + 1/360*o**5 + 2*o**f + 0*o. Factor c(t).
(t - 1)*(t + 1)**2/6
Let a(c) be the second derivative of -3*c**6/50 - 6*c**5/25 - 3*c**4/10 + 3*c**2/10 + 26*c. Factor a(d).
-3*(d + 1)**3*(3*d - 1)/5
Solve 0*z + 0 + 10/11*z**3 - 4/11*z**2 - 6/11*z**4 = 0.
0, 2/3, 1
Let o(x) be the first derivative of 18/5*x + 2/15*x**3 - 5 + 6/5*x**2. Factor o(j).
2*(j + 3)**2/5
Let t(w) = -3*w**3 + 11*w**2 - 8*w. Suppose 0 = 3*n - 19 + 1. Let u = 3 - n. Let l(i) = -i**3 + 4*i**2 - 3*i. Let p(q) = u*t(q) + 8*l(q). Factor p(s).
s**2*(s - 1)
Suppose -2*c - 1 = -5. What is w in -5*w - 4*w**2 - 4*w**2 + 8*w**3 + 2*w**2 + c + w + 8*w**4 = 0?
-1, 1/2
Factor 3/5*j**2 - 3/5*j**5 - 9/5*j**3 + 0 + 0*j + 9/5*j**4.
-3*j**2*(j - 1)**3/5
Let y be (-53)/(-3) + (-3)/(-9). Suppose -y - 3 = -3*s. Factor o**2 + 6*o - s*o**2 - 2 - o**3 + 3*o**3.
2*(o - 1)**3
Suppose 0 = -s + 3*s - 18. Factor -s*h + 9*h - h**5 + h**3.
-h**3*(h - 1)*(h + 1)
Let a = 405/262 - 6/131. Suppose a*t**4 + 0 + 0*t**2 - 3/2*t**3 + 0*t = 0. Calculate t.
0, 1
What is n in 5/2*n**2 + 0 - 2*n**3 + 1/2*n**4 - n = 0?
0, 1, 2
Let r(m) be the first derivative of -2*m**5/75 - m**4/15 - 2*m**3/45 - 4. Factor r(z).
-2*z**2*(z + 1)**2/15
Let o(r) be the second derivative of -r**7/2940 - r**6/1260 - r**3/2 + 3*r. Let a(h) be the second derivative of o(h). Determine z so that a(z) = 0.
-1, 0
Let x(r) be the third derivative of 5*r**8/336 - r**7/14 + r**6/12 + 25*r**2 + 1. Factor x(t).
5*t**3*(t - 2)*(t - 1)
Suppose 0 = -6*x + 35 - 11. Let -14/5*v**x + 0 + 38/5*v**3 - 16/5*v**2 - 8/5*v = 0. What is v?
-2/7, 0, 1, 2
Suppose 1 = 4*f - 11. Suppose o + 4 = 2*b, b + f + 0 = 3*o. Factor -3 + 2 - 4*w + 2*w - w**o.
-(w + 1)**2
Suppose 4*s = 2*w + 2, 0 = -3*s + 2*w + 3*w - 9. Suppose 0*o**s + 2/13*o**3 + 0 - 2/13*o = 0. What is o?
-1, 0, 1
Factor 0 + 1/2*j**2 - j.
j*(j - 2)/2
Let q(n) = n**2 - 2*n - 1. Let s be q(3). Factor 4*o**3 + 8*o - 3*o**2 - 2*o**3 - o**2 - 4*o**s.
2*o*(o - 2)**2
Let z(y) be the first derivative of -9/20*y**4 - 1/30*y**6 - 1/5*y**2 + 1/5*y**5 + 7/15*y**3 + 0*y + 4. Solve z(h) = 0.
0, 1, 2
What is o in 0*o**2 + 2/21*o**4 - 4/21*o + 4/21*o**3 - 2/21 = 0?
-1, 1
Let x(v) be the third derivative of v**9/120960 - v**8/40320 - v**7/10080 + v**6/1440 - v**5/30 + 2*v**2. Let g(w) be the third derivative of x(w). Factor g(f).
(f - 1)**2*(f + 1)/2
Suppose x - 4*x = 27. Let f(z) = -4*z**2 + 5*z + 8. Let u(g) = g**2 - g - 2. Suppose 6*s = s - 10. Let r(y) = s*f(y) + x*u(y). Factor r(i).
-(i - 1)*(i + 2)
Factor -5*s**3 + s**3 + 5*s**3 - 4*s + 3*s**3.
4*s*(s - 1)*(s + 1)
Let h(o) be the second derivative of 0*o**3 + 0 - 7*o - 1/105*o**7 - 1/75*o**6 + 0*o**2 + 1/50*o**5 + 1/30*o**4. Factor h(p).
-2*p**2*(p - 1)*(p + 1)**2/5
Let g(w) be the third derivative of 0 + 0*w**3 + 0*w**5 + 4*w**2 - 1/420*w**6 + 0*w + 1/84*w**4. Determine d, given that g(d) = 0.
-1, 0, 1
Let h be (-4)/(-14) - 214/(-35). Let 144/5*o**2 - 54/5*o**4 + 0*o**3 + h + 128/5*o = 0. Calculate o.
-2/3, 2
Suppose -f - 2*p = 3*f - 14, -2*f - 2*p + 10 = 0. Factor -8*l**2 + 2*l**2 - 1 + 9 - f*l**3.
-2*(l - 1)*(l + 2)**2
Let p be (-1)/5 + (-160)/(-675). Let y(l) be the first derivative of -p*l**6 + 40/27*l**3 - 8/9*l**2 - l**4 - 3 + 14/45*l**5 + 0*l. Factor y(n).
-2*n*(n - 2)**3*(n - 1)/9
Let k(w) = -4*w**2 - w + 2. Let f be k(1). Let a(x) = x**2 + 5*x + 6. Let r be a(f). Factor 0*i**4 + r*i**2 + 0*i**3 + 0*i - 2/7*i**5 + 0.
-2*i**5/7
Let i(t) be the second derivative of -t**8/84 + t**6/10 - 2*t**5/15 - 3*t**2 - 9*t. Let r(h) be the first derivative of i(h). Solve r(a) = 0.
-2, 0, 1
Let b(c) be the first derivative of c**4/4 - c**3/9 - c**2/2 + c/3 + 1. Factor b(n).
(n - 1)*(n + 1)*(3*n - 1)/3
Let y(x) be the third derivative of x**5/90 + x**4/90 - 14*x**2. Factor y(v