**2 + 2/3*h**3 + 2*h + 0. Find x such that n(x) = 0.
2
Let k(l) = -14*l**4 + 16*l**3 + 10*l**2 + 12*l + 12. Let b(z) = -z**4 + z**3 + z**2 + z + 1. Let x(s) = -12*b(s) + k(s). Determine a so that x(a) = 0.
0, 1
Let s(r) = 5*r + 145. Let v be s(-29). Find o, given that v + 0*o**3 + 0*o**2 + 0*o + 2/7*o**4 = 0.
0
Let b(a) = -a. Let l be b(-4). Let c be 1 - 0 - (0 + -3). Determine x, given that 2*x**l + 0*x**4 - x**c = 0.
0
Find l, given that -3*l**3 + 4*l**3 - 1 - 5*l**3 - 7 + 12*l = 0.
-2, 1
Let d(y) be the second derivative of y**5/15 + y**4/18 - 5*y**3/9 + 2*y**2/3 - 7*y. Factor d(h).
2*(h - 1)*(h + 2)*(2*h - 1)/3
Let z be -1 - ((-966)/15 - 3). Let d = z - 66. Suppose -d + 0*i + 2/5*i**2 = 0. Calculate i.
-1, 1
Let t(z) be the first derivative of -z**3/9 - 2*z**2/3 - 4*z/3 - 2. Let t(l) = 0. Calculate l.
-2
Factor -81/2*g**3 + 18*g**2 - 2*g + 0.
-g*(9*g - 2)**2/2
Suppose 0 - 2/11*p**3 - 4/11*p**2 - 2/11*p = 0. What is p?
-1, 0
Let s(h) be the second derivative of -h**9/10080 - h**8/3360 - h**7/5040 + h**4/6 - 2*h. Let j(f) be the third derivative of s(f). Factor j(c).
-c**2*(c + 1)*(3*c + 1)/2
Let i = -2909/5 + 585. Find h such that -536/5*h**3 - 273/5*h**4 - i - 144/5*h - 49/5*h**5 - 88*h**2 = 0.
-2, -1, -2/7
Let o(b) = -b**2 - 14*b + 36. Let a be o(-16). Suppose -2/3*p + 0 - 5/3*p**a - 1/3*p**2 + 8/3*p**3 = 0. What is p?
-2/5, 0, 1
Let d(w) be the first derivative of 3*w - w**2 + 2 + 1/9*w**3. Factor d(h).
(h - 3)**2/3
Suppose 8 + 0 - 92*l**2 + 94*l**2 + 8*l = 0. Calculate l.
-2
Let c(z) be the first derivative of -z**4/10 - 2*z**3/3 - 8*z**2/5 - 8*z/5 + 6. Factor c(r).
-2*(r + 1)*(r + 2)**2/5
Let t(s) be the second derivative of 0*s**2 + 0*s**3 + 2*s + 1/48*s**4 + 0 + 1/80*s**5. Factor t(m).
m**2*(m + 1)/4
Let s = 2 - -3. Suppose h = s - 3. Solve h - 4*o - 3*o**2 + 6*o**2 + 2 - 2*o**2 = 0 for o.
2
Factor -3*u**2 - 12/7*u**3 - 6/7*u + 3/7.
-3*(u + 1)**2*(4*u - 1)/7
Let p be (-1)/2 - (-10)/4. Suppose -q - 5 = -0*m - p*m, -2*m = 3*q - 1. Factor 2*g**2 + g**2 - g**3 - 4*g**2 + 0*g**m.
-g**2*(g + 1)
Let q(b) be the second derivative of 2/9*b**3 + 2/3*b**2 - 3*b + 0 + 1/36*b**4. Factor q(x).
(x + 2)**2/3
Let -6*d - 16 - 4*d + 2*d - d**2 = 0. Calculate d.
-4
Let d(j) = -j**3 + 6*j**2 - 4*j + 1. Let l be d(5). Let h = l + -6. Factor 0*p**2 + h*p + 0 + 1/3*p**3.
p**3/3
Let z(m) be the third derivative of 0*m - 4*m**2 + 1/60*m**5 + 1/6*m**4 + 0 + 1/2*m**3. Find k such that z(k) = 0.
-3, -1
Let j(y) be the first derivative of -2*y**3/51 + 2*y/17 + 7. Determine a, given that j(a) = 0.
-1, 1
Let x(g) be the first derivative of g**4/4 + 2*g**3/3 - g**2/2 - 2*g - 22. Factor x(q).
(q - 1)*(q + 1)*(q + 2)
Let z = 205/669 + 6/223. Factor -7/3*h - 5/3*h**2 - 1 - z*h**3.
-(h + 1)**2*(h + 3)/3
Suppose -2*b**3 + 2/5 - 4/5*b**2 + 2/5*b**4 + b + b**5 = 0. What is b?
-1, -2/5, 1
Let l(k) = -3*k**3 + k**2 + 2*k + 4. Let f(t) = 4*t**3 - 2*t**2 - 2*t - 5. Let d(w) = 4*f(w) + 5*l(w). Find i such that d(i) = 0.
0, 1, 2
Let j be (-8)/(-12) - 8/(-6). Let i(s) be the second derivative of -1/20*s**5 - 1/2*s**3 + 1/2*s**j - s + 0 + 1/4*s**4. Factor i(g).
-(g - 1)**3
Suppose 5 = 5*b - 5. Factor -3*l**2 + l - b*l**2 + 2 + 3*l**2 + l**2.
-(l - 2)*(l + 1)
Let i(o) be the second derivative of 2*o - 11/30*o**6 + 0*o**2 - 1/12*o**4 + 9/20*o**5 + 0 - 1/6*o**3 + 2/21*o**7. Let i(a) = 0. What is a?
-1/4, 0, 1
Factor 3/2*n**2 + 9/2*n + 0.
3*n*(n + 3)/2
Let i(f) = -f**2 + 7*f + 6. Let p be i(8). Let w be p/(-4)*(-88)/(-16). Factor 0 + 7/4*a**4 + 4*a**3 + 1/2*a + w*a**2.
a*(a + 1)**2*(7*a + 2)/4
Let v(z) be the second derivative of -z**4/20 + 2*z**3/5 - 6*z**2/5 + 3*z. Determine l so that v(l) = 0.
2
Let l(i) = -i**2 - 2*i + 6. Let z be l(-3). Find x such that -9*x**2 - z + 3*x**4 - 6*x**3 + 7 + 8 + 3*x + 9*x = 0.
-1, 2
Let h(k) be the second derivative of 0 + k**5 + 1/3*k**4 - 2/7*k**7 + 0*k**2 - 4/3*k**3 - 2/15*k**6 + 5*k. Solve h(q) = 0 for q.
-1, 0, 2/3, 1
Find l, given that -12/5*l**3 - 4*l - 2/5*l**4 - 6/5 - 24/5*l**2 = 0.
-3, -1
Let v(n) be the second derivative of -n**8/13440 - n**7/2520 + n**4/3 + 6*n. Let g(x) be the third derivative of v(x). Factor g(d).
-d**2*(d + 2)/2
Factor 5/2*c**2 - 3/2*c - 1/2*c**4 - 1/2*c**3 + 0.
-c*(c - 1)**2*(c + 3)/2
Factor 0*w - 3*w - w - 485*w**2 + 486*w**2.
w*(w - 4)
Let m(u) be the first derivative of -1/18*u**3 + 0*u**2 - 4 + 1/6*u. Suppose m(y) = 0. Calculate y.
-1, 1
Let j(o) be the first derivative of o**4/20 + 4*o**3/15 + 2*o**2/5 - 11. Determine g, given that j(g) = 0.
-2, 0
Let k(a) be the first derivative of a**5/60 - a**4/12 + a**3/6 + 2*a**2 + 3. Let l(x) be the second derivative of k(x). Find y such that l(y) = 0.
1
Let w(p) be the first derivative of -2*p**5/5 + 2*p**3 - 2*p**2 + 7. Find q such that w(q) = 0.
-2, 0, 1
Let m(u) = 2*u**3 - u**2 + 1. Let x be m(1). Let d be 4/x - (-25)/(-15). Determine w, given that -w**3 + 1/3*w**2 + 0*w - d*w**5 + w**4 + 0 = 0.
0, 1
Suppose -2*m - y = 2*m - 154, 2*y = 5*m - 186. Let l = -113/3 + m. What is h in l*h**2 + 0 + 0*h + 1/3*h**4 + 2/3*h**3 = 0?
-1, 0
Let d(m) be the first derivative of 4*m**6 + 7 - 2*m**2 - 44/5*m**5 + 0*m + 3*m**4 + 4*m**3. Determine h, given that d(h) = 0.
-1/2, 0, 1/3, 1
Let n(v) be the first derivative of 2 - 2*v**4 + 4*v**3 + 2*v**4 - 2*v**4 + 3*v**4 - 12*v - 2*v**2. Factor n(t).
4*(t - 1)*(t + 1)*(t + 3)
Let u = 24/119 + 14089/357. Let -44/3*x**2 + u*x**4 + 6*x**3 + 0 + 8/3*x + 49/3*x**5 = 0. Calculate x.
-2, -1, 0, 2/7
Let g(i) be the third derivative of 1/945*i**7 + 1/27*i**3 + 0*i**4 + 0*i - 1/135*i**5 + 0 + 4*i**2 + 0*i**6. Factor g(j).
2*(j - 1)**2*(j + 1)**2/9
Solve -2*t - 28*t**3 - t + 31*t**3 + 3*t**4 - 3*t**2 = 0.
-1, 0, 1
Suppose 0 = 3*n - 2*n + 10. Let c be (42/35)/((-21)/n). Find v such that -2/7*v**5 - 2/7*v + c*v**3 - 2/7*v**4 - 2/7 + 4/7*v**2 = 0.
-1, 1
Let b(o) = -o**3 - 3*o**2 + o + 1. Let l be b(-3). Let n be -1 - ((3 - 2) + l). Factor 2/7*r**2 + 2/7*r**4 + n + 0*r + 4/7*r**3.
2*r**2*(r + 1)**2/7
Let s(u) be the second derivative of -u**4/60 + u**3/10 - u**2/5 + 8*u. Factor s(p).
-(p - 2)*(p - 1)/5
Factor -4*j**2 - 4 + 0*j - 19*j - 32 - 5*j.
-4*(j + 3)**2
Let m(z) be the third derivative of -z**8/1176 + z**7/245 - z**6/140 + z**5/210 - 19*z**2. Let m(w) = 0. Calculate w.
0, 1
Let u(k) be the second derivative of 1/3*k**4 - 2/21*k**7 + 0*k**2 + 1/5*k**5 - 2/15*k**6 + 0 + 4*k + 0*k**3. Factor u(h).
-4*h**2*(h - 1)*(h + 1)**2
Let a(g) = -g**4 + 4*g**3 - 14*g**2 + 20*g - 3. Let p(w) = 6*w**4 - 25*w**3 + 85*w**2 - 119*w + 19. Let h(q) = -34*a(q) - 6*p(q). Determine j so that h(j) = 0.
1, 2, 3
Factor 24 + 161*m**3 + 48*m**2 - 48*m - 52*m - 133*m**3.
4*(m - 1)*(m + 3)*(7*m - 2)
Suppose -4*t + 3 + 9 = 0. Let p = 11/3 - t. Factor 0 - p*q + 2*q**2.
2*q*(3*q - 1)/3
Let q(s) be the third derivative of -s**5/150 - s**4/20 - 2*s**3/15 + 2*s**2 + 8*s. Factor q(u).
-2*(u + 1)*(u + 2)/5
Let d(b) = -9*b**4 + 3*b**3 - 4*b**2 + 5*b + 5. Let w(p) = 4*p**4 - 2*p**3 + 2*p**2 - 2*p - 2. Let o(j) = 2*d(j) + 5*w(j). Suppose o(i) = 0. What is i?
0, 1
Factor 25/2*u**2 + 35*u - 15/2.
5*(u + 3)*(5*u - 1)/2
Let q = 2 + -11. Let j = -9 - q. Factor 1/5*z**2 + 0 + j*z.
z**2/5
Let a(x) = -12*x**2 + 2 + 0 - 5. Let q(p) be the second derivative of p**4 - p**3/6 + 2*p**2 - 7*p. Let f(d) = -6*a(d) - 5*q(d). Solve f(y) = 0 for y.
-2/3, 1/4
Suppose 129 + 1656 = 5*x. Let -42*u + 11*u - x*u**3 + 113*u**4 - 17*u - 4 - 205*u**2 - 309*u**4 = 0. What is u?
-1, -2/7, -1/4
Let q(d) = d + 13. Let n be q(-10). Factor -2*o + n*o**2 + 6*o + 3*o - 4*o.
3*o*(o + 1)
Let i(p) be the second derivative of p**4/84 - 5*p. Determine s so that i(s) = 0.
0
Let i(q) be the first derivative of -q**5/180 + q**4/18 - 2*q**3/9 + q**2/2 - 4. Let n(u) be the second derivative of i(u). Let n(y) = 0. What is y?
2
Suppose -3*c - 4 = -10. Let m(t) be the first derivative of -2 + 1/3*t**3 + 1/2*t**c + 0*t. Factor m(b).
b*(b + 1)
Let q = 103/198 - 2/99. Let o = -157/44 - -42/11. Factor 1/4 + o*f**2 + q*f.
(f + 1)**2/4
Suppose 90 = 5*s - 8*s. Let w be ((-2)/s)/(9/54). Factor w + 2/5*n**2 - 4/5*n.
2*(n - 1)**2/5
Find r, given that -3/2*r**5 - 18*r**3 - 9/2*r + 0 - 15*r**2 - 9*r**4 = 0.
-3, -1, 0
Suppose -3*f + 9 = 3*q, -q + 1 = 4*f - 14. Factor -4 - g**4 - 2*g**3 + 4 - 3*g**f.
-2*g**3*(2*g + 1)
Factor -4/7 + 32/7*x**4 - 20/