t x be (14/(-6))/((-13)/(-39)). Let s(a) = x*m(a) + 6*c(a). Find g, given that s(g) = 0.
1/3
Let w(j) be the third derivative of 1/200*j**6 - 1/560*j**8 + 0*j**3 + 0*j**4 + 0*j + 3*j**2 - 1/350*j**7 + 0 + 1/100*j**5. Factor w(t).
-3*t**2*(t - 1)*(t + 1)**2/5
Let z(i) be the third derivative of i**5/420 + i**4/168 - 13*i**2. Let z(l) = 0. What is l?
-1, 0
Let p(i) = -i**2 + 3*i + 7. Let b(r) = -r**2 + 4*r + 8. Let f(k) = -3*b(k) + 4*p(k). Solve f(o) = 0 for o.
-2, 2
Let l = -80 + 161/2. Let u(a) be the first derivative of -2/3*a**3 - a**2 + 0*a + 2/5*a**5 + 2 + l*a**4. Let u(x) = 0. Calculate x.
-1, 0, 1
Let n(v) be the first derivative of -1/3*v**6 - 12*v**4 - 1 - 16*v**2 - 64/3*v**3 - 16/5*v**5 + 0*v. Factor n(d).
-2*d*(d + 2)**4
Let t = 13 + -13. Let g(n) be the third derivative of 1/480*n**6 + 0 + 0*n + 0*n**5 + 0*n**4 + t*n**3 + n**2 + 1/840*n**7. What is h in g(h) = 0?
-1, 0
Let i(b) be the first derivative of -b**8/840 - 3*b**7/700 - b**6/300 + b**5/300 + 5*b**3/3 + 7. Let r(j) be the third derivative of i(j). Factor r(m).
-2*m*(m + 1)**2*(5*m - 1)/5
Let p = -6 + 8. Let l(g) = 3*g**3 + 3*g**2 - 2*g + 2. Let o(w) = 9*w**3 + 9*w**2 - 7*w + 7. Let n(y) = p*o(y) - 7*l(y). Factor n(r).
-3*r**2*(r + 1)
Suppose 4*l - 2*i = 2*l + 10, -4*i = 3*l + 6. Factor -2/5*g**l - 2/5 - 4/5*g.
-2*(g + 1)**2/5
Let -y**4 + 1/4*y**3 + 3*y**2 - 1/2 + 5/4*y = 0. What is y?
-1, 1/4, 2
Let x(z) be the second derivative of -1/8*z**3 - 1/8*z**2 + 0 + 5*z - 1/80*z**5 - 1/16*z**4. Let x(b) = 0. What is b?
-1
Let m(c) be the second derivative of 1/150*c**5 + 0 - 2/15*c**3 + c + 1/60*c**4 + c**2. Let l(b) be the first derivative of m(b). Factor l(d).
2*(d - 1)*(d + 2)/5
Let g(d) be the second derivative of d**7/6300 - d**6/900 + d**4/12 - 2*d. Let r(u) be the third derivative of g(u). Suppose r(s) = 0. Calculate s.
0, 2
Let r(l) = l**4 + 9*l**2 - 2*l. Let u(w) = -w**4 - w**3 - 8*w**2 + w. Let f(o) = -o. Let m be f(3). Let x(g) = m*r(g) - 4*u(g). Factor x(p).
p*(p + 1)**2*(p + 2)
Suppose s - 7 = -5*h + 3*h, -4*s + 18 = -2*h. Determine b so that -11*b**2 - s*b**2 + 3 + 13*b**2 = 0.
-1, 1
Let n(q) = -q + 48. Let j be n(0). Let r be ((-2)/(-5))/(j/180). Factor -3*t + 3/2*t**3 + 0 + r*t**2.
3*t*(t - 1)*(t + 2)/2
Let k = -14 + 16. Let -2*i + 3*i**k - 5*i**2 + 2*i - 4*i = 0. What is i?
-2, 0
Let w = 25/54 - 3499/54. Let c = 65 + w. Find y, given that c*y**2 + 0 + 0*y + 2/3*y**3 = 0.
-1, 0
Let j(n) be the third derivative of 1/24*n**4 + 2*n**2 + 1/3*n**3 + 0 + 1/720*n**6 + 1/80*n**5 + 0*n. Let w(f) be the first derivative of j(f). Factor w(m).
(m + 1)*(m + 2)/2
Let k(z) = -z**3 + 2*z**2 - 1. Let a be k(-1). Factor -4*t**a + 0*t**3 - 4*t**4 + 10*t**3 - 2*t**3.
-4*t**2*(t - 1)**2
Let h = 355 - 3903/11. Find a such that 0*a + 0 + h*a**4 - 2/11*a**2 + 0*a**3 = 0.
-1, 0, 1
Let c be (-44)/(-77)*(-14)/(-12). Let g(s) be the first derivative of c*s**3 + 0*s + 0*s**2 + 3/2*s**4 - 2. Factor g(x).
2*x**2*(3*x + 1)
Let c(a) = a + 2. Let r be c(4). Let y be -1 + (r/4)/1. Factor 1/2 - y*i**2 + 1/2*i**3 - 1/2*i.
(i - 1)**2*(i + 1)/2
Let r = -27 - -25. Let s be 128/40 + r/(-5). Find g, given that 2/5*g - 12/5*g**2 - 8/5*g**4 + 0 + s*g**3 = 0.
0, 1/4, 1
Factor 5/3*n**3 - 2*n**4 + 0*n + 0 + 1/3*n**2.
-n**2*(n - 1)*(6*n + 1)/3
Let v(f) be the second derivative of f**7/210 - f**5/60 - 2*f**2 + f. Let s(u) be the first derivative of v(u). Factor s(g).
g**2*(g - 1)*(g + 1)
Suppose 0 = 4*v - 9 - 11. Suppose g + 0 + v = 5*f, -5*g = -3*f - 19. Determine p, given that -2/7*p**f - 8/7 - 8/7*p = 0.
-2
Let p(b) be the third derivative of b**6/60 + b**5/10 + b**4/4 + b**3/3 - 8*b**2. Solve p(i) = 0.
-1
Let m(x) be the second derivative of -x**6/40 + x**5/20 - 2*x**2 - 4*x. Let d(u) be the first derivative of m(u). Factor d(y).
-3*y**2*(y - 1)
Let f be 8 - (-6)/(-9)*9. Suppose 1/6 + 1/3*r + 1/6*r**f = 0. Calculate r.
-1
Factor -i**2 + 3/4*i**4 - 1/2*i**3 + 0*i + 1/4 + 1/2*i**5.
(i - 1)*(i + 1)**3*(2*i - 1)/4
Let h(a) be the third derivative of a**5/30 - a**4/6 - 25*a**2. Suppose h(p) = 0. Calculate p.
0, 2
Solve 0 - 1/5*l**2 + l = 0.
0, 5
Let w be (-30)/(-18)*(-18)/(-15). Let n(f) be the second derivative of 0 + 3*f + f**w + 1/24*f**4 + 1/3*f**3. Let n(p) = 0. What is p?
-2
Let v(j) be the second derivative of j**4/18 + j**3/3 + 4*j. What is s in v(s) = 0?
-3, 0
Suppose -2*f + 6 = -2*z, -f + 0*f + 3 = 2*z. Let v(l) be the second derivative of -1/6*l**3 + z*l**2 + 0 + 2*l - 1/12*l**4. Solve v(n) = 0.
-1, 0
Let z = 10 - 16. Let p be (3 - -6)*(-2)/z. Suppose 2/3*k**p + 2/3*k**2 - 4/3*k + 0 = 0. Calculate k.
-2, 0, 1
Suppose -r - 22 = -2. Let m = r - -22. Factor -u + 5/2*u**3 + 0 + 3/2*u**m.
u*(u + 1)*(5*u - 2)/2
Let n = -10 - -14. Let o(c) = 5*c**4 + 4*c**3 - 5*c**2. Let f(g) = 6*g**4 + 5*g**3 - 6*g**2. Let z(w) = n*f(w) - 5*o(w). Solve z(r) = 0.
-1, 0, 1
Solve 1/6*u**2 + 1 - 7/6*u = 0.
1, 6
Suppose 2*o + 4 = 4*o - 2*f, -10 = -o - 3*f. Suppose 2*q = o*q. Factor -1/4*c**2 + 0 + q*c.
-c**2/4
Factor -1/2*l + 0 + 1/4*l**4 + 5/4*l**2 - l**3.
l*(l - 2)*(l - 1)**2/4
Let f(m) be the first derivative of -3*m**4/4 + 2*m**3 + 6*m**2 - 24*m + 7. Factor f(z).
-3*(z - 2)**2*(z + 2)
Let z be 10/4*(-8)/(-10). Let v(x) be the first derivative of -z - 4/3*x + 2/3*x**2 - 1/9*x**3. Find p such that v(p) = 0.
2
Let s(q) be the first derivative of -150*q**3 + 90*q**2 - 24*q - 2 + 375/4*q**4. What is c in s(c) = 0?
2/5
Factor 7/3*c**3 - 98/3 + 32*c**2 + 105*c.
(c + 7)**2*(7*c - 2)/3
Let j(t) be the first derivative of t**4/2 - 2*t**3 - 13. Factor j(o).
2*o**2*(o - 3)
Let i(o) be the first derivative of o**5/6 - o**4/12 + 9. Let i(p) = 0. Calculate p.
0, 2/5
Factor -t + 2*t - 3*t**2 - 2*t**3 + t**4 + 4 + 3*t.
(t - 2)**2*(t + 1)**2
Determine k so that 22*k**2 + 17*k**3 - 18*k**4 + 13*k**3 - 3 + 0 + 7 - 22*k = 0.
-1, 1/3, 2
Let i = 10 - 14. Let g(c) = -6*c**2 - 4*c - 4. Let j(t) = 7*t**2 + 5*t + 5. Let d(k) = i*j(k) - 5*g(k). Factor d(s).
2*s**2
Suppose -2*a - 1 - 1 = 0. Let m be 32/60 + a/5. Solve 1/3*k**3 + 1/3*k**2 - 1/3*k - m = 0.
-1, 1
Let o be -10*(-2)/2*1. Suppose -22 - 6 = -14*w. Factor -o + 0*h**2 + 0 + 1 + 6*h - h**w.
-(h - 3)**2
Let i = -3 + 5. Solve 2*x**2 - 65 + 4*x + 65 + 0*x**i = 0 for x.
-2, 0
Let g be (4/16)/(3/6). Determine q, given that 0 + g*q + 1/2*q**3 + q**2 = 0.
-1, 0
Suppose -4*x + 33 = 7*x. Let 3/5*t**4 - 6/5*t**x + 0 + 0*t + 3/5*t**2 = 0. What is t?
0, 1
Find h such that 4 - 6*h**2 - 5*h - 4 - 4*h**2 = 0.
-1/2, 0
Let u(r) = 2*r**3 - 2*r**2 + 4*r - 4. Let i(n) = 7*n**2 + 6 - 5*n**3 - 2*n**2 + 3 - 2*n - 6*n. Let g(m) = 4*i(m) + 9*u(m). Determine p so that g(p) = 0.
-1, 0, 2
Suppose 99*m**3 + 4*m**2 - 5*m**4 + 6*m**5 - 85*m**3 + 21*m**4 = 0. Calculate m.
-1, -2/3, 0
Suppose -2 = 2*s - 26. Let n be (s/(-2))/(6/(-4)). Factor a**2 - 4*a**4 + 3*a**n + 0*a**3 + a**3 - a**5.
-a**2*(a - 1)*(a + 1)**2
Let l be (-54)/9*2/(-4). Suppose l*p = 2*p. Let p + 2/3*b**3 - 8/9*b - 8/9*b**2 = 0. What is b?
-2/3, 0, 2
Let o = 14/33 + 43/11. Let v be (2/11)/((-84)/(-154)). Suppose -o*z**3 + v*z + 3*z**2 - 2/3 + 5/3*z**4 = 0. Calculate z.
-2/5, 1
Let t(n) = -2*n**3 + n**2 + 2*n + 1. Let b be t(-1). Let p = 0 + b. Let 7*m + 2 + 2*m**2 - 2*m**3 + p*m**3 + 0*m**2 - 3*m**3 = 0. What is m?
-1, -1/3, 2
Let o be 2 + (0 - -1 - 0). Factor 5*a**3 + a + a**2 - 11*a**2 + a**3 + o*a.
2*a*(a - 1)*(3*a - 2)
Factor 2*r**2 - 1 - 4 + 2 - 5.
2*(r - 2)*(r + 2)
Factor 0 + 36/11*q + 2/11*q**2.
2*q*(q + 18)/11
Let m(n) = -4*n**5 + 9*n**4 + 28*n**3 + n**2 - 57*n + 41. Let j(z) = -z**5 + 2*z**4 + 7*z**3 - 14*z + 10. Let a(t) = -9*j(t) + 2*m(t). Factor a(u).
(u - 2)*(u - 1)**2*(u + 2)**2
Let i(a) be the first derivative of -a**5/10 - a**4/4 + 2*a**3/3 + 2*a**2 + 16. Factor i(z).
-z*(z - 2)*(z + 2)**2/2
Solve -3/2*r**4 - 3/2*r**2 + 3 - 9/2*r**3 + 9/2*r = 0 for r.
-2, -1, 1
Factor -9*c - 3*c**2 + 7*c + 2*c**3 + c**2 - 2*c.
2*c*(c - 2)*(c + 1)
Let s(n) be the third derivative of 1/280*n**8 - 1/150*n**5 + 0*n**4 + 0 - 4*n**2 - 1/100*n**6 + 1/525*n**7 + 0*n + 0*n**3. Let s(v) = 0. Calculate v.
-1, -1/3, 0, 1
Let a(m) be the third derivative of 0*m**4 + 0*m**5 - 1/1050*m**7 + 0*m**3 - 2*m**2 + 0 + 0*m - 1/1680*m**8 + 0*m**6. Let a(g) = 0. Calculate g.
-1, 0
Let d(i) = i**2 + i - 1. Let g(x) = 5*x**2 + 2*x - 7. Let b(f) = -4*d(f) + g(f). Let s be b(4). Factor 5*a