 w, given that t(w) = 0.
-1, 0, 2/5
Let t(v) be the second derivative of 0*v**2 + 0 - 9/80*v**5 + 0*v**6 + 5*v + 0*v**3 + 1/8*v**4 + 1/56*v**7. Factor t(i).
3*i**2*(i - 1)**2*(i + 2)/4
Let q(k) be the second derivative of k**6/180 - k**5/90 + k**3/3 - 2*k. Let w(s) be the second derivative of q(s). Factor w(d).
2*d*(3*d - 2)/3
Let w be 189/168 + 6/(-8). Let r(y) be the third derivative of y**3 + 0*y + 1/20*y**5 - 4*y**2 - w*y**4 + 0. Suppose r(z) = 0. What is z?
1, 2
Let s be (2524/(-840) - -3)*-1. Let d(n) be the third derivative of -1/84*n**4 + 2*n**2 + 0 + 0*n - 2/21*n**3 + s*n**5. Factor d(z).
2*(z - 2)*(z + 1)/7
Let b be ((-11)/2)/(8/(-16)). Suppose b + 9 = 4*c. Factor 1/4*a + 0*a**4 - 1/2*a**3 + 0 + 0*a**2 + 1/4*a**c.
a*(a - 1)**2*(a + 1)**2/4
Let t be ((-5)/10)/(2/(-4)). Let x be -1 - 1*4/(-1). Solve -x*s**2 + 3*s - t + 3*s**3 - 5*s**3 + 3*s**3 = 0 for s.
1
Let u(i) = i**3 - i**2 - 2*i + 5. Let p be u(0). Solve -1/3*h**3 + 0*h**4 + 1/3*h**p + 0*h**2 + 0*h + 0 = 0 for h.
-1, 0, 1
Suppose -n + 6 = -0*n. Suppose -m + 20 = -4*f - n*m, 4*f + 8 = -2*m. Suppose 0*z**3 + 0*z + 1/3*z**5 + 0 - 1/3*z**4 + f*z**2 = 0. Calculate z.
0, 1
Let s = 64/9 + -637/90. Let q(j) be the third derivative of 0 + 0*j**4 + 1/3*j**3 - s*j**5 + 0*j - 3*j**2. Suppose q(k) = 0. Calculate k.
-1, 1
Suppose 2*j + 1 - 11 = 0. Suppose -2*c + 3 = -j. Determine h so that 0 + 0 + 3*h - h**3 - c*h - 2*h**2 = 0.
-1, 0
Let l be (-3)/3*1*-3. Factor -2 - 3*j**2 + 6*j**2 - 4*j**2 - l*j.
-(j + 1)*(j + 2)
Solve 3/8*d**5 - 15/8*d**4 + 27/8*d**2 + 9/8*d**3 + 0*d + 0 = 0.
-1, 0, 3
Let w(d) = -d**3 + d. Let z(y) = 2*y**3 + 12*y**2 + 10*y. Let s(j) = -2*w(j) + z(j). Factor s(f).
4*f*(f + 1)*(f + 2)
Let q(u) be the third derivative of 1/2*u**4 - 1/10*u**7 + 4/5*u**5 + 4*u**2 + 0 + 0*u**3 + 1/8*u**6 + 0*u. Determine t, given that q(t) = 0.
-1, -2/7, 0, 2
Let i be -1 - (27/2)/(-9). Let y(t) be the first derivative of 2 - 1/4*t**4 - 1/10*t**5 + 0*t**3 + 1/2*t + i*t**2. Factor y(h).
-(h - 1)*(h + 1)**3/2
Let u(c) be the second derivative of c**4/12 - 2*c**3/3 + 3*c**2/2 - 6*c. Find i such that u(i) = 0.
1, 3
Let p(a) be the second derivative of 4*a + 0 - 2/21*a**3 + 4/7*a**2 - 1/21*a**4. Factor p(s).
-4*(s - 1)*(s + 2)/7
Let h(d) be the first derivative of -d**8/1680 + d**7/1260 + d**6/1080 - 2*d**3/3 + 1. Let p(c) be the third derivative of h(c). Factor p(m).
-m**2*(m - 1)*(3*m + 1)/3
Let v(p) be the first derivative of p**6/27 - 8*p**5/45 + 5*p**4/18 - 4*p**3/27 + 8. Solve v(f) = 0.
0, 1, 2
Let u(d) = -5*d**4 - d**3 - d**2 - 5*d. Let z(t) be the second derivative of t**6/30 + t**3/6 - t. Let g(w) = -u(w) - 6*z(w). Factor g(x).
-x*(x - 1)**2*(x + 1)
Suppose 4*s - 25 = -13. Suppose 0 + 0*d**2 + 1/2*d**s + 0*d = 0. Calculate d.
0
Let r be 2 - ((-265)/(-55) - 3). Let b(w) be the first derivative of 4 + 0*w**3 + r*w**2 - 1/11*w**4 - 2/11*w + 2/55*w**5. Solve b(z) = 0.
-1, 1
Let z(l) be the third derivative of -l**2 + 0 - 1/3*l**3 + 0*l**4 + 1/30*l**5 + 0*l. Factor z(h).
2*(h - 1)*(h + 1)
Let z be ((-12)/45)/((-4)/10). Solve 4/3*b**3 + 4/3*b**2 - 2/3 - 2/3*b**4 - 2/3*b - z*b**5 = 0 for b.
-1, 1
Let f(c) = 7*c**4 - 7*c**3 + 4*c**2 - 9*c - 9. Let r(v) = v**3 - v - 1. Let t(u) = -4*f(u) + 36*r(u). Factor t(q).
-4*q**2*(q - 2)*(7*q - 2)
Solve 0*g - 3/7*g**2 + 3/7*g**3 + 0 - 3/7*g**5 + 3/7*g**4 = 0.
-1, 0, 1
Solve -16/17*v + 0 - 4/17*v**2 + 2/17*v**3 = 0 for v.
-2, 0, 4
Let c = -26 + 56. Let n be 13/52 + c/8. Suppose -2/5*v**2 + 0 - 8/5*v**n + 0*v + 2*v**3 = 0. What is v?
0, 1/4, 1
Let l be 2 + 0/(-1) + 10. Suppose -3*x + z - 3 = -l, -4*x = z - 5. Determine h so that 1/2*h + 0 + h**x + 1/2*h**3 = 0.
-1, 0
Let o = 3/379 - -3011/2653. Suppose 2/7*m**4 + 8/7*m**3 + 2/7 + 12/7*m**2 + o*m = 0. What is m?
-1
Let p(r) be the third derivative of r**6/600 - r**5/300 + 4*r**2. Factor p(y).
y**2*(y - 1)/5
Let m(r) = -r**2 - r + 2. Let u be m(0). Suppose -u*g + 5*g - 9 = 0. Factor g*d + d**3 - 5 + 4 + 0*d**3 - 3*d**2.
(d - 1)**3
Let z(f) be the first derivative of 3 - 15/2*f**2 + 6*f - 7*f**3. Factor z(u).
-3*(u + 1)*(7*u - 2)
Factor -2/7*f**2 - 4*f - 14.
-2*(f + 7)**2/7
Factor -8/5*y + 2/5*y**4 - 8/5 + 8/5*y**3 + 6/5*y**2.
2*(y - 1)*(y + 1)*(y + 2)**2/5
Let c be (-2)/3*10/(-14). Let k(r) be the first derivative of c*r**3 + 2 + 3/7*r**2 - 4/7*r. Determine t, given that k(t) = 0.
-1, 2/5
Let l(w) = -14*w**2 - 16*w + 12. Let r(y) = -15*y**2 - 16*y + 13. Let p(m) = 5*l(m) - 4*r(m). Factor p(z).
-2*(z + 2)*(5*z - 2)
Let v(a) be the third derivative of 0*a**3 - 5*a**2 + 0*a + 1/24*a**4 - 1/60*a**5 + 0. Factor v(l).
-l*(l - 1)
Let b(n) be the third derivative of n**10/453600 - n**8/30240 + n**6/2160 - n**5/30 + n**2. Let z(d) be the third derivative of b(d). Factor z(f).
(f - 1)**2*(f + 1)**2/3
Let l(s) be the first derivative of -s**4/14 + 8*s**3/21 - 5*s**2/7 + 4*s/7 + 7. Find q such that l(q) = 0.
1, 2
Let j = -48 - -50. Suppose -4*k + 22 = -0*x + 3*x, 3*k - 6 = 3*x. Factor b**4 + b**2 - 2*b**2 + 2*b**j - x*b**4.
-b**2*(b - 1)*(b + 1)
Let a be (-16)/(-6) + 5/15. Factor -w**2 + 4*w**5 + 53*w**a - 61*w**3 + 4*w + w**2.
4*w*(w - 1)**2*(w + 1)**2
Let o be 27/(-1215) + 1/18*4. Solve 1/5*u**2 - o*u - 2/5 = 0.
-1, 2
Let o be (0 - (-10)/2) + 0. Suppose -4*x - 3*g = 0, o*x = 2*x - 3*g. Factor -q + 2*q**4 + q**5 - q**2 - q**2 + x*q.
q*(q - 1)*(q + 1)**3
Let i(u) be the third derivative of u**7/1050 + u**6/200 + u**5/100 + u**4/120 - 16*u**2. Factor i(s).
s*(s + 1)**3/5
Let s(x) be the second derivative of -x**7/840 + x**6/160 - x**5/80 + x**4/96 - 5*x**2/2 + 5*x. Let l(g) be the first derivative of s(g). Factor l(b).
-b*(b - 1)**3/4
Let c(x) be the second derivative of x**7/14 - 9*x**5/20 - x**4/2 + 4*x. Factor c(u).
3*u**2*(u - 2)*(u + 1)**2
Let u = -17 - -19. Let b(g) be the third derivative of 0 + 1/108*g**4 + u*g**2 + 0*g - 1/270*g**5 + 0*g**3. Factor b(y).
-2*y*(y - 1)/9
Let b = 22/13 - 75/52. Factor b*x**3 + 1/4*x**2 - 1/4*x**4 + 0 - 1/4*x.
-x*(x - 1)**2*(x + 1)/4
Let p(t) = -t**2 + 4*t - 6. Let u(c) = -c**2. Let f(s) = -p(s) + 3*u(s). Suppose f(z) = 0. Calculate z.
-3, 1
Let s be ((-78)/(-54) - -8) + (0 - 5). Factor 50/9*c**2 + s*c + 8/9.
2*(5*c + 2)**2/9
Let i(n) be the first derivative of -5*n**6/6 + 35*n**4/4 + 10*n**3/3 - 30*n**2 - 40*n + 18. Determine j so that i(j) = 0.
-2, -1, 2
Let l = -10/29 + -182/145. Let c = l - -37/20. Solve 0*g**2 + 0 + 0*g - 1/2*g**3 - c*g**4 = 0 for g.
-2, 0
Suppose z + 4*z + 25 = 0, 4*z = -c - 18. Suppose -u = -2*u + 2*m - 3, 0 = 3*u - 3*m. Suppose -x**2 + c*x + 1 + 0*x**2 - x - x**u = 0. What is x?
-1, 1
Suppose 0 = 3*f + 3 - 9. Suppose -10 = -13*t + 8*t. Factor p**f + p - p - t*p.
p*(p - 2)
Let d(h) be the third derivative of h**9/30240 - h**7/2520 + h**5/60 - 2*h**2. Let r(p) be the third derivative of d(p). Factor r(f).
2*f*(f - 1)*(f + 1)
Let p(y) be the second derivative of 3/80*y**5 - 4*y - 1/8*y**3 - 3/8*y**2 + 0 + 1/16*y**4. Let p(d) = 0. What is d?
-1, 1
Let x = 24 + -16. Let u be 4/16 + 14/x. Let 14/5*n**3 - 14/5*n - 4/5 + 4/5*n**u = 0. What is n?
-1, -2/7, 1
Let x(o) be the third derivative of -o**8/210 + 4*o**7/525 + 7*o**6/60 + 23*o**5/75 + 23*o**4/60 + 4*o**3/15 + 4*o**2. Solve x(r) = 0.
-1, -1/2, 4
Solve 0 + 3/2*r**2 - 21/8*r**5 - 81/8*r**3 + 39/4*r**4 + 3/2*r = 0 for r.
-2/7, 0, 1, 2
Let v(q) be the third derivative of -q**6/360 - q**5/120 + q**3/3 + 3*q**2. Let f(g) be the first derivative of v(g). Suppose f(a) = 0. Calculate a.
-1, 0
Solve -75/2*l + 45/4*l**2 + 125/4 = 0.
5/3
Let 0 + p**2 + p + 1/4*p**3 = 0. What is p?
-2, 0
Find i such that 9 - i**2 + 3 - 7 + 4 = 0.
-3, 3
Find c such that 3*c**2 + 8*c + 24 + 22*c + 0*c - 3*c = 0.
-8, -1
Let t(k) = k**2 - 6*k + 6. Let g(j) = 4*j**2 - 25*j + 25. Let p = 1 - -3. Let n(h) = p*g(h) - 18*t(h). Factor n(l).
-2*(l - 2)**2
Factor 3*h**4 - 4154*h**2 + 36*h**3 + 4134*h**2 + 5*h**4.
4*h**2*(h + 5)*(2*h - 1)
Let m(f) be the second derivative of 7*f**6/480 - f**5/480 - f**4/48 + f**3/6 + 3*f. Let z(x) be the second derivative of m(x). Let z(u) = 0. What is u?
-2/7, 1/3
Suppose 0 = m - 3*i - 5, -3*i + 20 = 4*m - 7*i. What is y in 6*y**2 - m*y + 6*y - 1 + 7*y + 3 = 0?
-1, -1/3
Suppose n = 2*n - 3. Determine d, given that -4*d**4 - d**5 - 2*d**2 + 7*d**2 - 8*d + n*d**4 + 3*d**3 + 10*d = 0.
-1, 0, 2
Let u(w) be the second derivat