 6*f. What is v in 3/4*v**f + 1/4*v**l + 0 + 0*v**2 - v = 0?
-2, 0, 1
Suppose h - z = 4*h - 10, 5*h = -4*z + 5. Let o(d) be the second derivative of 1/10*d**h + 0 + 0*d**2 + 4*d + 0*d**4 + 0*d**3. Factor o(s).
2*s**3
Let p = -50 + 71. Factor 4 + 0 - p*j**3 - 4 + 6*j**2.
-3*j**2*(7*j - 2)
Let s(l) be the first derivative of -l**8/105 + l**7/210 - l**3/3 + 7. Let g(x) be the third derivative of s(x). Suppose g(b) = 0. Calculate b.
0, 1/4
Suppose 0*u + 2*u = 6. Let n(r) = -r**3 + 4*r**2 + 6*r - 3. Let y be n(5). Factor u*c**4 + 4*c**3 - 2*c**2 + 3*c**y + 0*c**2.
c**2*(c + 1)*(3*c + 1)
Let d = 158 - 155. Let r = 16/57 - -1/19. Factor 0 - r*l**2 + 0*l + 1/3*l**d.
l**2*(l - 1)/3
Let i = 970 + -6788/7. Factor 2/7*w - i*w**2 + 4/7.
-2*(w - 2)*(w + 1)/7
Let b(x) = x**4 + x**3 - x**2 - 1. Let u(w) = 21*w**4 - 15*w**3 - 15*w**2 + 21*w - 12. Let k(g) = 6*b(g) - u(g). Find p such that k(p) = 0.
-1, 2/5, 1
Let x = -2/27 - -64/135. Let k(l) be the first derivative of 1/15*l**3 - 3 - x*l**2 + 4/5*l. What is f in k(f) = 0?
2
Let q(a) = -12*a**4 + 12*a**2 + 11. Let l(b) = -b**4 + b**2 + 1. Suppose 53 = 4*k - 35. Let o(w) = k*l(w) - 2*q(w). Factor o(n).
2*n**2*(n - 1)*(n + 1)
Suppose 4*u - 1 = 3*u - g, 4*u - 4*g + 4 = 0. Suppose 3*c = -u*c. Factor -2/11*d**4 + 4/11*d**2 + c*d**3 - 2/11 + 0*d.
-2*(d - 1)**2*(d + 1)**2/11
Find b, given that -2*b**2 + 4/5*b + 8/5*b**3 - 2/5*b**4 + 0 = 0.
0, 1, 2
Let v(w) be the second derivative of w + 0 + 0*w**2 + 1/10*w**5 - 1/12*w**4 + 0*w**3. Let v(h) = 0. Calculate h.
0, 1/2
Let k(c) = 2*c**3 + 32*c**2 - 22*c + 12. Let d be (-31)/11 - (-6)/(-33). Let p(l) = -l**3 - 11*l**2 + 7*l - 4. Let x(m) = d*k(m) - 8*p(m). Factor x(z).
2*(z - 2)*(z - 1)**2
Let t(x) be the second derivative of -1/6*x**2 + 2*x + 1/36*x**4 + 0 + 0*x**3. Factor t(d).
(d - 1)*(d + 1)/3
Let k(b) be the first derivative of 0*b**3 - 1/5*b**5 + b**2 + 2 + b - 1/2*b**4. Suppose k(s) = 0. Calculate s.
-1, 1
Let r(s) be the first derivative of s**5/120 - s**4/24 + s**3/12 - s**2 - 3. Let d(c) be the second derivative of r(c). Factor d(t).
(t - 1)**2/2
Let t(j) be the second derivative of 0 + 1/4*j**4 - 1/6*j**3 - 3/20*j**5 - 5*j + 1/30*j**6 + 0*j**2. Find v such that t(v) = 0.
0, 1
Let h(q) be the first derivative of 0*q - 1/8*q**4 + 2/3*q**3 - q**2 - 4. Solve h(s) = 0 for s.
0, 2
Let s be 2/30*(-2 - -5). Factor -s*p**2 + 0 + 2/5*p.
-p*(p - 2)/5
Let q = 1487026/11 - 135092. Let h = q - 92. Factor -2/11*o**5 + 0 + h*o**3 - 2/11*o**4 + 2/11*o**2 + 0*o.
-2*o**2*(o - 1)*(o + 1)**2/11
Let o be (-9)/(-45) + 18/10. Suppose 2*m - o = -0*m. Factor t + m - 1/2*t**3 + 1/4*t**4 - 3/4*t**2.
(t - 2)**2*(t + 1)**2/4
Factor -16/5 - 24/5*w - 12/5*w**2 - 2/5*w**3.
-2*(w + 2)**3/5
Let y = 597 - 592. Factor 1/2*d**4 + 0*d - 1/2*d**y + 0 - 1/2*d**2 + 1/2*d**3.
-d**2*(d - 1)**2*(d + 1)/2
Let u(d) be the first derivative of 1/18*d**4 - 1/20*d**5 + 0*d**2 - 1 - d + 0*d**3. Let q(b) be the first derivative of u(b). Factor q(y).
-y**2*(3*y - 2)/3
Let a(p) be the third derivative of -1/1680*p**8 + 0*p + 0*p**4 - 1/300*p**5 + 1/600*p**6 + 0*p**3 + 1/1050*p**7 - 5*p**2 + 0. Let a(l) = 0. Calculate l.
-1, 0, 1
Let i(k) be the first derivative of -3/10*k**4 - 1/5*k**2 + 2/5*k**5 + 4/15*k**6 + 0*k - 2/3*k**3 + 6. Solve i(h) = 0 for h.
-1, -1/4, 0, 1
Let w(g) be the first derivative of -1 - 1/11*g**2 + 0*g - 2/33*g**3. Find d, given that w(d) = 0.
-1, 0
Let q(y) be the third derivative of -1/2*y**3 + 0*y + 4*y**2 - 1/20*y**5 + 1/4*y**4 + 0. Factor q(w).
-3*(w - 1)**2
Suppose 0 + 3/4*y**5 - 9/4*y**3 - 3/4*y**4 - 3/2*y + 15/4*y**2 = 0. What is y?
-2, 0, 1
Let d(n) be the third derivative of 5*n**6/216 - n**5/18 + n**4/18 - n**3/6 + 3*n**2. Let a(f) be the first derivative of d(f). Find g, given that a(g) = 0.
2/5
Suppose 7*g = 6*g + 2. Factor 8*q**2 - 1 + 0*q**g + 6*q - 1.
2*(q + 1)*(4*q - 1)
Suppose a - 7 = 1. Let t be 6/a*-2*-2. Factor 5*i - i**3 + 2*i**5 - 3*i**3 - t*i.
2*i*(i - 1)**2*(i + 1)**2
Let o(a) be the second derivative of 0*a**5 - 1/45*a**6 + 0 + 0*a**2 + 0*a**3 + 1/18*a**4 + a. Solve o(r) = 0.
-1, 0, 1
Find a, given that 1/8 - 1/4*a + 1/8*a**2 = 0.
1
Let y = -27 + 30. Let j = 166/9 + -18. What is z in 2/9*z**y + 2/9*z + 0 + j*z**2 = 0?
-1, 0
Suppose 4*r = -5*p - 17 + 43, r = 2*p. Factor 0 - 1/2*y**2 - 1/4*y**5 + 1/4*y + 1/2*y**r + 0*y**3.
-y*(y - 1)**3*(y + 1)/4
Let j(m) be the first derivative of m**5/90 - m**4/36 - m**2/2 - 2. Let r(f) be the second derivative of j(f). Factor r(i).
2*i*(i - 1)/3
Let m = 1125 + -2241/2. Determine d so that -6 + m*d**2 - 3/2*d**4 + 6*d - 3*d**3 = 0.
-2, 1
Let s(v) = 36*v**3 + 44*v**2 + 40*v. Let u(g) = -7*g**3 - 9*g**2 - 8*g. Let n(f) = 3*s(f) + 16*u(f). Factor n(k).
-4*k*(k + 1)*(k + 2)
Let p(i) = i + 11. Let o be p(-10). Suppose -8 = -3*j + o. Factor -2/3*n**5 + 0*n - 2/3*n**j + 0 + 0*n**2 - 4/3*n**4.
-2*n**3*(n + 1)**2/3
Let h(f) = -26*f**3 - f**2 + f + 1. Let b be h(-1). Let w be 10/b + (-4)/10. Factor -4/5*u**2 + 0 + w*u - 2*u**4 + 14/5*u**3.
-2*u**2*(u - 1)*(5*u - 2)/5
Suppose -19*l = -4*l - 30. Factor -3/2*m + 1/2*m**l + 1.
(m - 2)*(m - 1)/2
Let g be 2/(-3) - 55/(-15). Factor 0*c**5 + c**4 + 4*c + 2*c**5 - 11*c**4 - 14*c**2 + 18*c**g.
2*c*(c - 2)*(c - 1)**3
Let t(b) be the second derivative of -b**4/8 - b**3/2 + 9*b**2/4 + 45*b. Solve t(o) = 0.
-3, 1
Let v be (14/20)/((-17)/(-204)) - 6. Solve 4/5*i + 0 + 8/5*i**3 - v*i**2 = 0 for i.
0, 1/2, 1
Suppose 36 = g + 2*g + 5*m, m = -3*g + 36. Suppose -4 + g = 4*c. Factor 4*t**2 + 0*t**3 + c*t**3 + 4*t**3.
2*t**2*(3*t + 2)
Let t(q) = q**4 - q**3 - q**2 + q + 6. Let d(i) = -i**4 + i**3 + i**2 - i - 5. Let p(x) = -6*d(x) - 5*t(x). Factor p(k).
k*(k - 1)**2*(k + 1)
Let t be (12/(-213))/4*-4. Let d = 556/213 + t. Determine i, given that -2 + 14/3*i**2 - d*i = 0.
-3/7, 1
Let o(a) = -2*a**2 - 4 + 3*a**2 - a + 0*a**2 + 5. Let t(h) = 5*h**2 - 6*h + 6. Let n(j) = 6*o(j) - t(j). Factor n(k).
k**2
Factor -28/11 - 18/11*w - 2/11*w**2.
-2*(w + 2)*(w + 7)/11
Factor 6*g + 5*g**2 - 7*g**4 - g**4 + 7*g**4 - 2*g**3.
-g*(g - 2)*(g + 1)*(g + 3)
Let r be 4 + -7 + 4*1. Let z be r/(-21) - (-2)/6. Factor 4/7*f - 4/7*f**3 - 2/7*f**4 + 0*f**2 + z.
-2*(f - 1)*(f + 1)**3/7
Solve -6*u + 2*u**2 + 2*u - 2 - 4 = 0.
-1, 3
Let j(r) be the first derivative of -r**6/36 - r**5/5 - 3*r**4/8 - 21. Find h, given that j(h) = 0.
-3, 0
Factor 2/7*f - 6/7 - 2/7*f**3 + 6/7*f**2.
-2*(f - 3)*(f - 1)*(f + 1)/7
Let m(o) be the first derivative of -4*o**3/3 - 2*o**2 - 10. Factor m(u).
-4*u*(u + 1)
Let n(w) be the second derivative of w**4/4 + 3*w**3/2 + 41*w. Solve n(g) = 0 for g.
-3, 0
Let b = -3 + 2. Let g(k) = -k**3 + k**2 + k + 1. Let r(f) = -218*f**3 - 106*f**2 - 16*f + 1. Let t(x) = b*r(x) + 2*g(x). Find p, given that t(p) = 0.
-1/6
Let h be (-36)/(-234) + (-14)/(-78). Suppose h*j**5 + 1/3*j**4 + 0 - 1/3*j**3 - 1/3*j**2 + 0*j = 0. What is j?
-1, 0, 1
Let v(s) be the second derivative of 1/75*s**6 + 1/30*s**4 + 0*s**2 + 0 - 2*s + 0*s**3 - 1/25*s**5. Determine i so that v(i) = 0.
0, 1
Let p = 429 - 32174/75. Let s(i) be the second derivative of -1/25*i**5 + 0*i**4 - 1/5*i**2 + 2*i + 0 + p*i**6 + 2/15*i**3. Solve s(c) = 0 for c.
-1, 1
Let c be 0/(1*(3 - 4)). Find m such that -2/3*m**4 - 2/3*m**3 + c*m + 0 + 0*m**2 = 0.
-1, 0
Suppose 3*m = -8 + 14. Suppose 2*h = -m*h. Factor 0*r + h - 9/4*r**3 + 1/2*r**2.
-r**2*(9*r - 2)/4
Let m = -6 + 7. Let z = 3 - m. Solve t + 1 + 2*t**2 + 0*t**z + t**3 + 2*t + t**2 = 0 for t.
-1
Let a(w) = 86*w**2 + 40*w + 5. Let x(p) = -257*p**2 - 120*p - 15. Let i(d) = -17*a(d) - 6*x(d). Factor i(h).
5*(4*h + 1)**2
Factor 0 - 2/11*n**2 + 4/11*n.
-2*n*(n - 2)/11
Let v(g) be the first derivative of -343*g**4/2 - 588*g**3 - 756*g**2 - 432*g + 19. Factor v(l).
-2*(7*l + 6)**3
Let p(o) = -4*o + 1. Let u(z) = -z**2 + 3*z - 1. Let k be u(3). Let s be p(k). Factor -i**3 + s*i**2 - 13*i**2 + 7*i**2.
-i**2*(i + 1)
Find s such that 42/19*s**2 - 30/19*s**3 + 6/19 + 8/19*s**4 - 26/19*s = 0.
3/4, 1
Let g(n) be the third derivative of n**7/10080 + n**6/2880 - n**4/8 + n**2. Let v(q) be the second derivative of g(q). Find k, given that v(k) = 0.
-1, 0
Let k(j) = 6*j**2 - j**3 - 7*j**3 - j + 9*j**3 - 6. Let l be k(-6). Factor l + 1/2*b + 3/4*b**2 + 1/4*b**3.
b*(b + 1)*(b + 2)/4
Let d = 8 + -4. Factor 2*i**2 + 1 + d*i**3 + i**4 + 4*i**2 - i + 