or k(c).
5*c*(c - 2)*(7*c - 2)
Let y be (-8)/((-28)/12 + -1). Let u(m) be the first derivative of -5*m**3 - 9/4*m**4 + 1 + 9/2*m**2 + 3*m + y*m**5. Factor u(d).
3*(d - 1)**2*(d + 1)*(4*d + 1)
Let i(k) be the first derivative of k**6/12 + 4*k**5/5 + 5*k**4/2 + 5*k**3/3 - 21*k**2/4 - 9*k - 246. Solve i(s) = 0 for s.
-3, -2, -1, 1
Let o(s) be the third derivative of -s**8/1680 + 3*s**7/70 - 209*s**6/600 + 367*s**5/300 - 47*s**4/20 + 8*s**3/3 - 323*s**2. Let o(t) = 0. Calculate t.
1, 2, 40
Let m be 18/24*(1 - -51) + 131 + -138. What is o in 550/7*o**4 - 464/7*o**2 + m*o - 32/7 - 250/7*o**5 + 80/7*o**3 = 0?
-1, 2/5, 2
Factor 0 + 1/3*s**2 - 1/6*s**4 + 1/6*s**3 + 0*s.
-s**2*(s - 2)*(s + 1)/6
Let z = 1811/700 + 27/100. Solve -4*r**2 + 0 + 12/7*r + z*r**3 - 4/7*r**4 = 0.
0, 1, 3
Factor 11*m**3 - 1 + 9*m**3 + 1859*m**5 - 14*m**4 - 1857*m**5 + 1.
2*m**3*(m - 5)*(m - 2)
Let w be ((-2)/(-8))/(10/(-60))*2. Let d = 0 - w. Factor -6 + 3/4*m**d - 9/2*m**2 + 9*m.
3*(m - 2)**3/4
Let q(r) be the third derivative of 0*r - 1/3*r**4 - 2 + 1/30*r**6 - 1/15*r**5 + 0*r**3 - 28*r**2. Let q(v) = 0. Calculate v.
-1, 0, 2
Let a(o) be the third derivative of o**5/2 + 77*o**4/8 - 12*o**3 + 4*o**2 - 52*o. Let a(s) = 0. What is s?
-8, 3/10
Let n(t) = -t**2 - t + 11. Let f(g) = 5*g**2 - 12*g - 20. Let d(v) = -f(v) - 3*n(v). Suppose d(b) = 0. Calculate b.
1, 13/2
Let x(y) be the third derivative of y**5/210 + 5*y**4/14 + 75*y**3/7 - 106*y**2. Suppose x(n) = 0. What is n?
-15
Let z(x) be the first derivative of 0*x + 2/3*x**6 + 2*x**4 + 16/3*x**3 - 16/5*x**5 - 5 - 6*x**2. Factor z(t).
4*t*(t - 3)*(t - 1)**2*(t + 1)
Let f(q) = -q**2 + 13*q - 12. Let o be f(13). Let r be (-74)/(-26) + o/(-78). Factor 4*h**4 + h**r - 17*h - 12*h**2 + 6*h - 2 + 0*h.
(h - 2)*(h + 1)**2*(4*h + 1)
Let w(v) = v**3 - 7*v**2 + 16. Let f be w(6). Let x be (2/(f/(-15)))/(3/4). Factor 14/3*d + 8/3*d**x + 2.
2*(d + 1)*(4*d + 3)/3
Let y be (-148)/(-20) + 10/(-50). Let x = 921/20 - 165/4. Solve y*d**3 - 54/5*d**4 + x*d**2 + 0 + 3*d**5 + 0*d = 0 for d.
-2/5, 0, 2
Let k = -144 - -138. Let b be -1 - (k/8 - 132/144). Factor 2/3*g**2 + b*g - 4/3.
2*(g - 1)*(g + 2)/3
Let r(d) be the third derivative of -d**7/6300 + d**6/360 - d**5/50 - 5*d**4/12 + 2*d**2. Let x(t) be the second derivative of r(t). Solve x(b) = 0.
2, 3
Suppose 0 = i - 5 + 3. Let x(b) be the first derivative of 0*b - 2 + 3/2*b**i - b**3. Let x(s) = 0. What is s?
0, 1
Let y(f) = -3*f**3 - 49*f**2 - 5*f - 10. Let j(c) = -c**3 - c**2 - c - 2. Let r(t) = -5*j(t) + y(t). Let r(o) = 0. Calculate o.
0, 22
Let n(a) be the second derivative of -8/3*a**3 - 7*a - 24*a**2 - 1/9*a**4 + 0. Factor n(m).
-4*(m + 6)**2/3
Solve 18*t**2 - 18*t**2 - 123*t + 3*t**2 + 52272 - 669*t = 0 for t.
132
Let j(l) = -l**2 + l + 9. Let n be j(4). Let v be (n + 1/(-2)*-3)*-1. Solve -v*i**3 - 1/2*i**4 - 1/2*i - 3/2*i**2 + 0 = 0.
-1, 0
Let x(d) be the third derivative of -d**7/2520 + d**5/120 + 31*d**4/24 + 21*d**2. Let k(a) be the second derivative of x(a). Factor k(m).
-(m - 1)*(m + 1)
Let x(i) be the second derivative of i**4/6 - i**3/3 - 2*i. Let d(m) = -m**2 + m. Suppose v + 4 + 3 = 0. Let g(l) = v*d(l) - 4*x(l). Factor g(u).
-u*(u - 1)
Factor z**2 + 25 - 24 + 16 + 7 - 10*z.
(z - 6)*(z - 4)
Let v(x) be the first derivative of x**7/84 + x**6/12 + x**5/8 + 13*x**2/2 + 16. Let z(a) be the second derivative of v(a). Determine f, given that z(f) = 0.
-3, -1, 0
Solve 0 + 1/4*z**4 + 0*z**2 + 3/4*z**3 - z = 0.
-2, 0, 1
Let s(b) be the first derivative of 5*b**6/12 - 45*b**4/8 - 3. Determine p so that s(p) = 0.
-3, 0, 3
Let c(l) = -2*l + 8. Let s be c(-4). Suppose 0 = -s*m + 11*m. Find g such that 2*g**2 - 4*g + m*g + 0*g**2 + 6*g**2 = 0.
0, 1/2
Let c(k) = -15*k - 5. Suppose 36 = -2*f + 5*f. Let s = 18 - f. Let l(a) = a**2 - 15*a - 4. Let v(m) = s*c(m) - 5*l(m). Determine w so that v(w) = 0.
-2, -1
Determine c so that 0*c + 129/4*c**4 + 0 - 39/4*c**2 - 21/8*c**5 + 201/8*c**3 = 0.
-1, 0, 2/7, 13
Let p(g) be the second derivative of g**7/14 - g**6/5 - 3*g**5/10 + 2*g**4 - 7*g**3/2 + 3*g**2 - g + 14. Determine h, given that p(h) = 0.
-2, 1
Factor 0 + 90/7*t - 2/7*t**3 + 24/7*t**2.
-2*t*(t - 15)*(t + 3)/7
Let a(r) be the third derivative of -13*r**5/80 - r**4/32 - 52*r**2. Factor a(y).
-3*y*(13*y + 1)/4
Suppose o - k - 4*k = 60, -2*o - k + 65 = 0. Factor -5 + 15*z**3 - 56*z - o*z**2 - 26*z + 107*z.
5*(z - 1)**2*(3*z - 1)
Let -204*d**4 + 6*d + 117/2*d**5 - 4 + 117*d**2 + 229/2*d**3 = 0. What is d?
-1/3, 2/13, 2
Let x(b) be the first derivative of -b**4/2 + 8*b**3 + 13*b**2 - 144. Factor x(h).
-2*h*(h - 13)*(h + 1)
Suppose 4*f - 17 = 5*a, 0*f + 2*f + 5*a = 1. Factor -5*t**3 + t**4 + 0*t**3 - 2*t - 1 + 6*t**f + t**3.
(t - 1)*(t + 1)**3
Let b(l) be the second derivative of -l**6/210 + l**5/28 - l**4/28 - 5*l**3/42 + 2*l**2/7 - 93*l. Factor b(f).
-(f - 4)*(f - 1)**2*(f + 1)/7
Let s = -37 + 41. Factor 10*c**s - c**5 - 2*c**4 - 8*c**4.
-c**5
Let b = 458 + -450. Let h(u) be the first derivative of -4/3*u**3 - 2*u**2 + b + 0*u. Factor h(m).
-4*m*(m + 1)
Let p(u) be the second derivative of -3/2*u**2 + 0 - 9*u - 1/28*u**7 + 1/10*u**6 + 3/20*u**5 - u**4 + 7/4*u**3. Find g, given that p(g) = 0.
-2, 1
Suppose 0 = -n + 2. Let t be (12 + (-168)/16)*8/15. Factor 6/5*z - t - 2/5*z**n.
-2*(z - 2)*(z - 1)/5
Suppose -40 = -5*m - 5*m. Factor -4*u**3 + 6*u**m + u**5 + 2*u**4 - 4*u**5 - u**5.
-4*u**3*(u - 1)**2
Let c(w) = 11*w**2 - 94*w - 42. Let h be c(9). Factor h*p - 3/5*p**2 - 12/5.
-3*(p - 4)*(p - 1)/5
Let u be (-2)/((-30)/(-3)) + (-234)/(-120). Factor 5/4*w**2 - 1/4*w**3 - u*w + 3/4.
-(w - 3)*(w - 1)**2/4
Let u(q) be the second derivative of -q**6/225 + 4*q**5/75 - 2*q**4/9 + 16*q**3/45 + 2*q - 39. Solve u(i) = 0 for i.
0, 2, 4
Let 0*o**3 - 5/2*o**2 + 1/2*o**4 + 0*o + 2 = 0. What is o?
-2, -1, 1, 2
Let h(j) = -j**3 - 3*j + 1. Let r(v) = -v**3 + v**2 - v. Let t(o) = -2*h(o) + 6*r(o). Factor t(p).
-2*(p - 1)**2*(2*p + 1)
Let w be (4/(-3))/((-2040)/85). Let k(i) be the second derivative of -w*i**3 - 1/60*i**5 + 0 - 1/18*i**4 + 0*i**2 + 6*i. What is f in k(f) = 0?
-1, 0
Let q = -5 + 7. Suppose 0 = 4*g + 2*l - 40 + 6, 3*g = 4*l - 2. Factor g*c**3 - 3 - c**2 + 8*c**q + 2*c**2.
3*(c + 1)**2*(2*c - 1)
Let t(q) be the second derivative of -q**7/42 - q**6/8 - q**5/4 - 5*q**4/24 - 2*q**2 + 16*q. Let c(n) be the first derivative of t(n). Factor c(j).
-5*j*(j + 1)**3
Let x be 3 + -3 + ((-788)/(-112) - 3). Let r = x + -23/7. Suppose -1/4*b**2 - 1/4*b**4 - 3/4*b + r*b**3 + 1/2 = 0. What is b?
-1, 1, 2
Let a = 735 - 735. Let q(f) be the third derivative of 3*f**2 + 0*f**4 + 0 + 0*f**3 + 1/60*f**5 - 1/210*f**7 + a*f + 0*f**6. Factor q(h).
-h**2*(h - 1)*(h + 1)
Let r(g) be the third derivative of g**7/2520 - g**5/120 + 9*g**4/8 - 23*g**2. Let y(k) be the second derivative of r(k). Suppose y(j) = 0. What is j?
-1, 1
Suppose -3*a = 2*a. Suppose a*w = r + 3*w - 7, 0 = 5*r - 5*w - 15. Factor -8*c**4 + 7*c**2 + c**4 + 3*c**3 - 3*c + c**r - c**2.
-3*c*(c - 1)*(c + 1)*(2*c - 1)
Let x(q) be the third derivative of -q**8/504 - q**7/315 + q**6/30 + 207*q**2. Factor x(s).
-2*s**3*(s - 2)*(s + 3)/3
Let p(q) = q**5 + 16*q**4 - 26*q**3 + 15*q**2 - 3. Let b(u) = 8*u**5 + 112*u**4 - 182*u**3 + 106*u**2 - 22. Let c(k) = -6*b(k) + 44*p(k). Factor c(h).
-4*h**2*(h - 6)*(h - 1)**2
Factor -734472/7*p**2 - 864/7 - 4121204/7*p**3 - 43632/7*p.
-4*(101*p + 6)**3/7
Let j = 10743 + -42969/4. What is w in 1/4*w**5 + 1/2*w**2 - 3/4*w - j*w**4 + 1/2*w**3 + 1/4 = 0?
-1, 1
Let p(s) be the second derivative of 3*s**5/80 + s**4 - 3*s - 13. Solve p(k) = 0.
-16, 0
Let s = 1390 - 25019/18. Let q(w) be the second derivative of -4*w - s*w**3 + 0 + 0*w**2 + 1/36*w**4. What is x in q(x) = 0?
0, 1
Let m be -1*(-11)/(1*(-1)/(-3)). Factor 10 - 39*f**2 + 2 - 6 + m*f.
-3*(f - 1)*(13*f + 2)
Let s = -582 - -585. Let -162/17*x + 90/17*x**2 + 108/17 - 22/17*x**s + 2/17*x**4 = 0. Calculate x.
2, 3
Let k(t) = t**3 - 7*t**2 + 6*t + 3. Let a be k(6). Factor 3*c**2 + 2*c**3 - 1 + 2*c**3 + 0 - 2*c**4 + c - 5*c**a.
-(c - 1)*(c + 1)**2*(2*c - 1)
Factor -r + 3/2 + 1/8*r**3 - 1/8*r**2.
(r - 2)**2*(r + 3)/8
Let x(m) be the first derivative of m**6/195 + m**5/130 - m**4/26 - 5*m**3/39 - 2*m**2/13 - 8*m - 6. Let p(n) be the first derivative of x(n). Factor p(y).
2*(y - 2)*(y + 1)**3/13
