*4 - 8*v + 0.
-2*v*(v - 2)**2*(v + 3)/3
Let z(m) = 2*m**3 - 11*m**2 - 7*m + 9. Let c be z(6). Find k, given that 3*k**2 + 6 + 3*k**3 - 2*k**2 + 3*k**4 - 6*k**2 - c*k - 4*k**2 = 0.
-2, -1, 1
Let g(m) be the second derivative of -1/50*m**5 + 11*m + 1/15*m**3 + 1/5*m**2 - 1/30*m**4 + 0. Determine c so that g(c) = 0.
-1, 1
Let o(i) be the second derivative of i**8/3360 + i**7/1680 - i**6/720 - i**5/240 + i**3 + 5*i. Let y(j) be the second derivative of o(j). Factor y(l).
l*(l - 1)*(l + 1)**2/2
Factor -35*j**3 - 237*j**2 + 200 - 135*j**2 + 72*j**2 + 10*j**2 + 620*j.
-5*(j - 2)*(j + 10)*(7*j + 2)
Let b be 106/408 + (3 - (-52)/(-16)). Let a(r) be the second derivative of 0 - 6*r + 0*r**2 - b*r**4 - 2/51*r**3. Solve a(c) = 0 for c.
-2, 0
Let -28/9*f**5 + 32*f**2 - 196/9*f**3 - 208/9*f**4 + 16*f + 0 = 0. What is f?
-6, -2, -3/7, 0, 1
Let s = -403 + 2016/5. Let o(k) be the first derivative of -s*k**2 - 2/15*k**3 + 8 + 0*k. Find m, given that o(m) = 0.
-1, 0
Let c(a) be the second derivative of 25*a + 0 - 3/100*a**5 + 0*a**2 - 1/5*a**3 - 3/20*a**4. Suppose c(l) = 0. What is l?
-2, -1, 0
Solve -2/11*d**4 + 72/11*d + 112/11 - 20/11*d**2 - 18/11*d**3 = 0 for d.
-7, -2, 2
Factor 295*a**2 - 298*a**2 - 15*a - 4 + 22.
-3*(a - 1)*(a + 6)
Let u(d) be the first derivative of -d**8/112 + 2*d**7/35 - d**6/8 + d**5/10 + 9*d**2 + 21. Let f(o) be the second derivative of u(o). Let f(l) = 0. What is l?
0, 1, 2
Let y be (-1 - 0) + 2 - -5. Let k(f) = -30*f - 177. Let z be k(-6). Find n, given that -4*n - y*n**2 - 4*n**z - 8*n**2 + 4*n**2 + 2*n**2 = 0.
-1, 0
Let c(m) be the first derivative of m**5/180 + m**4/72 - m**3/3 - 6*m**2 + 18. Let x(b) be the second derivative of c(b). Let x(w) = 0. Calculate w.
-3, 2
Let a(z) be the second derivative of 5*z**4/24 - 5*z**2/4 - 73*z. Solve a(p) = 0 for p.
-1, 1
Let w(z) = -z**2 - 2*z + 9. Let i be w(0). Factor k - 2*k + 3*k + 3 + i*k**3 + 13*k + 21*k**2.
3*(k + 1)**2*(3*k + 1)
Let q be ((-1)/(-5))/((-67)/(-670)). Let w(j) be the third derivative of 1/2*j**4 + 0*j + 0 - 4*j**2 + q*j**3 + 1/20*j**5. Solve w(g) = 0.
-2
Let x = -3216 + 16081/5. Let i = -72 + 362/5. Suppose -1/5*y + 1/5*y**4 + x - 2/5*y**2 - 1/5*y**5 + i*y**3 = 0. Calculate y.
-1, 1
Suppose 64/7*s**4 + 2/7*s**5 + 1936/7*s**2 + 0 + 660/7*s**3 - 2662/7*s = 0. Calculate s.
-11, 0, 1
Let b(r) = 10*r**3 - 20*r**2 + 14*r. Let c(q) = -q**4 + 41*q**3 - 79*q**2 + 57*q. Let z(g) = -9*b(g) + 2*c(g). Factor z(n).
-2*n*(n - 1)**2*(n + 6)
Let s(y) = 2*y**4 + 12*y**3 - 10*y**2 - 9*y + 11. Let c(v) = 9*v**4 + 48*v**3 - 40*v**2 - 35*v + 44. Let i(r) = 6*c(r) - 26*s(r). Factor i(f).
2*(f - 11)*(f - 1)**2*(f + 1)
Factor 3*l**2 - 12*l - 3*l + 2*l**2 - 231 + 31.
5*(l - 8)*(l + 5)
Let b = 205/88 + -53/44. Factor 5/8*a**3 + 1/4 - b*a**2 + 7/8*a**4 - 5/8*a.
(a - 1)*(a + 1)**2*(7*a - 2)/8
Factor 0 + 1/7*m**3 - 19/7*m + 18/7*m**2.
m*(m - 1)*(m + 19)/7
Let r(j) be the first derivative of 3*j - 7/12*j**4 - 6 + 23/6*j**3 - 3*j**2. Let u(w) be the first derivative of r(w). Let u(x) = 0. Calculate x.
2/7, 3
Let s be -3*(0 + (-8)/3). Let j(v) = -v**3 + 8*v**2 + v - 4. Let t be j(s). Suppose 0 + 12*p - 12*p**2 + 5 + t*p**3 - 1 - 3*p**2 = 0. What is p?
-1/4, 2
Let g(a) be the second derivative of -a**7/14 + a**6/10 + 3*a**5/4 - 5*a**4/4 - 2*a**3 + 6*a**2 - 20*a + 3. Determine b, given that g(b) = 0.
-2, -1, 1, 2
Let d(o) be the first derivative of o**5/5 + o**4/4 + o**2/2 + o + 27. Let p(a) = -6*a**3 - 6*a**2 + 14*a - 10. Let k(y) = 2*d(y) + p(y). Factor k(b).
2*(b - 2)*(b - 1)**2*(b + 2)
Let y(h) be the third derivative of -h**8/47040 + h**6/1680 - h**5/60 - 7*h**2. Let f(k) be the third derivative of y(k). Find z, given that f(z) = 0.
-1, 1
Let b be (-36)/(-15)*(-2)/(-32). Let n(j) be the second derivative of -j**3 - b*j**5 + 3*j + 0 + 0*j**2 + 3/4*j**4. Suppose n(g) = 0. What is g?
0, 1, 2
Suppose 2*h - 3*h + 3 = 0. Let x = -714 - -735. Factor 1 + g**h + x*g + g**2 - 23*g - 1.
g*(g - 1)*(g + 2)
Factor 8*u**2 + 10*u**2 - 2*u**3 - 3*u - 7*u - 6*u**2.
-2*u*(u - 5)*(u - 1)
Let o(y) be the third derivative of -y**5/30 + y**3/3 + 21*y**2. Let n be o(1). Factor n + 26/9*z**2 - 8/3*z**3 - 2/3*z.
-2*z*(3*z - 1)*(4*z - 3)/9
Factor 18/7*t + 20/7 - 2/7*t**2.
-2*(t - 10)*(t + 1)/7
Factor -9*i**2 + 1/7*i**4 - 270/7 - 243/7*i - 1/7*i**3.
(i - 10)*(i + 3)**3/7
Let f be 0*(-1 + (-1)/(-2)). Let c = 30 + -30. What is x in 2/3*x**2 + f*x + c = 0?
0
Let c(o) be the first derivative of -27*o**5/10 - 345*o**4/8 + 287*o**3/2 - 579*o**2/4 + 45*o + 78. Let c(s) = 0. Calculate s.
-15, 2/9, 1
Let r(t) be the third derivative of -t**6/540 + t**5/30 - 5*t**4/36 - t**3/2 + 2*t**2 - 2. Let d(v) be the first derivative of r(v). Factor d(p).
-2*(p - 5)*(p - 1)/3
Suppose 33 + 3 = 3*q. Suppose 4*j = 7*j - q. Factor -6*p**3 - 2*p**4 - 2*p**2 + p + 3*p + 2*p + j.
-2*(p - 1)*(p + 1)**2*(p + 2)
Find v, given that 336/13*v - 446/13*v**2 + 392/13 - 334/13*v**3 + 54/13*v**4 - 2/13*v**5 = 0.
-1, 1, 14
Let n(c) = -5*c + 3. Let v(u) = -6*u + 3. Let x(q) = 7*n(q) - 6*v(q). Let w be x(6). Factor t**3 + 2 - 2*t**3 + 3*t**3 - w*t - 2*t**2 + 7*t.
2*(t - 1)**2*(t + 1)
Let w(v) be the second derivative of v**6/1080 - v**5/360 - v**4/36 + 3*v**3/2 + 6*v. Let n(z) be the second derivative of w(z). Solve n(f) = 0.
-1, 2
Let g be 34/221 - 2/13. Let j be -1 + (-13 + 11)/(-2 - g). Factor j*o - 2/5*o**2 + 2/5*o**3 + 0.
2*o**2*(o - 1)/5
Suppose -3 = -3*t, 2*y + 5*t = 20 + 1. Solve 2*m + 6*m**4 - y*m**2 + 6*m**2 - 9*m**2 + 4 + m**2 - 2*m**3 = 0 for m.
-1, -2/3, 1
Let i = -1865/2 + 934. Let q(s) be the second derivative of -s**2 + 4*s - 7/12*s**4 + i*s**3 + 0. Factor q(c).
-(c - 1)*(7*c - 2)
Suppose 0 = -7*f + f + 36. Factor -28*q - 2*q**2 - 13*q**2 + f*q**2 + 5*q**2.
-4*q*(q + 7)
Let g(s) be the third derivative of s**7/42 + s**6/6 - s**5/6 - 5*s**4/2 + 15*s**3/2 + 687*s**2. Factor g(i).
5*(i - 1)**2*(i + 3)**2
Suppose 11 = a + 3*g, -15 = -2*a + 5*g - 26. Let n(h) be the first derivative of 3 - 1/5*h**3 + 3/5*h**a - 3/5*h. Factor n(x).
-3*(x - 1)**2/5
Let m(c) be the second derivative of 0 - 5/168*c**7 - 3/80*c**5 + 1/48*c**4 - 3/40*c**6 + 0*c**2 - 6*c + 0*c**3. Factor m(f).
-f**2*(f + 1)**2*(5*f - 1)/4
Let k = 3688/5313 - -16/483. Find d such that 6/11*d**2 - k*d + 0 + 2/11*d**3 = 0.
-4, 0, 1
Let p(l) be the third derivative of 0*l + 0 + 0*l**4 + 1/15*l**5 - 8/3*l**3 + l**2. Factor p(u).
4*(u - 2)*(u + 2)
Determine i, given that -1/4*i**4 + 0*i + 3/2*i**2 + 1/4*i**3 + 0 = 0.
-2, 0, 3
Let o = 5 - 5. Let c(h) = h - 3 - 1 + 4*h**2 - 5*h**2 + o. Let u(x) = x**2 + 3. Let n(s) = 2*c(s) + 3*u(s). What is m in n(m) = 0?
-1
Factor -1398 + 11*h**2 + 2803 - 1405 - h**3 + 13*h**3 + h**4.
h**2*(h + 1)*(h + 11)
Let k(p) = -4*p**4 - 3*p**3 - 5*p + 5. Let q(m) be the third derivative of -m**6/120 + m**4/24 - m**3/6 - 4*m**2. Let r(j) = -k(j) - 5*q(j). Factor r(x).
4*x**3*(x + 2)
Let w(f) be the second derivative of -f**6/150 - 33*f**5/50 - 363*f**4/20 + 67*f - 1. What is c in w(c) = 0?
-33, 0
Let r(l) be the first derivative of l**3/8 + 51*l**2/16 - 5. Find d, given that r(d) = 0.
-17, 0
Factor 11 - 4*o**4 + 38*o + 5 - 20*o - 14*o**2 + 2*o**4 - 18*o**3.
-2*(o - 1)*(o + 1)**2*(o + 8)
Let p(a) be the second derivative of 5*a**7/42 + a**6/2 + a**5/2 - 5*a**4/6 - 5*a**3/2 - 5*a**2/2 + 45*a. Determine x, given that p(x) = 0.
-1, 1
Let c(l) be the second derivative of l**4/32 - 17*l**3/16 - 57*l**2/8 - 124*l - 2. Factor c(n).
3*(n - 19)*(n + 2)/8
Suppose -3*r + 18 = 3*s + s, -r = 5*s - 6. Factor 2/3*b**3 + 2/3*b**4 - 2/3*b**2 + s - 2/3*b.
2*b*(b - 1)*(b + 1)**2/3
Let r(m) = 35*m**2 + 60*m - 25. Let g(k) = -k**3 + 9*k**2 + k - 8. Let y be g(9). Let p(t) = 1. Let u(d) = y*r(d) + 5*p(d). Let u(j) = 0. Calculate j.
-2, 2/7
Let n(y) = -5*y**2 + 8*y. Let s(t) be the first derivative of -t - 1. Let h(w) = -3*n(w) + 12*s(w). Determine i so that h(i) = 0.
-2/5, 2
Let o(j) be the second derivative of j**9/7560 - j**8/672 + 2*j**7/315 - j**6/90 + 5*j**4/12 - 17*j. Let d(n) be the third derivative of o(n). Factor d(s).
2*s*(s - 2)**2*(s - 1)
Let a(g) = 2 - g**3 + g**2 - 5 + 2 - 2*g**2. Let z(m) = 8*m**3 + 4*m**2 - 10*m. Let l(o) = 12*a(o) + 2*z(o). Determine t so that l(t) = 0.
-1, 3
Let 8/7*c + 22/7*c**2 + 2/7*c**4 + 18/7*c**3 + 0 - 2/7*c**5 = 0. What is c?
-1, 0, 4
Let s(w) = 3*w**2 - 3