*p**4/96 + 3*p**3/4 + 8*p**2 + 3*p. Factor k(s).
(s + 9)*(2*s - 1)*(3*s - 2)/4
Let m(f) be the third derivative of -4*f**7/105 + f**6/12 - f**5/30 + f**2. Factor m(s).
-2*s**2*(s - 1)*(4*s - 1)
Let w(q) = 4*q**3 + 2*q**2 + 2*q + 1. Let x be w(-1). Let b = x - -3. Determine t so that -1/2*t + b + 1/2*t**2 = 0.
0, 1
Let d(f) be the first derivative of 2 + 8/5*f**2 + 2/15*f**3 - 1/2*f**4 + 1/15*f**6 + 8/5*f - 2/25*f**5. Solve d(m) = 0 for m.
-1, 2
Let q(v) be the third derivative of 1/180*v**6 + 0 - 2*v**2 + 0*v**5 - 1/315*v**7 + 0*v + 0*v**4 + 0*v**3. Factor q(s).
-2*s**3*(s - 1)/3
Let g(y) be the second derivative of -3/5*y**2 - 3*y - 1/10*y**3 + 0 + 1/20*y**4. Suppose g(n) = 0. What is n?
-1, 2
What is m in -87*m**3 - 294 + 651*m + 102*m**3 - 32*m**2 + 236*m**2 = 0?
-7, 2/5
Let i be ((-6)/(-12))/(2/4). Factor 3/4*x**2 - 1/4*x**3 - i + 0*x.
-(x - 2)**2*(x + 1)/4
Factor 10*v**5 + 24*v**5 + 15*v**4 - 9*v**5 + 0*v**5 - 10*v**3.
5*v**3*(v + 1)*(5*v - 2)
Let y(w) be the first derivative of -2*w**5/3 + w**4/2 + 4*w**3/9 - 6. Factor y(r).
-2*r**2*(r - 1)*(5*r + 2)/3
Let f(b) be the first derivative of -b**4/44 - b**3/33 + b**2/11 + 12. Suppose f(d) = 0. Calculate d.
-2, 0, 1
Suppose 3*k = 31 - 7. Factor 6*w - 2*w**5 + 0*w**3 - k*w + 4*w**3.
-2*w*(w - 1)**2*(w + 1)**2
Let k(z) be the third derivative of 0*z**7 + 0*z**3 + 0*z**5 + 1/1680*z**8 + 10*z**2 + 1/120*z**4 + 0*z - 1/300*z**6 + 0. Factor k(y).
y*(y - 1)**2*(y + 1)**2/5
Let d be 46/11 - 6/33. Let -4*z**3 + 7*z**d + 2*z**4 - z**4 + 0*z**4 - 4*z**5 = 0. Calculate z.
0, 1
Let g(v) be the first derivative of -4 + 0*v + 3/2*v**2 - v**3. Factor g(c).
-3*c*(c - 1)
Suppose -5*v = 2*c + c - 37, 0 = 5*v - 25. What is g in -5/4*g**3 + 1/2*g**c + 1/4*g + 3/4*g**2 - 1/4 = 0?
-1/2, 1
Let j(c) be the third derivative of -c**7/1260 + c**6/240 - c**5/120 + c**4/144 - 4*c**2. Suppose j(l) = 0. Calculate l.
0, 1
Let b(r) be the third derivative of -2*r**6/105 + 11*r**5/105 - 5*r**4/42 - 4*r**3/21 + 4*r**2. Find j, given that b(j) = 0.
-1/4, 1, 2
Suppose 0 = l - 3*u - 4 - 14, -3*l - 5*u = 16. Let c(f) be the first derivative of -2/27*f**l + 1 + 2/9*f + 1/9*f**2 - 1/18*f**4. Factor c(m).
-2*(m - 1)*(m + 1)**2/9
Let j be (-4)/10 - (-8)/20. Let f be (-4)/6*(-3 + j). Factor 4/9*u + 2/9*u**f + 0.
2*u*(u + 2)/9
Let b = -196 + 198. Let x(d) be the third derivative of 0*d + 0*d**4 + 1/20*d**6 + 0 + 3*d**b + 0*d**3 - 1/20*d**5 - 1/70*d**7. Determine c so that x(c) = 0.
0, 1
Let l(v) = -4*v**2 - 2*v + 10. Let j(z) = 21*z**2 + 11*z - 51. Let q(k) = 4*j(k) + 22*l(k). Factor q(y).
-4*(y - 2)*(y + 2)
Let r(a) = -a**2 + 2*a + 7. Let s be r(3). Suppose 4/3 - 4*l**2 - 14/3*l**3 - 4/3*l**s + 2/3*l = 0. What is l?
-2, -1, 1/2
Let k(n) be the first derivative of -n**5/40 - 3*n**4/32 - n**3/12 + 20. Suppose k(z) = 0. What is z?
-2, -1, 0
Factor 5/7*c + 1/7*c**2 + 3/7 - 1/7*c**3.
-(c - 3)*(c + 1)**2/7
Let q(c) be the second derivative of -4/9*c**2 - 3*c - 1/54*c**4 - 4/27*c**3 + 0. Factor q(d).
-2*(d + 2)**2/9
What is y in -20*y + 7*y**4 + 12*y**3 - 11*y**4 + 4*y = 0?
-1, 0, 2
Let h(g) be the first derivative of -2*g**5/5 - 2*g**4 - 10*g**3/3 - 2*g**2 - 9. Determine m, given that h(m) = 0.
-2, -1, 0
Suppose -6*p = -c - p, 5*c = 4*p. Suppose -48 + c = -4*i. Find t such that -i*t**2 + 5*t - 1 + 10*t**3 + 13*t**2 - 11*t**2 - 5*t**4 + t**5 = 0.
1
Let x be (3/(-2))/(9/(-12)). Factor 6/7*y**x - 6/7*y + 2/7 - 2/7*y**3.
-2*(y - 1)**3/7
Let w(r) be the first derivative of -r**7/168 + 11*r**6/180 - 7*r**5/30 + r**4/3 - r**3 - 4. Let a(z) be the third derivative of w(z). Factor a(v).
-(v - 2)**2*(5*v - 2)
Let h(l) be the second derivative of -2*l**7/21 + 4*l**6/15 + 3*l**5/5 - 4*l**4/3 - 8*l**3/3 + 37*l. Factor h(b).
-4*b*(b - 2)**2*(b + 1)**2
Let b = 464 - 5080/11. Solve -8/11 + b*d + 14/11*d**2 = 0 for d.
-2, 2/7
Solve 16*i**3 - 7*i**4 - 6*i**2 + 4*i**4 - 7*i**3 = 0.
0, 1, 2
Suppose 4*q + 8 = 4*t, 3*q + 0*t = 5*t - 16. Suppose 7 = o - q. Solve -o*y**2 - 2*y - 3*y + y = 0.
-2/5, 0
Let x(a) = -a**3 - a**2 + 1. Let j be (-2)/4 - 6/4. Let u(d) = -d**4 + 6*d**3 + 2*d**2 - 7*d - 13. Let s(o) = j*u(o) - 22*x(o). Suppose s(g) = 0. What is g?
-2, -1
Let g = -128 + 132. Let d(h) be the first derivative of -1 - 1/5*h**5 - 1/2*h**2 - h**3 + 0*h - 3/4*h**g. Determine j, given that d(j) = 0.
-1, 0
Let w(o) be the third derivative of 1/84*o**8 - 2/15*o**5 + 1/2*o**4 - 2/15*o**6 + 0*o + 0*o**7 + 0 + 4/3*o**3 + o**2. Factor w(k).
4*(k - 2)*(k - 1)*(k + 1)**3
Let b(w) be the second derivative of w**6/10 + 6*w**5/25 + w**4/20 - w**3/5 + 2*w. Factor b(m).
3*m*(m + 1)**2*(5*m - 2)/5
Let a(l) = l**2 + l + 2. Let w(f) = -3*f**3 - 15*f**2 - 24*f - 6. Let b(g) = -3*a(g) + w(g). Factor b(x).
-3*(x + 1)**2*(x + 4)
Let i(z) be the second derivative of -z**7/42 - z**6/10 + z**5/2 - z**4/6 - 3*z**3/2 + 5*z**2/2 - 7*z. Solve i(c) = 0.
-5, -1, 1
Let c(n) = n**3 + 18*n**2 + 18*n + 19. Let o be c(-17). Factor 6*d**o + 2/3 - 4*d.
2*(3*d - 1)**2/3
Suppose -3*t + 14 = 2*j, 4*t + 5 + 7 = 5*j. Let x be ((-4)/(-10)*-2)/(-2). Factor 6/5*p - x*p**t - 4/5.
-2*(p - 2)*(p - 1)/5
Let m(a) be the third derivative of a**7/70 - a**6/20 - a**5/20 + a**4/4 - 7*a**2. Determine k, given that m(k) = 0.
-1, 0, 1, 2
Let m = -2/201 + 23/67. Factor 2/3 + 5/3*y + 4/3*y**2 + m*y**3.
(y + 1)**2*(y + 2)/3
Let s(c) be the third derivative of c**6/100 + 13*c**5/150 + 2*c**4/15 - 4*c**3/5 - 11*c**2 - 1. Determine h so that s(h) = 0.
-3, -2, 2/3
Suppose 3*z = -z + 4. Let k be 30/9 + -2 - z. Let -1/3*p**4 + k*p**2 + 1/3*p**3 - 1/3*p + 0 = 0. What is p?
-1, 0, 1
Suppose -5*h - 1 = -16. Suppose 3*g - 16 = -0*v - 2*v, 2*g = 2*v + 4. Factor z**h - z**3 + z**v - z**3.
-z**2*(z - 1)
Let z(s) = 19*s**3 - 37*s**2 + 11*s - 13. Let b(t) = -9*t**3 + 18*t**2 - 6*t + 6. Let n(d) = 13*b(d) + 6*z(d). Factor n(g).
-3*g*(g - 2)**2
Let j(p) be the second derivative of -1/10*p**5 + 0*p**4 + p + 0 - 1/15*p**6 + 0*p**3 + 0*p**2. Factor j(g).
-2*g**3*(g + 1)
Let m(d) = -d. Let c(i) = -2*i**2 + 3. Let s(v) = v**2 - v - 1. Let h(a) = -c(a) - 3*s(a). Let w(x) = -h(x) - 4*m(x). Factor w(b).
b*(b + 1)
Let o be 0 - (27/(-3))/3. Suppose -2*q**o + 0*q**2 + 0*q**2 - 4*q**2 = 0. What is q?
-2, 0
Let o = -134 - -134. Suppose -2/3*q + o - q**2 + 0*q**3 + 1/3*q**4 = 0. What is q?
-1, 0, 2
Let j(z) = -z**5 - z**4 + z**3 - z + 1. Let q(x) = 15*x**5 + 63*x**4 + 101*x**3 + 76*x**2 + 27*x + 5. Let y(w) = -j(w) + q(w). Factor y(o).
4*(o + 1)**3*(2*o + 1)**2
Let y(l) = -l**2 + 10*l - 8. Let o be y(9). Suppose 5*z - 16 = -o, u - 1 = 2*z. Factor -4*i**3 + 6*i**3 + 0*i - 2 + 0*i**2 - u*i**2 + 7*i.
(i - 2)*(i - 1)*(2*i - 1)
Let q(i) = -i - 1. Let r be q(-3). Let k be (4/(-6))/(2/(-9)). Factor -p + k*p**r - p**4 - 3*p**3 - 8*p**2 - p - p**3.
-p*(p + 1)**2*(p + 2)
Suppose -8 = 5*o + t, -5*t = -2*t + 9. Let c be 27/72*(o - -3). Factor 0 - c*y**2 + 21/4*y**4 - 3*y**5 - 3/2*y**3 + 0*y.
-3*y**2*(y - 1)**2*(4*y + 1)/4
Let q(b) be the first derivative of 6*b**2 + b**3 + 16 + 0*b**3 + 12*b - 20. Factor q(m).
3*(m + 2)**2
Let h = 395 + -1579/4. Determine u so that -5/4*u**4 + 1/2*u**5 + u**2 + 1/2*u**3 - u + h = 0.
-1, 1/2, 1
Let c(h) be the second derivative of 1/24*h**4 + h + 0 - 1/24*h**3 + 0*h**5 - 1/60*h**6 + 0*h**2 + 1/168*h**7. Factor c(m).
m*(m - 1)**3*(m + 1)/4
Factor -16/7*o + 4/7*o**3 + 2/7*o**2 - 8/7.
2*(o - 2)*(o + 2)*(2*o + 1)/7
Let t(r) be the first derivative of 2*r**5/7 - 3*r**4/14 - 4*r**3/21 - 1. Factor t(i).
2*i**2*(i - 1)*(5*i + 2)/7
Let g(z) = 2*z**3 + 65*z**2 + 28*z - 126. Let d be g(-32). Factor -1/5*h**d + 3/5 - 2/5*h.
-(h - 1)*(h + 3)/5
Determine p so that -104/11*p**3 - 2028/11*p**2 - 17576/11*p - 2/11*p**4 - 57122/11 = 0.
-13
Let x(b) be the second derivative of -b**4/24 - b**3/4 - 2*b. Factor x(k).
-k*(k + 3)/2
Let c(d) = -24*d**3 + 24*d**2 + 4*d + 16. Suppose 2*u - 7*u = -4*y + 9, -5*u - 1 = 4*y. Let z(p) = p**3 - p**2 - 1. Let r(g) = u*c(g) - 20*z(g). Factor r(b).
4*(b - 1)**2*(b + 1)
Let b be 6/(-4)*1/(-3). Let q(h) = h**2 - 21*h - 72. Let v be q(24). Suppose b*p + v + 2*p**2 = 0. What is p?
-1/4, 0
Let j(f) be the first derivative of 3*f**4/20 + 3*f**3/5 - 12*f/5 - 10. Find y, given that j(y) = 0.
-2, 1
Suppose 0 = -2*u - s + 20, 3*u - 3*s = 2*s + 4. Let m = 6 - u. Let k(j) = 3*j**2 - 2. Let p(i) = 3*i**2 - i - 3. Let d(v) = m*p(