
Let g(x) be the third derivative of 25*x**8/336 + 17*x**7/42 + 7*x**6/8 + 11*x**5/12 + 5*x**4/12 - 9*x**2. Factor g(h).
5*h*(h + 1)**3*(5*h + 2)
Suppose 4*q - 9*q + 10 = 0. Determine k so that k**3 + 5*k**q - 4*k**5 - 3*k + k**5 + k - 5*k**4 + 4*k = 0.
-1, -2/3, 0, 1
Let f(a) be the third derivative of a**7/42 + a**6/12 - 5*a**4/12 - 5*a**3/6 + 21*a**2. Let f(n) = 0. What is n?
-1, 1
Let 8/3*v**3 - 4/3*v**2 + 0*v + 0 + 4*v**4 = 0. What is v?
-1, 0, 1/3
Let g(f) be the third derivative of 2*f**7/315 + f**6/36 + 2*f**5/45 + f**4/36 + 4*f**2. Solve g(t) = 0 for t.
-1, -1/2, 0
Suppose 1/2*c**3 - 1/2*c - 3/8*c**2 + 1/2 - 1/8*c**4 = 0. Calculate c.
-1, 1, 2
Let p = -8 - -17. Let q be 3/p + (-46)/(-42). Factor q*s**2 - 4/7*s**3 + 2/7 - 8/7*s.
-2*(s - 1)**2*(2*s - 1)/7
Factor 4 + 19*u - 12 - 6*u**2 + 7*u.
-2*(u - 4)*(3*u - 1)
Let a(p) be the third derivative of p**7/315 - p**6/60 + 13*p**5/360 - p**4/24 + p**3/36 - 6*p**2. Factor a(c).
(c - 1)**2*(2*c - 1)**2/6
Let d(a) be the second derivative of -a**4/60 + 4*a**3/15 + 9*a**2/10 - a - 8. Factor d(m).
-(m - 9)*(m + 1)/5
Suppose -5*p**3 - 5*p - 18*p**2 + 4*p**2 + 4*p**2 = 0. What is p?
-1, 0
Factor 8/13*v**2 + 8/13*v**4 + 2/13*v + 2/13*v**5 + 12/13*v**3 + 0.
2*v*(v + 1)**4/13
Let 19*l**4 + 6*l**3 + 3*l**3 - 8*l**2 - 3*l**4 - 4*l + 3*l**3 - 16*l**5 = 0. What is l?
-1/2, 0, 1
Let b be (1 + 0)/(-1)*-8. Let p(l) = -l**3 + 9*l**2 - 8*l + 3. Let a be p(b). Suppose -4 + 0*g**2 + g**2 + a*g**2 - 6*g - 6*g**2 = 0. What is g?
-2, -1
Let k be (-6)/(-4)*16/12. Factor -c**3 + 0*c**3 - 2*c**2 - c**k - c - 2*c - 1.
-(c + 1)**3
Let d(w) be the first derivative of w**7/210 + w**6/120 - w**5/60 - w**4/24 - w**2 - 1. Let p(r) be the second derivative of d(r). Find u such that p(u) = 0.
-1, 0, 1
Let b(d) be the first derivative of -2 + 2/9*d**3 - 1/9*d**2 + 0*d + 2/45*d**5 - 1/6*d**4. Factor b(z).
2*z*(z - 1)**3/9
Suppose -11*a = 9 - 31. Factor -u**3 + 1/2 + 1/2*u**4 + 1/2*u**5 + 1/2*u - u**a.
(u - 1)**2*(u + 1)**3/2
Solve -148/5*p**3 - 96/5*p**2 + 0 - 16/5*p - 16/5*p**5 - 84/5*p**4 = 0 for p.
-2, -1, -1/4, 0
Let u(j) be the second derivative of -j**4/24 + 5*j**3/12 - 3*j**2/2 + 31*j. Let u(n) = 0. Calculate n.
2, 3
Let g(k) be the third derivative of 0*k**4 - k**2 + 1/504*k**8 + 0 + 0*k**3 + 1/90*k**5 - 1/180*k**6 - 1/315*k**7 + 0*k. Factor g(l).
2*l**2*(l - 1)**2*(l + 1)/3
Let o be (-4)/7*14/(-4). Factor 0*s + 0*s**3 + 0 + 1/3*s**o - 1/3*s**4.
-s**2*(s - 1)*(s + 1)/3
Let h(i) be the second derivative of 1/6*i**2 + 4*i + 0*i**4 + 1/12*i**3 + 0 - 1/120*i**5. Let h(l) = 0. What is l?
-1, 2
Let k(o) = -9*o**2 + 9*o + 8. Let w(h) = 6*h**2 - 6*h - 5. Suppose 5*m + 0*m - 25 = 0. Let b(a) = m*k(a) + 8*w(a). Factor b(i).
3*i*(i - 1)
Let j(w) be the second derivative of -w**4/2 + 13*w**3/3 + 10*w**2 - 29*w. Determine s so that j(s) = 0.
-2/3, 5
Let w(l) = 7*l**4 + 12*l**3 + 21*l**2 + 29*l + 8. Let g(p) = 3*p**4 + 6*p**3 + 11*p**2 + 14*p + 4. Let q(j) = 5*g(j) - 2*w(j). Factor q(i).
(i + 1)**2*(i + 2)**2
What is b in 0 - 2/3*b**2 + 6*b**4 + 4*b**3 - 9*b**5 - 1/3*b = 0?
-1/3, 0, 1/3, 1
Let q(n) be the first derivative of -n**6/10 + 9*n**5/20 - 3*n**4/4 + n**3/2 - n + 2. Let v(x) be the first derivative of q(x). Determine b so that v(b) = 0.
0, 1
Factor -4/5*j**2 - 12/5*j - 9/5.
-(2*j + 3)**2/5
Let -4 + 0 + 2 - 6*l**2 + 8*l**4 - 10*l + 10*l**3 = 0. What is l?
-1, -1/4, 1
Let r(i) be the first derivative of i**7/420 - i**3 - 3. Let u(o) be the third derivative of r(o). Let u(d) = 0. Calculate d.
0
Let b = -30 + 32. Suppose -1/4*q**3 + 1/2*q**b - 1/4*q + 0 = 0. Calculate q.
0, 1
Let w(t) be the third derivative of t**8/168 + t**7/35 + t**6/30 - 8*t**2. Find y, given that w(y) = 0.
-2, -1, 0
Find i, given that 0 + 3/4*i**2 - 3/2*i**3 + 3/4*i**4 + 0*i = 0.
0, 1
Let j(z) be the first derivative of z**6/160 - z**5/48 - z**4/24 + z**3/6 - 4*z**2 + 4. Let y(o) be the second derivative of j(o). Factor y(m).
(m - 2)*(m + 1)*(3*m - 2)/4
Let r(o) = o**4 + 4*o**3 + o**2 - 4*o - 6*o**4 + o**4. Let i(k) = -23*k**4 + 23*k**3 + 6*k**2 - 23*k. Let b(f) = -6*i(f) + 34*r(f). What is j in b(j) = 0?
-1, 0, 1
Let g(p) = p**2 + p. Let u be g(1). Let o(h) = h**4 + h**3 + h. Let t(m) = 2*m**4 - m**4 + 6*m**3 + m**2 - m - 4*m**3. Let v(s) = u*o(s) + 2*t(s). Factor v(l).
2*l**2*(l + 1)*(2*l + 1)
Let b be 6/48*(-1)/((-1)/2). What is q in b*q**3 + 1/4*q**4 + 0 + 0*q - 1/2*q**2 = 0?
-2, 0, 1
Suppose -4*r = -2*r - 4. Suppose -2 = 3*u - r*a, 3*a - 3 = -0*u + 3*u. Factor u*f**2 + 0 + 2/9*f**3 - 2/9*f.
2*f*(f - 1)*(f + 1)/9
Let q(t) be the first derivative of 2*t**5/5 + t**4/2 - 2*t**3/3 - t**2 + 63. Determine c so that q(c) = 0.
-1, 0, 1
Let y = -20 - -22. Factor -4/9 - 2/9*u + 4/9*u**y + 2/9*u**3.
2*(u - 1)*(u + 1)*(u + 2)/9
Let z(y) = 4*y**2 + 7*y + 8. Let h(m) = 2*m**2 + 4*m + 4. Let p(v) = -5*h(v) + 2*z(v). Factor p(b).
-2*(b + 1)*(b + 2)
Suppose 0 = 3*n + 3*m - 45, 0*m + 5*m - 57 = -4*n. Determine k so that -n*k - 27*k**3 + 2 + 18*k**2 - 27*k**3 + 36*k**2 = 0.
1/3
Factor 4/5*u**2 - 4/5*u - 8/5.
4*(u - 2)*(u + 1)/5
Factor -1/7 - 2/7*v - 1/7*v**2.
-(v + 1)**2/7
Factor 2*m**4 + 18 - 35 + 12*m**3 + 17.
2*m**3*(m + 6)
Find f such that 2 + 6*f + 4*f**2 - 12*f**2 + 0*f**2 = 0.
-1/4, 1
Let x(p) = -p**3 - 11*p**2 - 8*p + 20. Let z be x(-10). Let r(d) be the second derivative of -1/6*d**4 - 1/3*d**3 + z - 3*d + 0*d**2. Factor r(y).
-2*y*(y + 1)
Let o(d) be the second derivative of d**9/1512 - d**8/280 + d**7/140 - d**6/180 - d**3/2 + d. Let j(q) be the second derivative of o(q). Factor j(r).
2*r**2*(r - 1)**3
Let m(g) be the third derivative of -8/21*g**3 + 2*g**2 + 0*g + 1/21*g**4 + 0 - 1/420*g**5. What is s in m(s) = 0?
4
Factor -n**5 + 4*n**3 - 10*n**3 + 3*n + 4*n**2 + 4*n**3 - 4*n**4.
-n*(n - 1)*(n + 1)**2*(n + 3)
Let u(m) be the first derivative of 40*m**2 + 7*m**4 + 24*m**3 + 7 + 32*m + 4/5*m**5. Factor u(a).
4*(a + 1)*(a + 2)**3
Let t = -9 + 13. Suppose -8*i**3 + 4*i**2 + 15*i**t + 6 - 23*i**2 - 2*i**2 - i**3 + 9*i = 0. Calculate i.
-1, -2/5, 1
Suppose -5/4 - o + 1/4*o**2 = 0. What is o?
-1, 5
Let c(v) = v**3 + 3*v**2 - 4*v - 3. Let j = 13 - 6. Let u(f) = 3*f**3 + 5*f**2 - 8*f - 7. Let l(w) = j*c(w) - 3*u(w). Factor l(r).
-2*r*(r - 2)*(r - 1)
Let w be (1 + 2)/((-3)/(-4)). Let k(g) be the second derivative of -1/3*g**3 + 1/2*g**2 + 1/10*g**6 + 0 + 1/10*g**5 - g - 1/3*g**w. Factor k(t).
(t - 1)*(t + 1)**2*(3*t - 1)
Let g = -22 + 18. Let a be -3 - ((-308)/36 - g). What is s in -4/9*s**3 + a*s**4 - 14/9*s**2 + 0 + 4/9*s = 0?
-1, 0, 2/7, 1
Let 0*o - 2/11*o**3 - 2/11*o**2 + 0 = 0. What is o?
-1, 0
Let b(w) be the second derivative of 25*w**7/98 - w**6/2 - 9*w**5/140 + 11*w**4/28 + w**3/7 + 13*w. Suppose b(c) = 0. What is c?
-2/5, -1/5, 0, 1
Let c(w) = -w**3 - w**2 - w + 1. Let t(h) = h**4 + 2*h**3 - h**2 + h - 1. Let b(m) = -c(m) - t(m). Factor b(u).
-u**2*(u - 1)*(u + 2)
Let l(c) be the second derivative of -c**6/105 + 4*c**5/35 - 4*c**4/7 + 32*c**3/21 - 16*c**2/7 - c. Solve l(s) = 0.
2
Let 5*q + 8*q**4 - 3*q**4 + 15*q**2 - 9*q**3 + 24*q**3 = 0. What is q?
-1, 0
Let b(a) = -a**5 + a**2 - a. Let f(p) = -3*p**5 + 16*p**4 - 20*p**3 + 7*p**2 + p. Let q(t) = b(t) + f(t). Factor q(k).
-4*k**2*(k - 2)*(k - 1)**2
Let q(b) be the third derivative of b**11/266112 - b**10/201600 - b**9/120960 + b**5/30 + 2*b**2. Let m(a) be the third derivative of q(a). Factor m(s).
s**3*(s - 1)*(5*s + 2)/4
Let r(u) be the first derivative of -2*u - 9/40*u**5 + 5/4*u**4 + 2*u**2 - 1 - 7/3*u**3. Let t(k) be the first derivative of r(k). Solve t(y) = 0 for y.
2/3, 2
Suppose -1/2*q**2 + 1/2 + 0*q = 0. What is q?
-1, 1
Let q be ((-9)/6)/(6/(-16)). Factor -8*v**3 - 8*v + 12*v**2 + 2*v**4 + v**4 + 3*v**4 - 4*v**q + 2.
2*(v - 1)**4
Let z(n) = -n - 6. Let o be z(-11). Let j be (-28)/(-2)*(-2)/(-4). Let -o*g**2 + 0*g + j*g - 2 + 0 = 0. What is g?
2/5, 1
Let c(l) be the third derivative of l**9/15120 - l**8/5040 - l**7/630 + 7*l**5/60 - 7*l**2. Let v(d) be the third derivative of c(d). Factor v(f).
4*f*(f - 2)*(f + 1)
Suppose 4*h - 1 = 15. Suppose 2*y = -0*y + h. Factor 0*n + 0*n - y*n**2 + 0*n.
-2*n**2
Let j(f) be the first derivative of -f**6/30 + f**5/5 - f**4/4 - 2*f**3/3 + 2*f**2 + 2*f - 2. Let c(a) be the first derivative of j(a). Factor c(w).
-(w - 2)**2*(w - 1)*(w + 1)
Let g be (-2)/1 + -3 + 