 + 24/5*f**2 + 4/5*f**4 - 4*f**3 + 16/5*f.
4*(f - 2)**3*(f + 1)/5
Factor -9*c**3 - 16*c + 24*c**2 + c**3 - 13*c - 3*c + 16 + c**4.
(c - 2)**4
Determine q so that -3*q**4 + 2 - 11*q**4 + 11*q**3 - 4*q**5 + 11*q + 10*q**4 + 20*q**2 = 0.
-1, -1/2, 2
Let q(k) be the third derivative of -k**7/105 - k**6/15 - k**5/10 + k**4/3 + 4*k**3/3 - 3*k**2. Find v such that q(v) = 0.
-2, -1, 1
Let n be 40/(-36)*-3 + -2 + -1. Factor 2/3*o + 1/3 + 0*o**2 - 2/3*o**3 - n*o**4.
-(o - 1)*(o + 1)**3/3
Let r(n) = 3*n - 1. Let s be r(1). Let -8 - v + 1 + v**s + 5 = 0. What is v?
-1, 2
Suppose 5*i + 2*j = 32 - 8, 3*i - 33 = 5*j. Factor -5*k**3 - 3 + 6*k**2 + 3*k**4 - i*k**4 + 5*k**3.
-3*(k - 1)**2*(k + 1)**2
Let j(u) be the second derivative of -u**6/15 + 3*u**5/5 - 2*u**4 + 8*u**3/3 + 4*u. Find m, given that j(m) = 0.
0, 2
Let z(l) be the second derivative of l**5/50 + l**4/30 - l. Factor z(s).
2*s**2*(s + 1)/5
Suppose 5 - 20 = -3*z. Factor 5*l**3 - l**z - l**2 - 2 - 8*l + l**4 + 4 - 6 + 0*l**2.
-(l - 2)**2*(l + 1)**3
Let j = 270 - 269. Solve -1/2*x**2 + 3/2*x - j = 0 for x.
1, 2
Let h be (0 - 2/(-3))*3/5. Factor 4/5*f**2 + 0 + 0*f + h*f**3 - 2/5*f**4.
-2*f**2*(f - 2)*(f + 1)/5
Let w(g) be the third derivative of 8*g**7/105 + 7*g**6/60 - 13*g**5/60 - 7*g**4/12 - g**3/2 - 39*g**2. Suppose w(z) = 0. What is z?
-1, -1/2, -3/8, 1
Let p be (-20 + 20)*(-1)/(-2). Determine f so that -1/6*f**3 + 1/6*f**2 + 0*f + p = 0.
0, 1
Factor -92 + f**4 + 35*f**2 - 9*f**3 + 56 + 12*f - 3*f**3.
(f - 6)**2*(f - 1)*(f + 1)
Let u(m) be the second derivative of -m**4/42 + 4*m**3/21 - 4*m**2/7 - 9*m. Solve u(g) = 0 for g.
2
Factor 0*c + 1/2*c**3 + c**2 + 0.
c**2*(c + 2)/2
Let g(z) = 2 - 8 + 4*z - 5*z + 0. Let w be g(-6). Factor 0 + w*j - 1/5*j**2.
-j**2/5
Solve 15*h**2 - 33*h**3 - 9*h**4 + 23*h**3 + 10*h**5 - 6*h**4 = 0 for h.
-1, 0, 1, 3/2
Let g be (-2)/3 - 14/(-12). Suppose -8 = 14*y - 50. Factor 2*n**y - g*n**4 + n - 5/2*n**2 + 0.
-n*(n - 2)*(n - 1)**2/2
Let u be (-4)/5 - 704/(-480). Factor 1/3*x + 2/3*x**2 - u - 1/3*x**3.
-(x - 2)*(x - 1)*(x + 1)/3
Let d = -59 + 63. Let m(s) be the first derivative of -5*s**2 + d*s + 14/5*s**5 + 2 + 5/2*s**4 - 6*s**3. Factor m(u).
2*(u - 1)*(u + 1)**2*(7*u - 2)
Let r = 4 + -4. Suppose 0 = -6*d + d. What is h in 0 + 2/3*h**2 + d*h + r*h**3 - 2/3*h**4 = 0?
-1, 0, 1
Let g = -7 + 9. Let -1/5*y**g + 0 - 1/5*y = 0. What is y?
-1, 0
Suppose 19*j = 6 - 6. Solve 1/3*o**2 + j + 1/3*o**3 - 1/3*o**5 - 1/3*o**4 + 0*o = 0.
-1, 0, 1
Let t be 216/135*2/8. Let t*d**2 + 0 - 2/5*d = 0. Calculate d.
0, 1
Let g(y) be the second derivative of y**6/30 + 3*y**5/10 + 2*y**4/3 - y**3 - 9*y**2/2 - 6*y. Factor g(s).
(s - 1)*(s + 1)*(s + 3)**2
Let o(n) be the second derivative of -n**5/10 + 5*n**4/3 + n**3/3 - 10*n**2 - 44*n. Factor o(p).
-2*(p - 10)*(p - 1)*(p + 1)
Let m = 6 + -3. Suppose -k - m*k = 0. Factor 2/9*t**2 - 4/9*t**3 + 0*t + k + 2/9*t**4.
2*t**2*(t - 1)**2/9
Factor 0 - 1/2*b**2 - 3/2*b.
-b*(b + 3)/2
Let h = 2592/5 - 514. Factor -18/5*n**2 - 4/5 + h*n.
-2*(n - 1)*(9*n - 2)/5
Let v(n) = -n**3 - 6*n**2 + 8*n + 4. Let c be v(-7). Let b be c + (-10)/(-4) + 1. Factor -1/2*o**2 + b*o**3 + 0*o + 0.
o**2*(o - 1)/2
Suppose -4*m - 16 = m - 4*t, 0 = 2*t - 8. Let b = -7 - -12. What is f in f - 2*f**2 + 4*f**4 - f**b + 0*f**3 + m*f**3 - 2*f**4 = 0?
-1, 0, 1
Let q be (-3 - -2) + 30/6 + 0. Let s(y) be the third derivative of 0*y**5 + 0*y + 0 - q*y**2 + 0*y**3 - 1/8*y**4 + 1/40*y**6. Factor s(k).
3*k*(k - 1)*(k + 1)
Let v be 3/3 - 17 - -2. Let s be (-6)/(-56) - 2/v. Factor 1/4*u**5 - 3/4*u**4 + 3/4*u**3 - s*u**2 + 0*u + 0.
u**2*(u - 1)**3/4
Let v(y) be the first derivative of y**4/22 + 2*y**3/11 - 4*y**2/11 + 11. Factor v(j).
2*j*(j - 1)*(j + 4)/11
Let z = -18 + 21. Let u(f) be the first derivative of 0*f**2 + 0*f + z + 1/20*f**5 + 1/24*f**6 + 0*f**3 + 0*f**4. Factor u(x).
x**4*(x + 1)/4
Solve 2*s**3 + 4 + 26/3*s + 58/9*s**2 + 2/9*s**4 = 0 for s.
-3, -2, -1
Let v(l) be the third derivative of l**6/720 + l**5/90 + l**4/48 + 2*l**2. Factor v(j).
j*(j + 1)*(j + 3)/6
Let n(f) be the second derivative of 3*f**7/56 - f**6/4 + 9*f**5/20 - 3*f**4/8 + f**3/8 + f. Factor n(s).
3*s*(s - 1)**3*(3*s - 1)/4
Factor -3/7*b - 6/7*b**3 + 0 + 9/7*b**2.
-3*b*(b - 1)*(2*b - 1)/7
Let g be (-119)/34*5/(-14). Factor g*c - 3/4*c**2 - 1/2.
-(c - 1)*(3*c - 2)/4
Let a be 1*2 + (-8 - -8). Let m(w) be the first derivative of 0*w + 1 + w**a - 4/3*w**3. Find z, given that m(z) = 0.
0, 1/2
Let q(g) be the second derivative of g**4/42 - g**3/7 - 4*g**2/7 + 10*g. Factor q(j).
2*(j - 4)*(j + 1)/7
Suppose 1 + 3 = g. Let -7*l**2 - 9*l**3 - 3*l**3 - 4*l - 7*l**4 + 3*l**g - 5*l**2 = 0. What is l?
-1, 0
Let j(p) be the first derivative of -p**5/20 + p**3/6 - p/4 - 7. Factor j(h).
-(h - 1)**2*(h + 1)**2/4
Let b = 106/15 + -12/5. Determine i, given that -b*i**3 - 8*i**2 + 0 + 8/3*i = 0.
-2, 0, 2/7
Let w be (12/36)/((-2)/(-36)). Let x(m) be the third derivative of 1/9*m**3 + 1/15*m**5 + 1/9*m**4 + 1/315*m**7 + 0 + 0*m - m**2 + 1/45*m**w. Factor x(h).
2*(h + 1)**4/3
Determine r so that -12*r**4 + 9/2*r**5 + 0 - 4*r**2 + 11*r**3 + 1/2*r = 0.
0, 1/3, 1
Let x(q) be the third derivative of -q**9/393120 + q**8/65520 - q**7/32760 + 7*q**5/60 - 4*q**2. Let l(r) be the third derivative of x(r). Factor l(f).
-2*f*(f - 1)**2/13
Let t(i) be the second derivative of i**8/2240 + i**7/560 - i**5/80 - i**4/32 + 4*i**3/3 + 5*i. Let x(l) be the second derivative of t(l). Factor x(j).
3*(j - 1)*(j + 1)**3/4
Let t be 0/(8/(6 + -2)). Let g = -94 + 660/7. Factor g*l**2 - 2/7*l + t.
2*l*(l - 1)/7
Factor -3/5*z**2 - 18/5*z - 27/5.
-3*(z + 3)**2/5
Let v be 7/3 + -2 + 198/54. What is a in -1/2*a**v - 1/2*a + 1/2*a**3 + 0 + 1/2*a**2 = 0?
-1, 0, 1
Let w be 8/(-16) + (-26)/(-4). Suppose -v - 3*a + w*a + 2 = 0, -2 = -v - 5*a. Determine f so that 0 - 2/3*f**4 + 1/3*f**5 - 1/3*f + 0*f**3 + 2/3*f**v = 0.
-1, 0, 1
Let b(l) be the second derivative of l**4/60 + l**3/30 - l**2/5 - 37*l. Suppose b(k) = 0. Calculate k.
-2, 1
Let z be -4 - 91/(-21) - 1/(-3). Let -4/3*d**2 + z*d**3 + 0 + 2/3*d = 0. What is d?
0, 1
Suppose -16*s = -20*s. Let q(l) be the first derivative of s*l + 2/15*l**3 - 1/20*l**4 + 2 - 1/10*l**2. Factor q(m).
-m*(m - 1)**2/5
Let t(s) = 3*s**5 - 2*s**4 - 2*s**3 - s - 2. Let z(h) = 2*h**5 - h**4 - h**3 - h**2 - h - 1. Let l(g) = 3*t(g) - 4*z(g). Factor l(a).
(a - 2)*(a - 1)**2*(a + 1)**2
Let y(q) be the second derivative of -q**9/756 - q**8/240 + 4*q**7/315 + q**6/45 + q**4/4 + 5*q. Let c(j) be the third derivative of y(j). Factor c(x).
-4*x*(x - 1)*(x + 2)*(5*x + 2)
Let c(k) = -k**2 - 10*k + 13. Let b be c(-11). Let -5*f**b + f**2 + 2*f + f**3 + f**3 = 0. Calculate f.
0, 1
Let h(v) be the first derivative of -1/4*v**2 + 1/8*v**4 + 1/2*v**3 - 1/10*v**5 - v - 1. Factor h(m).
-(m - 2)*(m - 1)*(m + 1)**2/2
Let g be (-22)/(-220) - (0 - -2)/(-4). Factor 0 + 0*p + g*p**2 + 3/5*p**3.
3*p**2*(p + 1)/5
Let z(m) be the first derivative of m - 2*m**2 + 7 - 1/3*m**3 + m**4. Determine h, given that z(h) = 0.
-1, 1/4, 1
Let j(l) be the third derivative of l**8/1344 + l**7/280 - l**5/60 + 17*l**2. Factor j(o).
o**2*(o - 1)*(o + 2)**2/4
Let c(h) be the second derivative of 3/70*h**7 + 1/10*h**2 + h - 1/10*h**4 + 7/50*h**6 + 1/10*h**5 - 1/10*h**3 + 0. Suppose c(o) = 0. What is o?
-1, 1/3
Let j(n) = -n. Let k = -5 + 3. Let o be j(k). Factor -2*y**4 + 4*y**2 - o*y**2 + 4*y**3 - 4*y**2.
-2*y**2*(y - 1)**2
Let i(x) be the first derivative of -x**5/5 + 2*x**4/3 - x**3/9 - 4*x**2/3 + 4*x/3 - 18. Find j such that i(j) = 0.
-1, 2/3, 1, 2
Let f(r) = -3*r. Let z be f(5). Let i = -10 - z. Find j such that -i*j + j + 2*j + j**2 + 1 = 0.
1
Let u(s) be the first derivative of -s**4/26 + 2*s**3/13 - 2*s**2/13 - 4. Suppose u(l) = 0. Calculate l.
0, 1, 2
Let k(s) = s**4 + s**3 - s**2. Let d(o) = -9*o**4 - 14*o**3 + 7*o**2 + 3*o + 2. Let f(a) = -2*d(a) - 22*k(a). Determine r so that f(r) = 0.
-1, -1/2, 1, 2
Let w be 59/3 + 1/3. Suppose n - 6*n = -w. What is q in 2*q**5 + 4/3*q**2 - 14/3*q**n - 2/3*q + 20/9*q**3 - 2/9 = 0?
-1/3, 1
Suppose -3*x + 4*r + 4 = -5, 5*r - 6 = -2*x. Factor 0 + 2/9*h**4 + 2/9*h**x + 0*h + 0*h**2.
2*h**3*(h + 1)/9
Let y = -19/4 + 99/20. Factor -y*l**5 + 0 + 0*l**2 + 0*l + 2/5*l**4 - 1/5*l**3.
-l**3*(l - 1)**2/5
Let i be (-18)/(-28) + (-5)/10. Let y(h) be the se