he second derivative of -f**4/48 - f**3/8 + f**2/2 - 8*f. Factor r(q).
-(q - 1)*(q + 4)/4
Let l(m) = -m + 13. Let h be l(10). Suppose -z**3 - z**2 - z**h + z**3 + 11*z**4 + z**5 - 10*z**4 = 0. What is z?
-1, 0, 1
Let x(j) be the second derivative of -j**7/14 - j**6/5 - 3*j**5/16 - j**4/16 - 8*j. Factor x(y).
-3*y**2*(y + 1)*(2*y + 1)**2/4
Let u(m) be the third derivative of -49*m**6/40 + 63*m**5/10 - 15*m**4/2 + 4*m**3 + 14*m**2. Factor u(x).
-3*(x - 2)*(7*x - 2)**2
Factor 2*q + 4/3 + 2/3*q**2.
2*(q + 1)*(q + 2)/3
Let z(g) = -g**2 - 4*g. Let i be z(-3). Suppose 5*r - i = d - 6, 15 = 5*d + 2*r. Factor -d*c**3 - 2*c**2 + 2*c**2 + 4*c**3 - c**5.
-c**3*(c - 1)*(c + 1)
Let c be (-16)/(-48) - 1/3. Find r, given that 0*r**2 + 1/4*r**4 + 0*r**3 + 0*r + c = 0.
0
Suppose 2*f = 4*j - 14, -4*j = -3*j - 4*f. Factor 4/5*l**j + 0*l**2 - 2/5*l**5 + 0 - 2/5*l**3 + 0*l.
-2*l**3*(l - 1)**2/5
Let -8 - 3*p**2 + p**2 + 8*p + p**2 - p**2 = 0. Calculate p.
2
Suppose h - 11 - 20 = 0. Suppose -41*x**2 - 10*x**3 + 6*x + h*x**3 + 14*x**2 = 0. Calculate x.
0, 2/7, 1
Let i(n) = 2*n**5 + 4*n**4 + 6*n**3 - 18*n**2 - 6*n - 6. Let t(h) = -h**4 - h - 1. Let m(g) = i(g) - 6*t(g). Find k, given that m(k) = 0.
-3, 0, 1
Let s be 2/7 + 38/14. Let x = s + 3. Factor -x*q**3 + 2*q**3 + 2*q**2 - q**4 + 3*q**4.
2*q**2*(q - 1)**2
Suppose 57*w = 52*w + 15. Factor -6/5*f**2 + 6/5*f**w - 2/5*f**4 + 2/5*f + 0.
-2*f*(f - 1)**3/5
Find n such that -72/13*n**2 + 16/13*n - 50/13*n**5 + 4*n**3 + 0 + 90/13*n**4 = 0.
-1, 0, 2/5, 2
Let g(b) = -23*b**3 + 38*b**2 - 13*b - 8. Let k(y) = 47*y**3 - 77*y**2 + 27*y + 17. Let c(d) = -7*g(d) - 3*k(d). Find p, given that c(p) = 0.
-1/4, 1
Let x(v) be the second derivative of 0 - 1/273*v**7 + 0*v**3 + 0*v**5 - v + 2/195*v**6 + 0*v**4 + 0*v**2. Suppose x(c) = 0. What is c?
0, 2
Suppose -6*x - 20 = -x. Let y = 7 + x. Factor 1/2*c**4 + 0*c + 1/2*c**2 + 0 + c**y.
c**2*(c + 1)**2/2
Factor 1/2*m**3 - 1/4*m**5 + 1/4*m**4 + 1/4 - 1/2*m**2 - 1/4*m.
-(m - 1)**3*(m + 1)**2/4
Let j(t) be the first derivative of t**3 + 3*t**2 + 3*t - 21. Factor j(n).
3*(n + 1)**2
Let z = 2/301 + 27682/1505. Let 4/5 + z*p**4 - 22/5*p**5 - 38/5*p - 148/5*p**3 + 112/5*p**2 = 0. Calculate p.
2/11, 1
Let 0*y**2 - 3/5 - 6/5*y + 6/5*y**3 + 3/5*y**4 = 0. Calculate y.
-1, 1
Let n(o) be the first derivative of -o**4/24 - 5*o**3/6 - 25*o**2/4 - 125*o/6 + 32. Factor n(c).
-(c + 5)**3/6
Let h(u) = u**4 - u**3 - u. Let l(i) = -3*i**5 + 3*i**3 + 6*i. Let b(n) = -6*h(n) - l(n). Factor b(x).
3*x**3*(x - 1)**2
Solve 0 + 0*h - 1/6*h**5 + 0*h**2 - 1/3*h**3 - 1/2*h**4 = 0 for h.
-2, -1, 0
What is h in h - h - 4*h**2 - 126*h**4 + 2*h**3 + 128*h**4 = 0?
-2, 0, 1
Let a(o) = o**2 - 7*o + 8. Let j(f) = f**2 + 2*f + 6. Let r be j(0). Let h be a(r). Factor -2*u + 2/3*u**h + 4/3.
2*(u - 2)*(u - 1)/3
Let c(u) be the first derivative of 10*u**3/9 - 11*u**2/3 + 4*u/3 + 5. Factor c(h).
2*(h - 2)*(5*h - 1)/3
Let v(g) = 13*g**2 + 9. Suppose l - 6*l = -30. Let d(n) = -n**2 - 6*n**2 - 1 - 4. Let j(m) = l*v(m) + 11*d(m). Factor j(s).
(s - 1)*(s + 1)
Let a(x) be the second derivative of 0*x**2 + 0 - 1/66*x**4 + 2*x - 1/110*x**5 + 0*x**3. Factor a(y).
-2*y**2*(y + 1)/11
Let -g**5 - 3*g + 4*g**4 - 6*g**3 + 3*g + 4*g**2 - g = 0. What is g?
0, 1
Let x(q) be the third derivative of 0*q**5 - 1/60*q**6 + 0*q**3 + 0 + 0*q**4 + 0*q - 3*q**2. Let x(j) = 0. Calculate j.
0
Let z be 2 - (-7 - (-12 + 6)). Suppose 2*r = -l + 8, -r = -6*r - 2*l + 21. Find x such that 2/3*x**z + 0 + 0*x**2 + 4/3*x**4 + 0*x + 2/3*x**r = 0.
-1, 0
Let c be (-21)/(-14) + (-3)/(-2). Let h(p) be the first derivative of 2*p - 7*p**2 + 16/3*p**c + 8*p**4 + 2. Factor h(m).
2*(m + 1)*(4*m - 1)**2
Let s(l) = -4*l**2 - 21*l - 2. Let g be s(-5). Let q(u) be the first derivative of 2/3*u**g + 1/8*u**4 + u**2 - 3 + 0*u. Factor q(x).
x*(x + 2)**2/2
Let h(z) be the third derivative of -z**8/3360 - z**7/315 - z**6/90 + 5*z**4/24 + 3*z**2. Let f(y) be the second derivative of h(y). What is k in f(k) = 0?
-2, 0
Suppose 3*w - w - 4 = 0. What is k in 2*k**4 + 1 + k**2 + 1 - 5*k**w = 0?
-1, 1
Let k(m) be the second derivative of -3/4*m**4 + 0*m**3 + 0 + 4*m - 3/20*m**5 + 6*m**2. Factor k(i).
-3*(i - 1)*(i + 2)**2
Let w(x) = -3*x**3 + 7*x**2 - x - 3. Let j(i) = 2*i**3 - 6*i**2 + 2. Let t(b) = 4*j(b) + 3*w(b). Solve t(u) = 0 for u.
-1
Let y(t) = t**3 + 10*t**2 + 18*t + 4. Let o be y(-8). Let k(q) = q**2 + 11*q - 9. Let a be k(o). Factor -2/7*l**a - 16/7*l + 8/7 + 10/7*l**2.
-2*(l - 2)**2*(l - 1)/7
Let t(h) be the first derivative of h**4/16 - h**3/6 + h**2/8 + 18. What is d in t(d) = 0?
0, 1
Let h(b) = b**5 - 15*b**4 + b**3 + 15*b**2 - 14*b - 4. Let f(x) = 4*x**5 - 45*x**4 + 4*x**3 + 45*x**2 - 41*x - 11. Let c(m) = 4*f(m) - 11*h(m). Factor c(r).
5*r*(r - 2)*(r - 1)**2*(r + 1)
Suppose -4*n = -1 - 15. Suppose 0 = 5*i - n*h, 0 = i - 3*i - h. Let i + 0*j - 1/3*j**2 = 0. What is j?
0
Let p(l) be the first derivative of 2*l**3/27 - 4*l**2/9 + 2*l/3 + 11. Factor p(w).
2*(w - 3)*(w - 1)/9
Find l, given that 2/3*l - 1/3*l**3 + 0 + 1/3*l**2 = 0.
-1, 0, 2
Let s(t) be the second derivative of 0 - 3*t - 1/21*t**3 - 1/42*t**4 + 2/7*t**2. Determine l, given that s(l) = 0.
-2, 1
Let d(q) be the third derivative of q**5/60 + q**4/6 + q**3/6 - 2*q**2. Let h(t) = -2*t**2 - 9*t - 3. Let i(x) = 7*d(x) + 3*h(x). Factor i(b).
(b - 1)*(b + 2)
Let m be (1/(-2))/(2 + 133/(-28)). Let 4/11 - 2/11*b - m*b**2 = 0. What is b?
-2, 1
Suppose 4*x - 3*h = 13 - 5, -3*x + 6 = -h. Let l(z) be the first derivative of -1/15*z**5 + 0*z - 1/6*z**4 + 2 + 0*z**3 + 0*z**x. Factor l(a).
-a**3*(a + 2)/3
Factor -q**2 + 0*q + 0 + 1/2*q**4 + 1/2*q**3.
q**2*(q - 1)*(q + 2)/2
Let i = -21 + -6. Let j be (-14)/21*i/12. Factor -1/2*z**5 - 3/2*z**3 + 0 + 0*z - 1/2*z**2 - j*z**4.
-z**2*(z + 1)**3/2
Let x(k) = 8*k**4 + 4*k**3 + 4. Let s(b) = 9*b**4 + 4*b**3 + b**2 + b + 5. Let y(p) = -4*s(p) + 5*x(p). Factor y(r).
4*r*(r - 1)*(r + 1)**2
Solve 3/4*c**2 - 1/4*c**3 + 0*c + 0 = 0 for c.
0, 3
Suppose 24 + 44 = 2*u - 4*k, -4*k - 152 = -5*u. Suppose 2 + 4 = a + b, u = 4*a + 5*b. Solve -2*m**2 + a*m - 2 + m + m = 0.
1
Let c = 5259/10 + -525. Let u(b) be the second derivative of 4*b + 0 - 6/5*b**3 - 27/100*b**5 - c*b**4 - 4/5*b**2. Factor u(t).
-(3*t + 2)**3/5
What is u in -1/4*u**2 - u + 5/4 = 0?
-5, 1
Suppose 72*g**3 + 6 - 6*g - 14*g - 84*g**3 + 2*g**4 + 24*g**2 = 0. Calculate g.
1, 3
Let q be (35/(-10))/7 + 2. Solve 0*h + 3/2*h**3 + 0 + q*h**2 = 0.
-1, 0
Let o(p) = -9*p**5 - 3*p**4 + 10*p**3 + 6*p**2 + 2. Let q(a) = -18*a**5 - 6*a**4 + 21*a**3 + 13*a**2 + 5. Let t(v) = 5*o(v) - 2*q(v). Find r such that t(r) = 0.
-2/3, 0, 1
Let s(g) be the third derivative of g**5/150 + g**4/10 + 20*g**2. Factor s(v).
2*v*(v + 6)/5
Let l(s) be the first derivative of 2*s**3/9 + 8*s**2/3 - 24. Find z such that l(z) = 0.
-8, 0
Let k(s) be the third derivative of -s**6/60 + s**5/15 - s**4/12 - s**3/3 - 3*s**2. Let f(p) be the first derivative of k(p). What is b in f(b) = 0?
1/3, 1
Let b(d) be the third derivative of -d**5/30 - d**4/2 - 3*d**3 + 9*d**2. Find p, given that b(p) = 0.
-3
Let q be 4/(-28)*(-84)/8. Suppose 3/4 - 3/4*z - q*z**2 = 0. What is z?
-1, 1/2
Let q = 8 - 5. Suppose -q*h = 3*u - 9, 2*h = 5*h - 5*u - 1. Factor h*m - 3*m**3 - 4*m**3 + 5*m**3 + 2*m**2 - 1 - 1.
-2*(m - 1)**2*(m + 1)
Let k(t) = 20*t**4 - 40*t**3 - 4*t**2 + 24*t - 16. Let h(u) = 4*u**4 - 8*u**3 - u**2 + 5*u - 3. Let c(l) = -16*h(l) + 3*k(l). Factor c(v).
-4*v*(v - 2)*(v - 1)*(v + 1)
Let l(s) = -s**3 + 4*s**2 - 12*s + 8. Let z(m) = -5*m**3 + 19*m**2 - 60*m + 40. Let k(a) = -11*l(a) + 2*z(a). Find t, given that k(t) = 0.
2
Suppose 0 = 8*b - 3*b - 15. Suppose 4*n - 12 = 0, 3 + 5 = -l + b*n. Factor -q**2 - l + 0*q**2 + 6*q - 4*q.
-(q - 1)**2
Let d = -444/11 - -4304/99. Let r = 32/9 - d. Solve -2/9*c + 0 - r*c**2 - 2/9*c**3 = 0.
-1, 0
Factor -32/11 - 16/11*l - 2/11*l**2.
-2*(l + 4)**2/11
Let a(g) be the first derivative of 2*g**6/9 + 91*g**5/15 + 649*g**4/12 + 1112*g**3/9 - 1184*g**2/3 + 512*g/3 + 4. Factor a(f).
(f - 1)*(f + 8)**3*(4*f - 1)/3
Let c(t) be the second derivative of 0 - 3/5*t**5 - 1/10*t**6 - 3/2*t**2 - 2*t**3 - 3*t - 3/2*t**4. Factor c(p).
-3*(p + 1)**4
Factor 6*w**5 + 12*w**3 + 4*w**2 - 2*w**5 + 8*w**4 + 4*w**4.
4*w**2*(w + 1)**3
Let s be 43/30 + 5/(-50). Factor -s*d + 4/3*d**