4*o.
2*o*(o + 1)
Let s(x) = -x - 10. Let f be s(-13). Let u(v) = 3. Let t(y) = -y**2 + y - 3. Let b(a) = f*t(a) + 3*u(a). Let b(q) = 0. What is q?
0, 1
Let z(a) = -9*a**2 - 6. Let k(n) = 10*n**2 + n + 7. Let m(w) = -6*k(w) - 7*z(w). Factor m(j).
3*j*(j - 2)
Let b = -91/88 + 9/8. Let g(h) be the first derivative of -1/22*h**4 + 0*h - 2 - 2/33*h**3 + b*h**2 + 2/55*h**5. Factor g(v).
2*v*(v - 1)**2*(v + 1)/11
Let s(o) = o**4 + o + 1. Let y(z) = 2*z**5 + z**4 - 8*z**3 - 4*z**2 + 7*z + 5. Let g(t) = 2*s(t) - 2*y(t). Determine v, given that g(v) = 0.
-1, 1, 2
Let g(c) = -3*c**4 + 2*c**4 + 2*c - 3*c. Let x = -5 + 1. Let p(t) = -t**5 + 3*t**4 + t**3 + t**2 + 4*t. Let l(y) = x*g(y) - p(y). Factor l(v).
v**2*(v - 1)*(v + 1)**2
Let t be ((-21)/(-5) - 1) + -2. Suppose -4*y = -5*c + 18, 0 = -3*c + 5*c + 5*y + 6. Solve -6/5*b - 4/5*b**4 - t*b**5 + 12/5*b**3 + 8/5*b**c - 4/5 = 0.
-1, -2/3, 1
Factor 4/3*h + 2/3 + 2/3*h**2.
2*(h + 1)**2/3
Let q(w) be the third derivative of 17/240*w**6 + 0 - 1/84*w**7 + 11/48*w**4 - 7/40*w**5 - 3*w**2 - 1/6*w**3 + 0*w. What is n in q(n) = 0?
2/5, 1
Let k(m) be the third derivative of 1/6*m**3 + m**2 + 0*m - 1/180*m**5 - 1/540*m**6 + 0*m**4 + 0. Let f(n) be the first derivative of k(n). Factor f(j).
-2*j*(j + 1)/3
Let f(q) = 5*q**4 - 5*q**3 - 5*q**2 + 7*q. Let k(t) = -60*t**4 + 60*t**3 + 60*t**2 - 85*t. Let c(l) = -25*f(l) - 2*k(l). Factor c(h).
-5*h*(h - 1)**2*(h + 1)
Let y(p) be the third derivative of -p**6/90 + p**4/6 + 4*p**3/9 + 5*p**2. Factor y(w).
-4*(w - 2)*(w + 1)**2/3
Let u(h) be the second derivative of 0*h**3 + 0*h**5 - 1/18*h**4 + 0 + 0*h**2 + h + 1/45*h**6. Factor u(r).
2*r**2*(r - 1)*(r + 1)/3
Let t(k) be the first derivative of -512/5*k**5 - 2*k - 64*k**3 + 16*k**2 - 2 + 128*k**4. Solve t(r) = 0 for r.
1/4
Let j = -90 - -92. Factor 0 + 2/5*i + 1/5*i**j - 1/5*i**3.
-i*(i - 2)*(i + 1)/5
Let o(n) be the second derivative of n**6/100 - n**5/75 - n**4/60 + n**2 - 5*n. Let j(p) be the first derivative of o(p). Find h such that j(h) = 0.
-1/3, 0, 1
Let g = 25/42 + 1/14. Solve 2/3*h**3 + 0*h - 4/3*h**4 + 0*h**2 + g*h**5 + 0 = 0.
0, 1
Suppose -2*j + 0*r + 34 = -4*r, 2*j - 3*r = 31. Solve -2*o**3 + 0*o**2 + j*o**2 + 8 - o**2 - 16*o = 0 for o.
1, 2
Let c(v) = -2*v**3 + v**2 + v + 1. Let m be c(-1). Let u be 4 + -3 + m - 1. Let -2/7 + 2/7*f**2 + 8/7*f - 8/7*f**u = 0. What is f?
-1, 1/4, 1
Let t be (-6)/(-2) + (-7620)/2828. Let u = -2/101 + t. Determine i, given that 0 + 4/7*i**3 - u*i**2 - 2/7*i**4 + 0*i = 0.
0, 1
Let n(q) be the third derivative of -q**6/180 + q**4/12 + 2*q**3/9 + 23*q**2. Let n(p) = 0. What is p?
-1, 2
Solve 0 + 1/5*k**3 + 0*k - 1/5*k**5 - 2/5*k**4 + 2/5*k**2 = 0.
-2, -1, 0, 1
Let v = 38 + -20. Let -39*t**2 - v*t**3 - 14 - 2*t**4 + 2 - 36*t - t**4 = 0. What is t?
-2, -1
Suppose 0*s + a = 4*s - 3, 5*s + 3*a = -9. Suppose 8*j = -10 + 42. Let 6/5*g**2 + 6/5*g**3 + 2/5*g**j + 2/5*g + s = 0. Calculate g.
-1, 0
Suppose -t - 57 = -5*f, 2*f + 4*t - 3 = f. Let s(d) = -15*d**2 - 7*d - 11. Let q(i) = -8*i**2 - 4*i - 6. Let m(c) = f*q(c) - 6*s(c). Find r such that m(r) = 0.
0, 1
Suppose -p = 2*p + 27. Let j = -7 - p. Factor 3/2 - 3/4*d**j - 3/4*d.
-3*(d - 1)*(d + 2)/4
Let y(s) be the first derivative of s**5/10 - 3*s**4/8 + s**2 - 3. Factor y(q).
q*(q - 2)**2*(q + 1)/2
Let m(u) = -u - 3. Let t be m(-5). Suppose -v + o = -11, -v = -t*v - 2*o + 2. Factor -2 + 2*k**3 - 3*k**3 + v*k - 5*k.
-(k - 1)**2*(k + 2)
Let z(t) be the third derivative of -6*t**5/95 - t**4/19 - t**3/57 - 26*t**2. Factor z(c).
-2*(6*c + 1)**2/19
Let v = 138/7 - 134/7. Solve 2/7*w - 2/7*w**3 - 4/7*w**4 + 0 + v*w**2 = 0.
-1, -1/2, 0, 1
Suppose 3 = -19*i + 3. Factor 2/13*c**2 + 0*c + i.
2*c**2/13
Let s(n) be the second derivative of 2*n + n**3 + 0 + 3/2*n**2 + 1/4*n**4. Factor s(k).
3*(k + 1)**2
Factor 1/10*d**2 + 0*d - 2/5*d**3 + 0.
-d**2*(4*d - 1)/10
Let i(o) be the second derivative of -o**4/60 - o**3/15 + 3*o**2/10 - 2*o - 5. What is k in i(k) = 0?
-3, 1
Let c(i) be the third derivative of i**8/60480 + i**7/5040 + i**6/1080 + i**5/30 - 2*i**2. Let t(d) be the third derivative of c(d). Find j such that t(j) = 0.
-2, -1
Let w be (-2*(-3)/(-8))/(714/(-272)). Find m, given that 4/7 + 2/7*m - w*m**2 = 0.
-1, 2
Suppose -4*z = -6 + 6. Let g(m) be the second derivative of z + 0*m**2 - 1/15*m**3 - 1/50*m**5 + 1/15*m**4 - m. Solve g(r) = 0.
0, 1
Factor 55*l**2 + 18 + 16 - 85*l - 4 + 0.
5*(l - 1)*(11*l - 6)
Let g(a) be the third derivative of a**8/560 + 3*a**7/350 + 3*a**6/200 + a**5/100 + 11*a**2 - 2*a. Let g(u) = 0. Calculate u.
-1, 0
Factor 0 + 0*a - 2/7*a**4 - 2/7*a**3 + 2/7*a**2 + 2/7*a**5.
2*a**2*(a - 1)**2*(a + 1)/7
Let h(l) be the second derivative of -5*l**4/12 - 5*l**3/3 - 5*l**2/2 - 7*l. Determine n, given that h(n) = 0.
-1
Let g(h) be the first derivative of -2*h**3/9 - h**2/6 + 8. Factor g(r).
-r*(2*r + 1)/3
Let v(d) be the first derivative of 2/27*d**3 + 2 - 1/9*d**2 + 0*d. Factor v(f).
2*f*(f - 1)/9
Factor 0*p**2 + 2/3*p**4 + 0 - 1/3*p**5 + 0*p - 1/3*p**3.
-p**3*(p - 1)**2/3
Factor -100/3 - 1/3*c**2 - 20/3*c.
-(c + 10)**2/3
Suppose -5*m = -3*a, -a = 5*m - 0*a - 20. Determine u, given that -2 - 1 - 12*u + 1 - m*u**2 - 7 = 0.
-3, -1
Factor -8/9*y + 0*y**2 + 2/3*y**3 + 0 + 2/9*y**4.
2*y*(y - 1)*(y + 2)**2/9
Suppose -4*g + 6 = -2*g. What is j in -2/3*j + 2/3*j**5 + 0 + 4/3*j**4 + 0*j**g - 4/3*j**2 = 0?
-1, 0, 1
Let k = -134 - -139. Factor -1/6*h**3 + 0*h**2 + 0 - 8/3*h**k - 4/3*h**4 + 0*h.
-h**3*(4*h + 1)**2/6
Let v(o) = -2*o**2 - o + 1. Let h(b) = 3*b**2 + 2*b - 1. Let q = -5 + 1. Let u(x) = q*v(x) - 3*h(x). Factor u(i).
-(i + 1)**2
Let o be 4/(3 - -5)*0. Factor 0*b**2 + 3/2*b**4 + 3*b**3 + o*b + 0.
3*b**3*(b + 2)/2
Let j be 4/14*(-10 + 11). Factor -18/7*r**5 - 6/7*r**4 + 0 + 10/7*r**3 + 0*r - j*r**2.
-2*r**2*(r + 1)*(3*r - 1)**2/7
Let v be (45/27 - 2)*(-18)/2. Factor -10/7*z**4 - 22/7*z - 6*z**2 - 34/7*z**v - 4/7.
-2*(z + 1)**3*(5*z + 2)/7
Let m(s) = 8*s**3 + 50*s**2 + 386*s - 6. Let o(p) = 7*p**3 + 51*p**2 + 387*p - 5. Let w(d) = -5*m(d) + 6*o(d). Suppose w(z) = 0. What is z?
-14, 0
Let s = 139 + -136. Determine m so that -4/9*m**2 - 2/9*m**s + 0 - 2/9*m = 0.
-1, 0
Let u(h) be the third derivative of h**8/336 + h**7/105 - h**5/30 - h**4/24 - 5*h**2. Determine c so that u(c) = 0.
-1, 0, 1
Suppose -2 + 1 = -y, 0 = -2*a - y - 45. Let j = a + 27. Factor 0*u - 2/3*u**j + 0*u**2 - 4/3*u**3 + 0.
-2*u**3*(u + 2)/3
Suppose 2*b - n = 6, -b + n = 5*n + 6. Suppose -b*o + 8 = 2*o. Factor -t**5 - 2*t**5 - t**4 + 4*t**5 + t + o*t**4 + 1 - 2*t**2 - 2*t**3.
(t - 1)**2*(t + 1)**3
Let d(z) = z**3 + 12*z**2 - 47*z - 28. Let i be d(-15). Factor -h - 1/3*h**i + 0.
-h*(h + 3)/3
Let t(y) be the third derivative of y**7/6300 + y**6/900 - y**4/6 - 4*y**2. Let c(o) be the second derivative of t(o). Factor c(f).
2*f*(f + 2)/5
Factor 4*u**2 + 0 + 8/3*u**4 - 2/3*u - 6*u**3.
2*u*(u - 1)**2*(4*u - 1)/3
Let z(t) be the third derivative of t**8/588 - 2*t**7/735 - t**6/210 + t**5/105 - 14*t**2. Factor z(n).
4*n**2*(n - 1)**2*(n + 1)/7
Suppose j - 4*j + 43 = y, 3*j + 5*y = 23. Suppose 2*u**5 - 2*u**3 - j*u + 16*u - 2*u**4 + 2*u**2 = 0. Calculate u.
-1, 0, 1
Let n(k) be the first derivative of -k**6/6 + 9*k**5/5 - 31*k**4/4 + 17*k**3 - 20*k**2 + 12*k - 13. Factor n(i).
-(i - 3)*(i - 2)**2*(i - 1)**2
Find v such that 52/7*v - 288/7*v**4 + 624/7*v**3 - 2/7 - 386/7*v**2 = 0.
1/12, 1
Let q(a) be the third derivative of a**8/336 + 4*a**7/105 + 5*a**6/24 + 19*a**5/30 + 7*a**4/6 + 4*a**3/3 - 4*a**2. Determine k, given that q(k) = 0.
-2, -1
Let m be (-72)/(-33) + (-2)/11. Factor 4*g**2 - 2*g**4 + 3*g**2 + 2*g**3 - m*g**5 - 3*g**2 - 2*g**2.
-2*g**2*(g - 1)*(g + 1)**2
Let o(u) = -u**3 + u**2 - u. Let s(k) = -5*k**3 + 7*k**2 - 5*k. Let v be (-3 - -1)*24/16. Let r(p) = v*o(p) + s(p). Factor r(j).
-2*j*(j - 1)**2
Let a(h) = h - 2. Let r be a(-7). Let f be 3 + (-3 - 24/r). Find c, given that 2/3*c**2 - f*c + 8/3 = 0.
2
Let j(n) be the third derivative of 5*n**8/336 - 4*n**7/21 + 25*n**6/24 - 19*n**5/6 + 35*n**4/6 - 20*n**3/3 - n**2. Factor j(u).
5*(u - 2)**3*(u - 1)**2
Factor 3/5 - 3/5*i**3 - 7/5*i**2 + 7/5*i.
-(i - 1)*(i + 3)*(3*i + 1)/5
Let r = -9 + 14. Factor r*l - l**2 + l - 2*l**2.
-3*l*(l - 2)
Let n(g) be the second derivative of 3*g**5/40 - g**4/4 + g**3/4 - 8*g. Factor n(s).
3*s*(s