*i + 2/3*i**2.
2*i*(i + 2)/3
Let u(s) be the first derivative of -2 - s**3 + 0*s - 3/4*s**4 - 1/5*s**5 - 1/2*s**2. Find h, given that u(h) = 0.
-1, 0
Let z = 567/4 - 141. Determine t, given that 3/4*t**3 - z*t - 1/4*t**2 - 1/4 + 1/2*t**4 = 0.
-1, -1/2, 1
Let t(n) be the second derivative of -n**4/48 + n**2/8 + 15*n. Factor t(g).
-(g - 1)*(g + 1)/4
Solve -2/7*s**5 + 2/7*s**3 - 4/7*s**2 + 0 + 0*s + 4/7*s**4 = 0.
-1, 0, 1, 2
Solve -10/3*g**3 - 2/3*g**2 + 0 - 8/3*g**4 + 0*g = 0.
-1, -1/4, 0
Suppose -3*v = -2*v. Let g(n) be the third derivative of 1/270*n**5 + 0*n**6 + 0 - n**2 + v*n + 0*n**3 - 1/945*n**7 + 0*n**4. Factor g(t).
-2*t**2*(t - 1)*(t + 1)/9
Let t = 11 + -26. Let a be (-36)/t - 2/5. Find m such that m**3 + 1/2 - m - 1/2*m**a = 0.
-1, 1/2, 1
Suppose -8*u + 3*u = -10. Suppose 5*l = -b + 12, -u*l = -0*b - 2*b. Find r such that -r**2 + 11*r**2 - l*r + 6*r = 0.
-2/5, 0
Let v(y) = -y**5 + y**4 + y**3 + y**2 + y. Let h(i) = -6*i**5 + 2*i**4 + 16*i**3 + 4*i**2 + 4*i. Let m(s) = h(s) - 4*v(s). Factor m(z).
-2*z**3*(z - 2)*(z + 3)
Let p be ((-2)/(-3))/((-3)/(-9)). Factor 1/2*g**2 + 2 + p*g.
(g + 2)**2/2
Suppose -5*x + 20 = 0, -2*x + 200 = 5*h + 72. Suppose 0 = -3*q - 3*p - 3 + h, 4*q = 3*p - 7. Factor -1/2*n**3 + 1/2*n - 1/2*n**q + 1/2.
-(n - 1)*(n + 1)**2/2
Let q(m) = -m**2. Let a(k) = -13*k**2 - 8*k - 6. Let y(v) = -2*a(v) + 22*q(v). Factor y(n).
4*(n + 1)*(n + 3)
Let a(o) = 4*o + o**2 + 7*o**2 - 2*o + 1 - 5*o**3. Let i(t) = t + 1. Let k(s) = 2*a(s) - 6*i(s). Factor k(q).
-2*(q - 1)**2*(5*q + 2)
Let t = 6 - 0. Let n(b) be the third derivative of b**2 + 1/120*b**5 + 0 + 0*b + 0*b**4 + 0*b**3 - 1/240*b**t. What is x in n(x) = 0?
0, 1
Let o(g) = g**3 + 7*g**2 - 36. Let j be o(-6). Factor 4/9*n + 2/9*n**3 - 2/3*n**2 + j.
2*n*(n - 2)*(n - 1)/9
Let d(w) be the first derivative of -w**6/1440 - w**5/240 - 2*w**3/3 + 6. Let c(y) be the third derivative of d(y). Factor c(r).
-r*(r + 2)/4
Suppose 3 = -y, l + 4*y = 2*l - 15. Let x = 382/3 - 126. Factor -8/3*z + x*z**2 - 2/9*z**l + 16/9.
-2*(z - 2)**3/9
Let w(j) = 4*j**2 + 4*j - 2. Let n(t) = 3 - 8*t**2 - t**2 + 0*t - 4*t + 5*t**2. Let z(i) = 6*n(i) + 5*w(i). Factor z(s).
-4*(s - 1)*(s + 2)
Let p(l) = 265*l**4 - 50*l**3. Let k(o) = -38*o**4 + 7*o**3. Let r(j) = -20*k(j) - 3*p(j). Factor r(g).
-5*g**3*(7*g - 2)
Let m = -1 - -1. Let h be 0/(-17 + 6) + (-1)/(-3). What is s in -s**4 + m - 1/3*s + h*s**3 + s**2 = 0?
-1, 0, 1/3, 1
Let g(d) be the first derivative of 5*d**6/6 - 6*d**5 + 10*d**4 + 80*d**3/3 - 120*d**2 + 160*d + 60. Solve g(i) = 0 for i.
-2, 2
Let j = 266/11 - 22. Factor -j*c + 16/11 - 10/11*c**3 - 36/11*c**2.
-2*(c + 2)**2*(5*c - 2)/11
Find g, given that 2/5*g**2 + 2/5*g**3 - 2/5 - 2/5*g = 0.
-1, 1
Let y(a) be the third derivative of -a**8/1176 - a**7/735 + 29*a**2. Determine w so that y(w) = 0.
-1, 0
Suppose 2*p - 14 = 4*r, 0 = -0*p - 2*p + 5*r + 16. Find u, given that 0*u + 0 + 4/7*u**p + 2/7*u**4 + 2/7*u**2 = 0.
-1, 0
Let j(l) = l**3 - 6*l**2 + 9*l + 3. Let g be j(3). Factor 0*q + 1/5*q**g - 1/5*q**2 + 0.
q**2*(q - 1)/5
Let o(m) be the second derivative of 1/30*m**4 + 2*m + 2/15*m**3 + 0*m**2 + 0. Factor o(k).
2*k*(k + 2)/5
Suppose 2*d - 13 = 5. Factor 42*n**4 - 38*n**4 + d*n - 12*n**3 + 7*n.
4*n*(n - 2)**2*(n + 1)
Let n(k) be the first derivative of k**4/48 + k**3/36 - 8. Factor n(s).
s**2*(s + 1)/12
Let m = -17567/48 - -366. Let z(r) be the second derivative of r + 0 - 1/6*r**3 - 1/2*r**2 - m*r**4. Suppose z(w) = 0. What is w?
-2
Let a(g) be the third derivative of g**8/100800 - g**7/8400 - g**5/10 - 7*g**2. Let d(n) be the third derivative of a(n). Factor d(f).
f*(f - 3)/5
Factor -14/9*x**3 + 2/3*x**4 - 1/9*x**5 - x + 2/9 + 16/9*x**2.
-(x - 2)*(x - 1)**4/9
Let g(i) = 5*i**3 + 6*i**2 + i - 2. Let k(r) = 6*r**3 + 6*r**2 - 3. Let y(x) = 3*g(x) - 2*k(x). Factor y(s).
3*s*(s + 1)**2
Let k(s) = -15*s**4 + 10*s**3 + 40*s**2 + 5*s - 5. Let v(w) = -16*w**4 + 11*w**3 + 41*w**2 + 6*w - 4. Let l(d) = 4*k(d) - 5*v(d). Solve l(i) = 0.
-1, -1/4, 0, 2
Let -8*s**3 - 5 - 34*s**2 - 23*s - 1 - 19*s + 10*s = 0. What is s?
-3, -1, -1/4
Let u(w) = 3*w**4 - 2*w**3 - 5*w**2 + 5*w - 5. Let t(h) = -h**3 - h**2 + h - 1. Let k(j) = -5*t(j) + u(j). Solve k(q) = 0 for q.
-1, 0
Suppose -4*s + 0 = -12. Let z(k) be the third derivative of 0 + k**2 + 0*k + 5/36*k**4 + 2/45*k**5 + 1/9*k**s. Let z(p) = 0. Calculate p.
-1, -1/4
Let z(h) be the second derivative of h**4/4 - 6*h**2 - 14*h. Suppose z(m) = 0. What is m?
-2, 2
Let l be ((-8)/(-3))/((-2)/(-3)). Let -4*r**2 + 15*r + l*r**3 - 42*r + 19*r = 0. Calculate r.
-1, 0, 2
Let p = 15 - 89/6. Let w(i) be the third derivative of -1/3*i**3 + 0 + 1/10*i**5 - 2*i**2 + p*i**4 + 0*i. Factor w(f).
2*(f + 1)*(3*f - 1)
Let y(t) be the second derivative of -t**6/70 - 9*t**5/140 - t**4/14 + 21*t. Solve y(k) = 0.
-2, -1, 0
Suppose 0 = -3*y - 5*n + 16, -4*n + 2*n = -y - 2. Factor y*z**2 + 4/3 - 14/3*z.
2*(z - 2)*(3*z - 1)/3
Let b be -1*1*33/(-3). Suppose -1 = 5*r - b. Suppose -3*j**3 + 7*j - 2 - j**r - 2*j**2 + 0*j**2 + j**2 = 0. What is j?
-2, 1/3, 1
Suppose -g + 0 = -3. Determine x, given that x**4 - 13*x + x**2 + 13*x + 2*x**g = 0.
-1, 0
Let x be (-5)/(-20)*2/12. Let v(t) be the second derivative of -x*t**3 - 1/4*t**2 + 0 + t + 1/48*t**4. Determine w, given that v(w) = 0.
-1, 2
Let d(f) be the first derivative of -2*f**3/15 - 6*f**2/5 - 18*f/5 - 3. Let d(q) = 0. What is q?
-3
Let q(j) = -j**2 + 9*j - 5. Let u be q(8). Let m = 5 - u. Suppose -4*c**3 - 7*c + 3 - 5 - 8*c**m + c**3 = 0. What is c?
-1, -2/3
Factor 15 + 115/4*f**2 - 35*f - 10*f**3 + 5/4*f**4.
5*(f - 3)*(f - 2)**2*(f - 1)/4
Let x(j) be the third derivative of -j**6/30 + 4*j**5 - 200*j**4 + 16000*j**3/3 - 72*j**2. Let x(f) = 0. What is f?
20
Let z(k) be the third derivative of k**7/3360 + k**6/360 + k**5/96 + k**4/48 + k**3/6 + 2*k**2. Let m(r) be the first derivative of z(r). Factor m(a).
(a + 1)**2*(a + 2)/4
Let h(c) be the first derivative of -c**6/90 - c**5/60 + c**4/18 + 3*c + 1. Let q(d) be the first derivative of h(d). What is r in q(r) = 0?
-2, 0, 1
Let z(v) = -113*v**2 - v. Let k be z(3). Let i = -9170/9 - k. Factor -i*u**2 - 14/9*u - 4/9.
-2*(u + 1)*(5*u + 2)/9
Let x(y) be the second derivative of y**5/20 + 5*y**4/12 + y**3/2 - 9*y**2/2 + 9*y. Let x(z) = 0. Calculate z.
-3, 1
Factor 3/5*y**3 + 1/5*y - 4/5*y**2 + 0.
y*(y - 1)*(3*y - 1)/5
Let t = -84 - -337/4. Solve -t*l**4 + 1/4*l**2 + 0 + 0*l**3 + 0*l = 0 for l.
-1, 0, 1
Let k(r) be the third derivative of r**2 - 1/12*r**4 - 1/9*r**3 + 0 + 1/105*r**7 - 1/45*r**5 + 1/90*r**6 + 0*r + 1/504*r**8. Factor k(h).
2*(h - 1)*(h + 1)**4/3
Let x be -2 + ((-13)/5 - -5). Solve x*y**5 + 0*y**2 + 4/5*y**4 + 0*y + 0 + 2/5*y**3 = 0 for y.
-1, 0
Let n(k) be the first derivative of -k**6/24 - 5*k**5/4 - 125*k**4/8 - 625*k**3/6 - 3125*k**2/8 - 3125*k/4 + 11. Factor n(s).
-(s + 5)**5/4
Let c(f) = 2*f**3 - 3*f**2 + 3*f + 3. Let g(m) = 4*m**3 - 5*m**2 + 5*m + 5. Suppose -3 = d - 2*d. Let l(b) = d*g(b) - 5*c(b). Factor l(z).
2*z**3
Factor -3*i - 3/2 - 3/2*i**2.
-3*(i + 1)**2/2
Let j(b) = -2*b**5 - 10*b**4 + 10*b**2 + 2*b - 6. Let m(o) = -2*o**5 - 9*o**4 + 9*o**2 + 2*o - 5. Let t(w) = -5*j(w) + 6*m(w). Find k such that t(k) = 0.
-1, 0, 1
Let s(j) = -j**3 - j**2 - j. Let l(o) = o**4 + 7*o**3 + 4*o**2 + 3*o. Let q(i) = -3*l(i) - 15*s(i). Determine r, given that q(r) = 0.
-2, -1, 0, 1
Let m(n) be the first derivative of -n**7/3360 - n**6/360 - n**5/120 + n**3 - 3. Let v(q) be the third derivative of m(q). Suppose v(g) = 0. Calculate g.
-2, 0
Factor -9*y**2 - 3/4*y**5 - 39/4*y**3 + 0 - 3*y - 9/2*y**4.
-3*y*(y + 1)**2*(y + 2)**2/4
Suppose 6*q + 4 = 10. Factor 9/4*m**2 - 3*m - 1/2*m**3 + q.
-(m - 2)**2*(2*m - 1)/4
Let j(p) be the first derivative of p**5/10 - 3*p**4/8 + p**3/2 - p**2/4 - 7. What is w in j(w) = 0?
0, 1
Let j(k) be the third derivative of k**6/60 + k**5/15 + k**4/12 - 2*k**2. Factor j(z).
2*z*(z + 1)**2
Solve 0*h - 2/9*h**4 - 2/3*h**3 + 0*h**2 + 0 = 0 for h.
-3, 0
Let t(w) be the second derivative of -w**7/168 + w**6/120 + w**5/80 - w**4/48 - 8*w. Let t(j) = 0. What is j?
-1, 0, 1
Let o(i) = i**3 - 3*i**2 + 3*i. Let h be o(2). Factor -2*c**3 - 2*c**4 + 4*c**h - 2*c**4 + 0*c**2 + 2*c.
-2*c*(c - 1)*(c + 1)*(2*c + 1)
Let f = -17455/13 + 1343. Find i, given that 0 + f*i**2 + 2/13*i**4 +