.
2*(j - 2)**3
Suppose 2*u - 3*q = 10, -q - 8 = u + 4*q. Solve 2*v + 0*v + 2*v + u*v + 3*v**2 + 3 = 0 for v.
-1
Let u be 5*12*(-2)/(-20). Let t = u - 4. Let 1/3*c**4 + 0*c**3 + 0*c**t + 0 - 1/3*c**5 + 0*c = 0. Calculate c.
0, 1
Let h = 45563/40 + -1139. Let m(i) be the third derivative of -3/70*i**7 + 4*i**2 + 0*i**4 + 0*i**3 + h*i**6 - 1/20*i**5 + 0*i + 1/112*i**8 + 0. Factor m(t).
3*t**2*(t - 1)**3
Let t(d) be the third derivative of -1/210*d**5 + 0 - 1/28*d**4 - d**2 - 2/21*d**3 + 0*d. Factor t(h).
-2*(h + 1)*(h + 2)/7
Let v(r) be the second derivative of 2*r**7/49 + r**6/14 - 9*r**5/140 - 5*r**4/28 - r**3/14 + 4*r. Find p such that v(p) = 0.
-1, -1/4, 0, 1
Let w(s) be the first derivative of s**7/1120 + s**6/720 - s**5/480 - 7*s**3/3 - 3. Let y(z) be the third derivative of w(z). Factor y(r).
r*(r + 1)*(3*r - 1)/4
Let z(a) be the second derivative of -6*a + 0 - 3/10*a**5 + 0*a**3 + 0*a**2 + 1/8*a**4. What is v in z(v) = 0?
0, 1/4
Suppose -2*i**2 + 4*i**4 - 16*i**4 - i**2 - i**2 + 12*i**3 + 4*i**5 = 0. Calculate i.
0, 1
Let v(w) = -2*w + 21. Let r be v(5). Let d = 12 - 8. Let x(k) = 15*k**2 - 24*k - 1. Let y(o) = -5*o**2 + 8*o. Let j(a) = d*x(a) + r*y(a). Factor j(i).
(i - 2)*(5*i + 2)
Let w(t) = t + 9. Let h be w(-5). Let s(v) be the third derivative of 1/21*v**h - 2/105*v**5 + 1/420*v**6 + 0*v**3 + 0*v + 0 - v**2. Factor s(o).
2*o*(o - 2)**2/7
Let w = -674 + 676. Let t be (2 - 4/3)*6. Find h such that -4/3*h + 0 + 10/3*h**w - 8/3*h**3 + 2/3*h**t = 0.
0, 1, 2
Let g(m) = 2*m**3 - 26*m**2 - 3*m + 39. Let c be g(13). Solve c - 2/7*d + 2/7*d**2 = 0 for d.
0, 1
Factor -24/5*l**3 + 0*l**2 + 4/5*l - 12/5*l**5 - 32/5*l**4 + 0.
-4*l*(l + 1)**3*(3*l - 1)/5
Let q(f) be the first derivative of -f**3 - 6*f**2 - 12*f + 58. Factor q(v).
-3*(v + 2)**2
Solve 0 + 6/7*o + 9/7*o**2 + 3/7*o**3 = 0.
-2, -1, 0
Suppose v - 4 = 4. Let i = -6 + v. Determine c so that 0 - c**i + 1/3*c = 0.
0, 1/3
Let t(g) be the second derivative of -1/2*g**3 + 4*g + 0 + 0*g**2 + 3/10*g**5 + g**4 - 6/5*g**6 - 9/14*g**7. Solve t(a) = 0.
-1, 0, 1/3
Let n(x) be the second derivative of x**6/255 - x**5/170 - x**4/34 + 5*x**3/51 - 2*x**2/17 - 3*x. Suppose n(o) = 0. Calculate o.
-2, 1
Let c(l) = 22*l**3 - 60*l**2 + 45*l - 7. Let b(v) = -7*v**3 + 20*v**2 - 15*v + 2. Let t(o) = -7*b(o) - 2*c(o). Suppose t(j) = 0. What is j?
0, 1, 3
Let l(i) be the second derivative of i**7/336 + i**6/120 - i**5/80 - i**4/24 + i**3/48 + i**2/8 + 5*i. Suppose l(a) = 0. Calculate a.
-2, -1, 1
Determine w, given that 24*w + 7*w**4 - 3*w**3 + 40*w**2 + 33*w**3 - 21*w**2 + 4 + 24*w**2 = 0.
-2, -1, -2/7
Let r(k) be the second derivative of 6/5*k**2 + 1/20*k**4 + k + 0 - 2/5*k**3. Factor r(s).
3*(s - 2)**2/5
Let q be -2 - -5 - (2 - 4). Let d(t) = -t**2 + t - 1. Let r be 1*-1 - (-2)/1. Let s(x) = 4*x**2 - 6*x + 5. Let c(y) = q*d(y) + r*s(y). What is o in c(o) = 0?
-1, 0
Let w(t) be the third derivative of t**8/2520 - t**6/90 + 2*t**5/45 - t**4/12 - t**3 + 5*t**2. Let v(p) be the first derivative of w(p). Factor v(l).
2*(l - 1)**3*(l + 3)/3
Let w(l) be the second derivative of -l**8/84 + l**6/15 - l**4/6 - 3*l**2/2 + 5*l. Let j(z) be the first derivative of w(z). Let j(b) = 0. Calculate b.
-1, 0, 1
What is m in 128/5*m + 24/5*m**3 + 0 - 2/5*m**4 - 96/5*m**2 = 0?
0, 4
Let w = 37 - 7. Let u = -59/2 + w. Determine k, given that 1/4*k**5 + 0*k + 0 + 1/4*k**3 + u*k**4 + 0*k**2 = 0.
-1, 0
Let u(p) be the second derivative of 0*p**2 + 0 - 1/40*p**5 - 1/12*p**3 - 3*p - 1/12*p**4. Suppose u(d) = 0. What is d?
-1, 0
Factor 2/3 - 5/3*h**3 - 8/3*h**2 - 1/3*h.
-(h + 1)**2*(5*h - 2)/3
Suppose 3*a - 21 = -3*r, 0*r + 3*r - 25 = -4*a. Let g(d) be the third derivative of -1/120*d**5 + 0*d**r + 1/48*d**4 + 2*d**2 + 0 + 0*d. Factor g(c).
-c*(c - 1)/2
Let z(g) be the second derivative of -g**5/10 + g**4 - 3*g**3 - 11*g. Let z(n) = 0. Calculate n.
0, 3
Factor -3*s**2 - 6*s**4 + 9*s**4 + 5*s - 2*s - 3*s**3.
3*s*(s - 1)**2*(s + 1)
Factor 0 - 1/3*i + 1/3*i**2.
i*(i - 1)/3
Factor -5 + 0 - 14*s**2 + 6*s**4 - 4*s**3 + 5 - 4*s.
2*s*(s - 2)*(s + 1)*(3*s + 1)
Let n(l) be the third derivative of -l**8/5880 - l**7/1470 + l**5/210 + l**4/84 - l**3/3 + l**2. Let j(z) be the first derivative of n(z). Factor j(o).
-2*(o - 1)*(o + 1)**3/7
Let u(a) be the third derivative of a**6/70 + 2*a**5/105 - 4*a**2. Factor u(h).
4*h**2*(3*h + 2)/7
Let -8/3*r + 0*r**2 + 2*r**3 - 2/3*r**4 + 0 = 0. What is r?
-1, 0, 2
What is k in -4*k**3 - 2*k**3 + 86 + 2*k**3 + 12*k**2 - 12*k - 82 = 0?
1
Let k = 926/3 - 308. Determine t so that -k*t**2 - 2/3*t + 0 = 0.
-1, 0
Let r(f) be the second derivative of -f**5/4 - 5*f**4/6 + 5*f**3/2 - 19*f. Factor r(i).
-5*i*(i - 1)*(i + 3)
Let h be (-21)/(-70)*(-5)/(-3). Factor 3/2*z - 1 - h*z**2.
-(z - 2)*(z - 1)/2
Factor 24*r + 16 + 112*r**2 + 2*r**3 + 10*r - 92*r**2.
2*(r + 1)**2*(r + 8)
Let b(x) be the third derivative of -x**6/1440 + x**5/480 + x**4/48 + x**3/6 - x**2. Let s(a) be the first derivative of b(a). Factor s(j).
-(j - 2)*(j + 1)/4
Let q be 3/5 + 3/(-5). Solve q - 1/3*u**3 - 1/3*u**4 + 0*u**2 + 0*u = 0 for u.
-1, 0
Let d(a) be the second derivative of 1/255*a**6 - 1/51*a**3 + 0*a**2 - 7*a - 1/102*a**4 + 1/170*a**5 + 0. Factor d(s).
2*s*(s - 1)*(s + 1)**2/17
Let h(d) be the first derivative of 1/8*d**2 - 1/12*d**3 - 1/16*d**4 + 1/20*d**5 - 1 + 0*d. Factor h(j).
j*(j - 1)**2*(j + 1)/4
Let i(f) = f**3 + 13*f**2 - 32*f - 25. Let m be i(-15). Factor -d**4 + 0 + 3/4*d**3 - d + 1/4*d**m + d**2.
d*(d - 2)**2*(d - 1)*(d + 1)/4
Suppose 0 = -o - 5*i + 1, -2*i + 49 - 15 = 2*o. Let p = 67/3 - o. Determine s, given that -p*s**3 - 1/3 - 2*s**2 - 1/3*s**4 - 4/3*s = 0.
-1
Let d be (1/((-15)/2))/((-136)/51). Let b(t) be the second derivative of 0*t**4 - d*t**5 + 0*t**6 + 1/84*t**7 + 0*t**2 + 1/12*t**3 + 3*t + 0. Factor b(q).
q*(q - 1)**2*(q + 1)**2/2
Factor -4*u**2 + 2/3*u**3 - 8/3 + 6*u.
2*(u - 4)*(u - 1)**2/3
Let n be ((-5)/(-15))/((-2)/(-24)). Factor n*j + 18 + 0 + 2*j**2 - 7*j - 9*j.
2*(j - 3)**2
Let m = 134 - 132. Factor 27/4*f - 21/4*f**m - 3/2.
-3*(f - 1)*(7*f - 2)/4
Let b(h) be the first derivative of 5*h**4/12 - 40*h**3/9 + 50*h**2/3 - 80*h/3 + 13. Factor b(u).
5*(u - 4)*(u - 2)**2/3
Let 2/13*i**4 + 64/13*i**3 + 444/13*i**2 - 1088/13*i + 578/13 = 0. Calculate i.
-17, 1
Let w be 21/(-12) - (-2)/(-8). Let a(b) = b**2 + b + 2. Let r be a(w). Determine u so that 3*u**2 + 5*u**4 + u**2 - 5*u**2 - 4*u**r = 0.
-1, 0, 1
Let j = -1002 + 1004. Factor 1/7*h**4 + 6/7*h**j - 4/7*h + 1/7 - 4/7*h**3.
(h - 1)**4/7
Let j(a) be the third derivative of -1/3*a**3 - 4*a**2 - 5/12*a**4 + 0*a + 0 + 1/12*a**6 - 1/10*a**5 + 4/105*a**7. Solve j(d) = 0 for d.
-1, -1/4, 1
Suppose 0 = u - 2*o + o - 6, 3*u = o + 18. Let s be 2/u + (-2)/6. Let -2/7*x**2 + 2/7 + s*x = 0. What is x?
-1, 1
Factor 3*i**4 + 2*i - 18*i**2 + i**4 - 2*i**5 + 14*i**2.
-2*i*(i - 1)**3*(i + 1)
Let v(q) be the first derivative of 8*q**5/15 - 17*q**4/6 + 16*q**3/3 - 13*q**2/3 + 4*q/3 + 41. Solve v(g) = 0 for g.
1/4, 1, 2
Let k(l) be the second derivative of l**5/60 + l**4/9 - l**3/6 - 3*l**2 + 49*l. Suppose k(t) = 0. What is t?
-3, 2
Let a(i) be the first derivative of 2*i**5/55 - i**4/11 + 2*i**3/33 + 10. Solve a(l) = 0.
0, 1
Let r(g) = 35*g**3 - 29*g**2 + g. Let m(l) = -17*l**3 + 15*l**2 - l. Let j(p) = -7*m(p) - 3*r(p). Let j(y) = 0. What is y?
0, 2/7, 1
Suppose 0 = -9*x - 6 + 33. Factor -8/5*o**x + 0*o + 0 + 4/5*o**2 + 4/5*o**4.
4*o**2*(o - 1)**2/5
Let s(v) be the second derivative of -1/3*v**4 + 0*v**5 + 0*v**3 + 0*v**2 + 1/10*v**6 + 0 - 4*v + 1/42*v**7. Find w such that s(w) = 0.
-2, 0, 1
Let p be 76/266 - 2/(-7). Let -2/7*w**2 - p + 6/7*w = 0. Calculate w.
1, 2
Factor -2/7*s**4 + 12/7*s**2 + 0 + 0*s + 2/7*s**3.
-2*s**2*(s - 3)*(s + 2)/7
Let u be 3/8*(-4)/(-630). Let z(g) be the third derivative of 0*g**5 - u*g**6 + 0*g + 2*g**2 + 0*g**3 + 0 + 1/84*g**4. Factor z(j).
-2*j*(j - 1)*(j + 1)/7
Let c be (-560)/(-180) - (-3)/(-27). Factor -4/7*m**2 + 2/7 + 0*m + 0*m**c + 2/7*m**4.
2*(m - 1)**2*(m + 1)**2/7
Let h be (-24)/108 - 89*1/(-36). Let l(i) be the first derivative of -1 - h*i + 1/4*i**3 + 3/4*i**2. Factor l(r).
3*(r - 1)*(r + 3)/4
Let -5*r - 5*r**2 + 0 - 9*r - 6*r - 20 = 0. Calculate r.
-2
Suppose 6 - 6 = -5*x. Let b(v) be the first derivative of -1 + 1/18*v**4 + 0*v**2 + x*v + 0*v**