et f(s) = a*i(s) - 7*z(s). Factor f(d).
-d**2
Let n(j) = j**2 - j + 1. Suppose 5*r - 1 = -6. Let d(a) = 10*a**2 + 20*a + 25. Let h(t) = r*d(t) + 5*n(t). Suppose h(f) = 0. What is f?
-4, -1
Suppose 0 = 4*k + 4*m - 24, 5*k - 43 = -3*m - 9. Let r be (-2)/(-4)*k/2. Factor 2*l - l - 3*l**r - l.
-3*l**2
Let i(n) be the second derivative of 0 + 1/2*n**5 + 10/3*n**3 - 25/12*n**4 - 5/2*n**2 + 24*n. Factor i(p).
5*(p - 1)**2*(2*p - 1)
Let o(f) be the first derivative of 0*f**3 + 0*f**2 + 3/28*f**4 + 0*f + 1/42*f**6 - 4/35*f**5 + 1. Factor o(l).
l**3*(l - 3)*(l - 1)/7
Let u(k) = -2*k - 1. Let q(s) = -s**3 + 17*s**2 - 22*s - 3. Let l(x) = -q(x) + 3*u(x). Suppose l(c) = 0. Calculate c.
0, 1, 16
Let d(p) be the second derivative of p**5/30 + 31*p**4/54 - 58*p**3/27 + 8*p**2/3 - 293*p. Suppose d(i) = 0. Calculate i.
-12, 2/3, 1
Find q, given that 58 + 3*q**4 - 63 - q**5 + 5 - q**3 - 3*q**2 + 2*q = 0.
-1, 0, 1, 2
Let k be (-16 + 20 - 2) + 1*(0 + 0). Factor -6860/11*q**k - 980/11*q**3 - 2/11*q**5 - 33614/11 - 70/11*q**4 - 24010/11*q.
-2*(q + 7)**5/11
Let h(t) be the first derivative of -t**6/3 + 8*t**5/5 - 3*t**4 + 8*t**3/3 - t**2 + 507. Suppose h(v) = 0. Calculate v.
0, 1
Factor 9*c**4 - 5*c**2 + 32*c**2 + 644*c**3 - 728*c**3.
3*c**2*(c - 9)*(3*c - 1)
Determine v so that 36/7*v - 38/7 + 2/7*v**2 = 0.
-19, 1
What is r in 4 + 1/2*r**3 - 15/2*r + 3*r**2 = 0?
-8, 1
Factor -2*o - 12/13 - 16/13*o**2 - 2/13*o**3.
-2*(o + 1)**2*(o + 6)/13
Let o be (702/1053)/(4/6 - 4/(-3)). Determine w, given that 75 + o*w**2 + 10*w = 0.
-15
Let a be (-608)/(-2432) - 1/(3*132/27). Find b, given that 8/11 + a*b**2 + 8/11*b = 0.
-2
Let x = -1131/10 + 3473/30. Factor -x - 46/3*u**2 + 14/3*u**3 + 40/3*u.
2*(u - 2)*(u - 1)*(7*u - 2)/3
Let p = -44 - -47. Suppose -p*n + s = -4, n = -4*n - 4*s + 18. Find x, given that 4/5*x + 0 - 6/5*x**n + 2/5*x**3 = 0.
0, 1, 2
Let z = 195 + -192. Let w(q) be the first derivative of 1/28*q**4 + 0*q - 1/7*q**z + 3 + 1/7*q**2. Let w(k) = 0. What is k?
0, 1, 2
Let u(r) be the second derivative of -8/3*r**2 - 1/9*r**4 + 0 - 8*r + 8/9*r**3. Solve u(k) = 0 for k.
2
Let z(h) = -11*h**2 + h**3 + 25*h**2 + 2 + 4*h - 10*h**2. Let q be z(-2). Solve -2*u**3 - 3*u**q + 3*u**3 + u**2 = 0 for u.
0, 2
What is t in 326*t + 4*t**4 + 40*t**3 - 156*t**2 - 162 - 80*t**2 + 34*t - 6*t**4 = 0?
1, 9
Let h(m) be the first derivative of 3*m**5/35 + 39*m**4/28 + 58*m**3/7 + 162*m**2/7 + 216*m/7 + 963. Solve h(r) = 0.
-6, -3, -2
Let p(h) be the first derivative of 2*h**3/3 - 134*h**2 - 270*h - 729. Suppose p(i) = 0. Calculate i.
-1, 135
Let v(k) be the third derivative of k**7/630 + k**6/360 - k**5/60 - 5*k**4/72 - k**3/9 - 2*k**2 - 471. What is p in v(p) = 0?
-1, 2
Let v(i) be the second derivative of 14*i**6/45 + 17*i**5/5 + 7*i**4/9 - 34*i**3/3 - 28*i**2/3 + 80*i. Determine a, given that v(a) = 0.
-7, -1, -2/7, 1
Let q = 43/83 - 3/166. Determine g so that 1/6*g**4 + 1/3*g + 0*g**3 - q*g**2 + 0 = 0.
-2, 0, 1
Let j(o) be the second derivative of 0 - 9/2*o**3 - 10*o + 27/2*o**2 - 1/20*o**5 + 3/4*o**4. Find r such that j(r) = 0.
3
Find v, given that -64/5 + 4/5*v**2 - 126/5*v = 0.
-1/2, 32
Let g be (((-108)/(-15))/(-9))/((-4)/70). Factor 6 - l + g*l**3 - 8*l - 2*l**3 - 6*l**2 + 0*l - 3*l**5.
-3*(l - 1)**3*(l + 1)*(l + 2)
Let f(r) = -r**3 + 2*r**2 - 1. Let g(a) = 16*a**3 - 54*a**2 - 16*a + 18. Let k(h) = 36*f(h) + 2*g(h). Let k(t) = 0. Calculate t.
-8, -1, 0
Let w(u) be the second derivative of 32*u**5/75 - 4*u**4/5 + 3*u**3/5 + 3*u**2 + 30*u. Let x(g) be the first derivative of w(g). Factor x(t).
2*(8*t - 3)**2/5
Let k(d) be the second derivative of d**5/8 - 5*d**4/4 + 55*d**3/12 - 15*d**2/2 + 143*d - 1. Find i, given that k(i) = 0.
1, 2, 3
Let d be (-4)/(-20) + 8*(-18)/(-480). Determine j, given that 0 + 1/2*j + d*j**2 = 0.
-1, 0
Suppose -h - h - 4 = 0, 0 = -2*o - 2*h - 4. Let t be 1 - o - -1 - -1. Factor 0*u + 4*u**3 - u**3 + 0*u**t + 5*u**2 - 2*u.
u*(u + 2)*(3*u - 1)
Factor -600*o + 540*o + 20 - 5*o**4 + 10*o**4 + 30*o**2 - 30*o**3 + 35*o**2.
5*(o - 2)**2*(o - 1)**2
Let d be (64/80)/((-1)/(-5)). Suppose 0 = k - 8 + d. Determine t so that 4*t - 2*t + t**k - 4*t**3 + t**3 + t**3 - 1 = 0.
-1, 1
Suppose 4*f + 2 = 2*p + 12, p = -3*f + 10. Factor 9*v**2 + 12*v**2 - 21*v**2 - 2*v + 5*v**2 - f*v**3.
-v*(v - 1)*(3*v - 2)
Let c(v) be the third derivative of 0*v**3 + 9*v**2 + 1/20*v**6 - 3/40*v**7 + 1/16*v**4 + 0 + 11/80*v**5 + 0*v. Let c(j) = 0. What is j?
-1/3, -2/7, 0, 1
Let m = -5 - -8. Find r, given that -441*r**m + 436*r**3 - 4*r**2 - 6*r**2 = 0.
-2, 0
Let f(q) be the third derivative of q**6/300 + q**5/15 + 7*q**4/20 + 23*q**2. Let f(g) = 0. Calculate g.
-7, -3, 0
Let i(l) = -118*l**2 + 82*l + 16. Let j(d) = 37*d**2 - 27*d - 5. Let y(v) = -5*i(v) - 16*j(v). Determine q, given that y(q) = 0.
0, 11
Suppose 5*c = b - 7, c + 5 = -4*c. Factor a**2 - a**b - 254*a + 6 - 3*a**3 + 263*a.
-3*(a - 2)*(a + 1)**2
Let c(j) = j**2 + 6*j - 5. Let g be c(-7). Solve -4*l + 42 - 44 + 2*l**g + 4*l = 0.
-1, 1
Let z(l) = -18*l**2 - 10*l**3 + 19*l + 239 - 3*l - 233. Let p(f) = 21*f**3 + 37*f**2 - 32*f - 13. Let a(s) = 6*p(s) + 13*z(s). Solve a(k) = 0 for k.
-4, 0, 1
Let u = -72 - -105. Factor 5 - 3*c**4 - 33*c**3 - 10*c**2 + 8*c**4 + u*c**3.
5*(c - 1)**2*(c + 1)**2
Let b = 3993/155 + -780/31. Find o, given that -3/5 + 6/5*o - b*o**2 = 0.
1
Suppose 25*p - 30*p - 102 = -39*p. Factor 3/5 - 3/5*r**2 - 1/5*r + 1/5*r**p.
(r - 3)*(r - 1)*(r + 1)/5
Suppose -5*v = 3*n - 391, -2*v + 3*n - 17 = -186. Factor 10 - 2 + c**3 - v*c + 4*c**2 + c**3 + 66*c.
2*(c - 1)**2*(c + 4)
Let g(j) be the third derivative of 1/270*j**5 + 2*j**2 + 7/1620*j**6 + 0*j**4 + 0 - 5/6*j**3 + 0*j. Let w(v) be the first derivative of g(v). Factor w(s).
2*s*(7*s + 2)/9
Let b(f) be the second derivative of -2*f**7/63 - 38*f**6/45 - 101*f**5/12 - 73*f**4/2 - 54*f**3 - 36*f**2 - 6*f - 12. Solve b(u) = 0.
-6, -1/2
Let t(a) be the third derivative of -a**8/80640 - a**7/4032 - a**6/720 - 23*a**5/60 + 26*a**2. Let c(b) be the third derivative of t(b). Factor c(v).
-(v + 1)*(v + 4)/4
Let k(h) be the third derivative of h**8/112 - h**7/40 - h**6/40 + 7*h**5/40 - h**4/4 - h**3/2 - 5*h**2. Let b(t) be the first derivative of k(t). Factor b(p).
3*(p - 1)**2*(p + 1)*(5*p - 2)
Let s(x) be the first derivative of -2*x**3/15 + 6*x**2 - 58*x/5 - 105. Factor s(o).
-2*(o - 29)*(o - 1)/5
Suppose 0 - 20/3*x**2 + 16*x**3 + 2/3*x**5 + 20/3*x**4 - 50/3*x = 0. Calculate x.
-5, -1, 0, 1
Let 14*g**2 - 3/2 - g + 9*g**3 - 9/2*g**4 = 0. What is g?
-1, -1/3, 1/3, 3
Let u(c) be the third derivative of -5*c**8/112 - c**7/42 + 5*c**6/24 + c**5/12 - 5*c**4/12 + 2*c**2 - 40*c. Let u(b) = 0. What is b?
-1, 0, 2/3, 1
Let v(o) = 2*o**3 + 40*o**2 + 296*o + 684. Suppose 4*i - 13*i + 36 = 0. Let b(t) = -2*t**3 - 39*t**2 - 297*t - 683. Let p(j) = i*b(j) + 6*v(j). Factor p(c).
4*(c + 7)**3
Suppose -5*w = -q - 15, 4*w + 3*q = 2*w + 6. Suppose -5*p = w*y + 14, -3*p - 18 = y + 2*p. Factor -5/2*g - 1 - 1/2*g**3 - 2*g**y.
-(g + 1)**2*(g + 2)/2
Let -2/5*b**4 - 4/5*b**2 + 30 - 16/5*b**3 + 32*b = 0. What is b?
-5, -1, 3
Factor -6*s**2 - 10*s**3 - 80 - 101*s + 8*s**4 + 111*s + 78.
2*(s - 1)**2*(s + 1)*(4*s - 1)
Let r(w) = 5*w**3 + 15*w**2 + 40*w + 40. Let i(k) = -4*k**3 - 15*k**2 - 42*k - 41. Let y(f) = -4*i(f) - 3*r(f). Determine g, given that y(g) = 0.
-11, -2
Let r(b) be the first derivative of -b**3/2 + b**2/4 + b - 129. Factor r(k).
-(k - 1)*(3*k + 2)/2
Let q(h) be the third derivative of -h**6/40 + 39*h**5/20 - 399*h**4/8 + 361*h**3/2 + 2*h**2 - 6*h. Factor q(s).
-3*(s - 19)**2*(s - 1)
Let o = 19323 + -19321. Factor -5/3 - 1/2*z**o - 31/6*z.
-(z + 10)*(3*z + 1)/6
Find u such that -26275 - 4*u**2 + 960*u + 0*u**2 + 1480 - 29976 - 2829 = 0.
120
Let b be ((-132)/(-48))/((-3)/(-32)). Let q = 30 - b. Factor -2/3*s**4 + q*s**2 + 0*s + 0*s**3 + 0.
-2*s**2*(s - 1)*(s + 1)/3
Suppose 5*h + 1 = 4*h. Let z be h/(-9 + 2)*(-5 + 13). Let -z*g + 4/7 + 4/7*g**2 = 0. What is g?
1
Suppose -7*v + 3*v + 4*t + 20 = 0, 17 = 3*v - t. Let m = 8 - v. Factor -d**3 - 4*d**2 + 3*d**4 - 3*d + 0*d**2 + d**m + 4*d**3.
3*d*(d - 1)*(d + 1)**2
Let l(n) = -3*n**2 + 4*n - 2. Let s be l(1). Let y(b) = 6*b**2 + 8*b + 1. Let v(h) = -h**2 - h - 1. Let o(j) = s*v(j) + y(j). Find c, given that o(c) = 0.
-1, -2/7
Let c(w) be the first