**2 + 4/3 = 0 for c.
-4
Let b be (-200)/(-40) + 536/(-108). Let v(j) be the second derivative of b*j**3 - 12*j - 1/9*j**2 + 1/27*j**4 + 0. Factor v(k).
2*(k + 1)*(2*k - 1)/9
Let d be 6 - (-6)/(-135)*(-9)/((-72)/1040). Find f, given that 2/9*f**2 - 4/9 + d*f = 0.
-2, 1
Let l(b) be the second derivative of -4*b**7/21 - 22*b**6/15 - 21*b**5/5 - 16*b**4/3 - 8*b**3/3 - 133*b. Determine o so that l(o) = 0.
-2, -1, -1/2, 0
Suppose 34 = 5*z - 1. Solve 16*h**2 - 18 + 2*h**4 - z*h**3 - 15*h + 19*h**3 + 3*h = 0.
-3, -1, 1
Factor -45/2*f**2 + 81/2*f**3 - 2 - 16*f.
(f - 1)*(9*f + 2)**2/2
Let y be (-1)/(-3) + (-25)/(-450)*48. Solve y - 3/2*z**3 + 0*z**2 + 9/2*z = 0 for z.
-1, 2
Suppose 4*w = 5*w. Suppose -2*b - 6 = w, -10 = -4*v + 4*b + 14. Suppose 3*u**4 - u**3 + 7*u**3 + 0*u**v = 0. What is u?
-2, 0
Let a = -29/72 + 4/9. Let k(m) be the third derivative of -12*m**2 + 0 + 0*m - 1/4*m**5 + a*m**6 + 0*m**3 + 5/12*m**4. Solve k(v) = 0 for v.
0, 1, 2
Let v(c) = 7*c + 49. Let d be v(-7). Let p be (-21)/(-18) - (6/12 - d). Suppose 2 - p*o**4 - 16/3*o + 0*o**3 + 4*o**2 = 0. Calculate o.
-3, 1
Let z(l) be the first derivative of 2*l**3/27 + 11*l**2/9 + 4. What is t in z(t) = 0?
-11, 0
Solve 108*x**4 + 19*x + 85*x**3 + 11*x + 5*x**5 - 73*x**4 + 85*x**2 = 0.
-3, -2, -1, 0
Let i(d) = 2*d**2 - d - 2. Let l be i(-1). Let c(s) = -s. Let y(m) = -4*m**2 - 9*m + 1. Let v(h) = l*y(h) - 6*c(h). Factor v(t).
-(t + 1)*(4*t - 1)
Solve 19/5*o + 32/5*o**2 + 2/5 + 3*o**3 = 0.
-1, -2/15
Let k(h) be the third derivative of h**4/24 - h**3/3 + 9*h**2. Let j be k(5). Let 3/5*x + 3/5*x**2 - 2/5 - 2/5*x**j = 0. Calculate x.
-1, 1/2, 2
Let s(w) = -w**3 - 7*w**2 + 7*w - 6. Let c be s(-8). Factor -4*g + 0*g**3 + 4*g**3 - c*g**3 - 2*g**2.
2*g*(g - 2)*(g + 1)
Let v(p) = p**3 - p**2 - 2*p - 4. Let w be v(3). Let y be 0 + 2/w + 42/280. Suppose 2/5*j**3 - y*j**4 + 6/5*j**2 + 4/5 - 2*j = 0. Calculate j.
-2, 1
Let v(p) be the third derivative of 1/270*p**5 + 0 - 7*p**2 - 1/108*p**4 + 0*p**3 + 0*p. Factor v(r).
2*r*(r - 1)/9
Solve 16/9 - 106/9*l**3 - 10/9*l**5 - 56/9*l**4 + 8/9*l - 68/9*l**2 = 0.
-2, -1, 2/5
Let h(b) be the first derivative of -2/9*b**6 + 0*b - 8/3*b**4 - 21 + 0*b**2 + 28/15*b**5 - 64/9*b**3. Factor h(x).
-4*x**2*(x - 4)**2*(x + 1)/3
Let c(f) be the third derivative of 7/20*f**5 + 1/112*f**8 + 0*f**3 + 1/4*f**4 + 0 + 1/14*f**7 + 9/40*f**6 + 0*f - 5*f**2. Factor c(o).
3*o*(o + 1)**3*(o + 2)
Suppose -29*k - 28 = -33*k. Let b be 12/k*2/4. Let 9/7*o**2 + 3/7*o**3 + 0 + b*o = 0. What is o?
-2, -1, 0
Let x(c) = -5*c**2 - 7. Let g(f) = -5*f**2 - 6. Suppose -3*j - 2 = 16. Let o(d) = j*x(d) + 7*g(d). Factor o(q).
-5*q**2
Let l(r) = 8*r**3 + 6*r**2 - 6*r + 6. Let s(z) = -z**3 - z**2 + z - 1. Let d(h) = l(h) + 6*s(h). Factor d(t).
2*t**3
Let j(w) be the first derivative of -1/6*w**4 + 0*w**2 - 11 + 8/3*w - 2/3*w**3. Suppose j(g) = 0. Calculate g.
-2, 1
Suppose 11/2 + 1/2*b**2 + 6*b = 0. What is b?
-11, -1
Let x(k) = -9*k**3 - 169*k**2 + 38*k. Let c be x(-19). Let m(b) be the first derivative of -15/2*b**2 - 5/3*b**3 + c*b + 14. Determine y, given that m(y) = 0.
-3, 0
Let q(y) be the second derivative of 1/80*y**5 - 1/2*y**2 - 7*y + 0 + 11/24*y**3 - 3/16*y**4 + 1/120*y**6. What is g in q(g) = 0?
-4, 1
Factor -2/3*j**2 + 60 + 178/3*j.
-2*(j - 90)*(j + 1)/3
Suppose -77*c**4 + 101*c**4 + 2*c - 17*c**2 - 25*c**4 + 24 - 8*c**3 = 0. What is c?
-4, -3, -2, 1
Suppose 9*q + 11 = 38. Determine s so that -s**5 - 5*s**q - s**5 + 6*s**4 + s**2 + s**2 - s**3 = 0.
0, 1
Let u(f) = -f**2 - 3*f + 5. Let g(d) = d**2 - 5*d - 4. Let x be g(5). Let v be u(x). Factor 2*p + 3 - 3 + 12*p**2 + 5*p + v.
(3*p + 1)*(4*p + 1)
Let g be (-318)/124*(-28)/(-126). Let a = 3/31 - g. Factor -a*l**2 + 0 + 2/3*l.
-2*l*(l - 1)/3
Suppose -3*k - 5 = 2*k, -b + 105 = -5*k. Let q = b + -100. Suppose 4/9*t**4 - 4/9*t**2 + q - 2/9*t + 0*t**3 + 2/9*t**5 = 0. What is t?
-1, 0, 1
Find c, given that -36/5*c**3 - 156/5*c + 116/5*c**2 + 72/5 + 4/5*c**4 = 0.
1, 2, 3
Let v(k) be the third derivative of 0*k**4 - 1/3*k**3 + 0 + 0*k + 2*k**2 + 1/30*k**5. Solve v(x) = 0.
-1, 1
Find t, given that 2*t**3 + 2*t**3 + 4 - 3*t**3 - 7*t**2 - 12 + 14*t = 0.
1, 2, 4
Let q(h) be the second derivative of 5/36*h**4 + 0*h**2 + 0 - 15*h - 5/6*h**3. Factor q(r).
5*r*(r - 3)/3
Let y be ((-264)/30 - -5) + 5. Let h be (-1 - -1)/(13/(26/4)). Suppose 3/5*j**4 + h*j + y*j**3 + 0 + 0*j**2 - 3/5*j**5 = 0. Calculate j.
-1, 0, 2
What is f in -19 + 56/3*f**2 - 58/3*f**3 + 1/3*f**4 + 58/3*f = 0?
-1, 1, 57
Suppose -4*a + 116 = -5*n, 8*n - 4*n + 3*a + 99 = 0. Let o be (-218)/n + (-9)/(54/(-4)). Factor 9/4*b**5 + 33/2*b**3 - 3/4 + 21/4*b - 27/2*b**2 - o*b**4.
3*(b - 1)**4*(3*b - 1)/4
Let s(n) be the second derivative of -n**5/180 + n**3/18 + 17*n**2/2 - 10*n. Let q(d) be the first derivative of s(d). Factor q(f).
-(f - 1)*(f + 1)/3
Suppose 0 = -5*o - 6 + 56. Suppose i - 3*i = -o. Find q, given that -i*q + q + 51*q**2 - 120*q**3 - 2*q + 48*q**4 = 0.
0, 1/4, 2
Let w(a) = a**3 + 3*a**2 - 15*a - 7. Let z be w(3). Factor 50/7*t + 10/7*t**z + 2/21*t**3 + 250/21.
2*(t + 5)**3/21
Let b = -35 + 45. Factor 4 + 5 + b - 3*n**2 - 16.
-3*(n - 1)*(n + 1)
Factor -4*y - 265 - 71 + 146 + 2*y**2 + 0*y - 24*y.
2*(y - 19)*(y + 5)
Let j(k) be the first derivative of k**4/18 + 2*k**3/27 - 2*k**2/3 + 3. Find g such that j(g) = 0.
-3, 0, 2
Let i(u) be the first derivative of -6/5*u - 3/20*u**4 + 3/10*u**2 - 25 + 2/5*u**3. Suppose i(j) = 0. What is j?
-1, 1, 2
Let t(j) be the second derivative of -j**8/33600 - j**7/1800 - j**6/225 - j**5/50 + 5*j**4/3 + 7*j. Let a(l) be the third derivative of t(l). Factor a(h).
-(h + 2)**2*(h + 3)/5
Factor -6/5*a**2 + 8/5 - 2/5*a**3 + 0*a.
-2*(a - 1)*(a + 2)**2/5
Let s(f) be the first derivative of 2*f**3/3 + 9*f**2 + 28*f + 76. Factor s(g).
2*(g + 2)*(g + 7)
Factor -t + 11/4*t**2 - 5/4 - 1/2*t**3.
-(t - 5)*(t - 1)*(2*t + 1)/4
Let r be 0/((3/(-1))/(-3)). Suppose -3*j + 2*b + 6 = -r*j, 3*j - 15 = -b. Factor -j*d**2 + 2*d + 0*d**2 + 5*d + d.
-4*d*(d - 2)
Let s(d) = -d**2 - 5*d + 17. Let m be s(-6). Suppose m*u**3 - 4*u**4 + u**4 + 3*u**5 - 35*u**3 + 36*u**2 = 0. What is u?
-3, 0, 2
Let -163/4*m + 11/4*m**2 - 15/2 = 0. Calculate m.
-2/11, 15
Factor 0 - 15/2*h + 3/4*h**4 + 51/4*h**2 - 6*h**3.
3*h*(h - 5)*(h - 2)*(h - 1)/4
Suppose -3*s = 5*p - 21, -3*p + 6 - 5 = -4*s. Let d(q) be the first derivative of 0*q**2 + 0*q**4 - 4*q**p - 5 + 3/5*q**5 + 0*q. Factor d(m).
3*m**2*(m - 2)*(m + 2)
Let b be 1 + (-16)/(-48)*(-1 + 2). Let c be 2/(2 + 3 - 2). Let -c*j - 10/3*j**3 + 16/3*j**2 - b = 0. Calculate j.
-2/5, 1
Let u = -847 + 850. Let j(g) be the first derivative of u*g**4 - 8*g + 4/5*g**5 - 6*g**2 + 4/3*g**3 - 3. Factor j(i).
4*(i - 1)*(i + 1)**2*(i + 2)
Suppose -17*z + 13*z + 36 = 0. Let v be (-9 + z)*1/2. Let 0*s + 3/4*s**2 + 3/2*s**3 + v + 3/4*s**4 = 0. Calculate s.
-1, 0
Let u(i) be the first derivative of 2*i**6/3 + 7*i**5/5 - 7*i**4/2 + i**3 + 186. Suppose u(p) = 0. Calculate p.
-3, 0, 1/4, 1
Let t = 126367/34760 - -3/3160. Let t*n**2 - 74/11*n**3 - 18/11*n**5 - 8/11*n + 60/11*n**4 + 0 = 0. Calculate n.
0, 2/3, 1
Let k(g) be the third derivative of g**5/20 - 7*g**4/8 + 6*g**3 - 17*g**2 + 2. Factor k(v).
3*(v - 4)*(v - 3)
Let c(p) = p**3 - 5*p**2 + 2. Let w be c(5). Factor w + o**2 - 2*o - 3*o**3 - 3*o**2 + 0*o**3 + 5*o**3.
2*(o - 1)**2*(o + 1)
Suppose -5*k - 13 = -5*f - 38, k = 5*f + 17. Determine x so that -12*x**2 + k*x**3 + 7*x**3 + 15*x**5 - 12*x + 6*x**4 - 18*x**5 = 0.
-1, 0, 2
Solve -136 + 433*l**2 + 264*l - 247*l**2 + 18*l**3 - 8*l**3 = 0 for l.
-17, -2, 2/5
Let f be 8 - (1 + 2) - (-3)/3. Let a(j) = 22*j**3 + 164*j**2 + 562*j + 352. Let p(t) = -2*t**3 - 15*t**2 - 51*t - 32. Let h(g) = f*a(g) + 68*p(g). Factor h(c).
-4*(c + 1)*(c + 4)**2
Let k(z) be the first derivative of -z**6/90 - z**5/20 - z**4/18 - 16*z - 3. Let r(w) be the first derivative of k(w). Determine t so that r(t) = 0.
-2, -1, 0
Suppose -9 = -2*a + 5*k + 14, -2*a - k = -5. Let r(d) be the second derivative of 0*d**2 + 0 - a*d - 1/4*d**4 - 1/2*d**3. Determine x, given that r(x) = 0.
-1, 0
Let k = -250/73 + 2219/584. Factor k*m**2 + 3/8 + 3/4*m.
3*(m + 1)**2/8
Let o be (-1 - (-1)/5)/(12/(-540)). Suppose 0 = 26*j - 17*j - o. Suppose -6/5*a**2 + 3/5*a**5 + 0*a**3 + 6/5*a**j - 3/5*a + 0 = 0. Calculate a.
-