 - 96/5*w + 0 = 0. What is w?
-8, -2, 0, 2/11
Suppose 0 = 5*f - 42 - 148. Let d(b) = 5*b**2 - 13*b - 3. Let s be d(-2). Factor -27*t**2 + 0 - s - f + 81*t + 3*t**3.
3*(t - 3)**3
Suppose -6*n - 2 = -4*n. Let b(c) = c**3 + 3*c**2 + 2*c - 3. Let h(o) = 1. Let s(g) = n*b(g) - 3*h(g). Factor s(m).
-m*(m + 1)*(m + 2)
Let c(k) = -k**2 + 200*k - 3072. Let v(f) = 12*f**2 - 2604*f + 39936. Let w(i) = 27*c(i) + 2*v(i). Solve w(p) = 0 for p.
32
Determine u so that -1/7*u**2 - 3*u + 45/7 + 1/7*u**3 = 0.
-5, 3
Let i be ((-4)/10)/(((-27)/18)/3). Determine n, given that 12/5*n - i - 7/5*n**3 + 9/5*n**2 = 0.
-1, 2/7, 2
Let c be (-2)/6 + 25/30 + 0/148. Factor c*f**2 + 3*f - 7/2.
(f - 1)*(f + 7)/2
Let x = 104 + -102. Let s(z) = z**3 + z + 1. Let f(k) = -2*k**4 + 6*k**3 - 4*k**2 - 10*k + 4. Let g(y) = x*s(y) + f(y). Suppose g(p) = 0. Calculate p.
-1, 1, 3
Let l be 1*(42 - 3) - 3. Let h be l/27 - (-16)/6. Factor -6*r**3 + 4 + 4*r**5 - 4 - 19*r**5 - 21*r**h.
-3*r**3*(r + 1)*(5*r + 2)
Let -20/3*r - 11/3*r**2 - 1/3*r**3 + 32/3 = 0. What is r?
-8, -4, 1
Suppose 0 = -3*y + 4*y - 0*y. Let h(w) be the second derivative of 0 + w + y*w**3 - 6*w**2 + 1/4*w**4. Determine a, given that h(a) = 0.
-2, 2
Let j = 35 - 30. Factor 12*v**4 - 12*v**2 + 6 - j*v**3 + 9*v**5 + 5 - 11 - 4*v.
v*(v - 1)*(v + 1)*(3*v + 2)**2
Let f(g) be the second derivative of g**7/5460 + g**6/585 + g**5/195 - g**3/3 - 14*g. Let a(n) be the second derivative of f(n). Factor a(b).
2*b*(b + 2)**2/13
Let x(m) be the first derivative of m**8/2520 - m**6/900 - 9*m**2/2 - 8. Let j(q) be the second derivative of x(q). Suppose j(s) = 0. What is s?
-1, 0, 1
Let m(b) be the first derivative of 20/3*b**3 + 10*b - 15 - 5/4*b**4 - 25/2*b**2. Let m(i) = 0. What is i?
1, 2
Let n(a) be the third derivative of 0*a + 0 + 0*a**3 + 1/240*a**5 + 0*a**4 - 1/280*a**7 + 15*a**2 - 1/240*a**6. Determine q so that n(q) = 0.
-1, 0, 1/3
Let j(t) = -4*t**2 - 6*t - 2. Let l be 39/(-4) + (-6)/(-8). Let m(o) = 17*o**2 + 24*o + 7. Let c(x) = l*j(x) - 2*m(x). Let c(q) = 0. What is q?
-2, -1
Let m(k) be the second derivative of -k**6/40 + 33*k**5/80 + 3*k**4/4 - 86*k. What is v in m(v) = 0?
-1, 0, 12
Suppose -44 = -2*g + 84. Let v be 2/(-3) + g/24. Factor -1/3*a + 0 - 1/3*a**3 - 2/3*a**v.
-a*(a + 1)**2/3
Let c(t) be the first derivative of t**3/8 - 315*t**2/16 + 39*t - 112. Factor c(q).
3*(q - 104)*(q - 1)/8
Let p(u) = u**2 + 1. Let n(t) = t**2 - 38*t + 2. Let q(l) = -n(l) + 2*p(l). Factor q(y).
y*(y + 38)
Let m(x) = 17*x**2 + 32*x + 25. Let z(n) = -7*n**2 - 16*n - 13. Let q(d) = 2*m(d) + 5*z(d). Factor q(g).
-(g + 1)*(g + 15)
Let b(v) = -11*v**5 + 5*v**3 + 6*v + 6. Let r(n) = -120*n**5 + 55*n**3 + 65*n + 65. Let l(j) = 65*b(j) - 6*r(j). Solve l(h) = 0 for h.
-1, 0, 1
Let y(i) = 6*i**2 - 3. Let p(k) be the second derivative of 11*k**4/12 + k**3/6 - 5*k**2/2 + 10*k. Let v(m) = 3*p(m) - 5*y(m). Determine q, given that v(q) = 0.
-1, 0
Let p(b) be the third derivative of -b**5/30 - 4*b**4/3 - 64*b**3/3 - 2*b**2 - 144. Find v, given that p(v) = 0.
-8
Suppose -5*u + 1 = -k, -u = k + 7 - 12. Let c(q) be the third derivative of -3*q**2 + 1/660*q**6 - 4/33*q**3 + 0*q**k + 1/110*q**5 + 0*q + 0. Factor c(w).
2*(w - 1)*(w + 2)**2/11
Let r(z) = 8*z**4 - 17*z**3 + 15*z**2 - 11*z - 10. Let x(w) = 9*w**4 - 18*w**3 + 15*w**2 - 12*w - 12. Let n(b) = 6*r(b) - 5*x(b). Factor n(i).
3*i*(i - 2)*(i - 1)**2
Let v(a) be the second derivative of -a**6/72 - a**5/30 + a**4/24 - 10*a**3/3 - 5*a. Let d(z) be the second derivative of v(z). Let d(r) = 0. What is r?
-1, 1/5
Let k be 1 - 0 - (1 + 44/(-5)). Let z = 9 - k. Factor 1/5*y - z*y**2 - 1/5*y**3 + 1/5.
-(y - 1)*(y + 1)**2/5
Factor 1/3*f**2 + 0 - 4/3*f.
f*(f - 4)/3
What is b in -15*b - 47/3*b**2 + 2/3 = 0?
-1, 2/47
Let 5*k**5 - 33*k**2 - 8*k**3 - 37*k**2 - 7*k**4 + 74*k**2 = 0. Calculate k.
-1, 0, 2/5, 2
Let y = 2508 + -2508. Factor 2/11*v**3 + y + 4/11*v - 6/11*v**2.
2*v*(v - 2)*(v - 1)/11
Let 15*a**2 - 4*a + 2*a - a**3 + a**2 + 8*a**2 - 27*a**2 = 0. Calculate a.
-2, -1, 0
Let a(d) be the second derivative of 5/3*d**4 - 3*d - 14/3*d**3 + 0 + 4*d**2. Factor a(q).
4*(q - 1)*(5*q - 2)
Let c(b) be the second derivative of -b**7/35 - 104*b**6/25 - 9003*b**5/50 - 1559*b**4 - 29596*b**3/5 - 57624*b**2/5 - 3*b - 12. Factor c(n).
-6*(n + 2)**3*(n + 49)**2/5
Factor 60 + 66 - 92*u + 12*u**2 - 70.
4*(u - 7)*(3*u - 2)
Let p be -147*20/180*(-126)/12. Factor 0 + 147/2*w**3 + 21/2*w**4 + 1/2*w**5 + p*w**2 + 0*w.
w**2*(w + 7)**3/2
Let q = 1496 + -31408/21. Let h(z) be the second derivative of -q*z**4 + 0 + 2*z + 3/7*z**3 + 1/147*z**7 - 2/35*z**6 - 2/7*z**2 + 1/5*z**5. Factor h(p).
2*(p - 2)*(p - 1)**4/7
Let s = 17177 - 17177. What is r in 1/4*r**3 + r + s + r**2 = 0?
-2, 0
Let j(v) be the first derivative of -1/18*v**4 - 2/3*v - 16 + 5/9*v**2 - 2/27*v**3. Let j(g) = 0. Calculate g.
-3, 1
Let h(q) be the first derivative of q**8/2520 + q**7/630 - q**3/3 - 2. Let g(j) be the third derivative of h(j). Factor g(f).
2*f**3*(f + 2)/3
Let o(l) = 5*l + 18. Let c be o(-3). Let t(i) be the second derivative of -i + 0*i**c + 1/90*i**5 + 0 - 1/54*i**4 + 0*i**2. Factor t(f).
2*f**2*(f - 1)/9
Suppose 0 = -p - 2*k - 0 - 2, 4*p + 5*k = -5. Suppose 0*l**2 - 7/3*l**4 + 2/3*l**3 + 0 + p*l = 0. What is l?
0, 2/7
Let -207/4*q**4 - 39*q**2 + 81/4*q**5 - 107*q**3 - 4*q + 0 = 0. What is q?
-1, -2/9, 0, 4
Suppose -4*i - 2*q = -26, 2*q + 2*q - 12 = 2*i. Suppose -2*r + 5*y + 21 = 0, -9 = r + i*y - 0. Factor 12*m**4 - 8*m**3 + 2*m**2 - 3*m**2 - 3*m**2 + 16*m**r.
4*m**2*(m + 1)*(3*m - 1)
Let m(k) = 2*k**3 + 2*k**2. Let a = 60 - 61. Let f(t) = -2*t**2 + 3*t**2 + t**3 - 1 + 2 + t. Let n(i) = a*f(i) + m(i). Determine z, given that n(z) = 0.
-1, 1
Determine w, given that -35/3*w**4 - 443/3*w**3 - 1880*w - 2449/3*w**2 - 1200 - 1/3*w**5 = 0.
-12, -5, -1
Let l = -10310 + 10313. Factor 5/3*x**2 + 0 + 11/3*x**l - 2/3*x + 4/3*x**4.
x*(x + 1)*(x + 2)*(4*x - 1)/3
Let z(d) be the third derivative of 0 - 1/15*d**5 - 4/3*d**3 + 0*d + 1/2*d**4 + 11*d**2. Determine n so that z(n) = 0.
1, 2
Suppose -q + 6 = 2. Let y(n) be the first derivative of 2*n**5 - q*n**4 + 3 + n**6 + n**6 - 3*n**6 + 3*n**4. Suppose y(a) = 0. What is a?
0, 2/3, 1
Let g be ((-198)/27)/11 - -1. Factor -w - 4*w**3 + 2*w**4 + 10/3*w**2 - g*w**5 + 0.
-w*(w - 3)*(w - 1)**3/3
Let s(q) = 10*q + 12. Let p be s(8). Let y = 646/7 - p. Factor 0*h**2 - y*h**3 + 2/7*h + 0.
-2*h*(h - 1)*(h + 1)/7
Let k be -2 + -10 - (7 - 7). Let v(d) = -d**2 - 14*d - 16. Let z be v(k). Determine b so that 10*b - 1 - 11*b**5 + z*b**4 - 3 + 9*b**5 - 8*b**3 - 4*b**2 = 0.
-1, 1, 2
Factor -26/9 + 1/9*o**2 - 25/9*o.
(o - 26)*(o + 1)/9
Factor -192/23*l + 2/23*l**2 + 4608/23.
2*(l - 48)**2/23
Let a(z) be the second derivative of 1/12*z**4 + 1/180*z**6 + 1/30*z**5 + 1/12*z**2 + 0 + 5*z + 1/9*z**3. Find c such that a(c) = 0.
-1
Let c(u) be the first derivative of -4*u**3/3 - 40*u**2 - 144*u - 92. Factor c(t).
-4*(t + 2)*(t + 18)
Suppose 4*z - 5*z + 5 = 0. Factor -20*w**2 + 31*w - 2 - 8 + z*w**3 - 6*w.
5*(w - 2)*(w - 1)**2
Let y(x) = -5*x**3 - 30*x**2 - 15*x + 40. Let o(j) = j**2 + 1. Suppose 4 = 5*l + 9. Let q(d) = l*y(d) - 5*o(d). Factor q(b).
5*(b - 1)*(b + 3)**2
Let s be 5/8 + (-35)/(-280). Factor 3/2 - s*t - 3/4*t**2.
-3*(t - 1)*(t + 2)/4
Let y(u) be the first derivative of 5*u**9/6048 + u**8/168 + u**7/84 - 10*u**3 + 22. Let p(w) be the third derivative of y(w). Factor p(o).
5*o**3*(o + 2)**2/2
Let y(u) = 110*u**2 + 2245*u + 10955. Let v(r) = 5*r**2 + 102*r + 498. Let d(j) = 45*v(j) - 2*y(j). Find s such that d(s) = 0.
-10
Let g(f) be the first derivative of f**6/30 + f**5/20 - f**4/4 - f**3/6 + f**2 + f - 3. Let l(o) be the first derivative of g(o). Factor l(v).
(v - 1)**2*(v + 1)*(v + 2)
Suppose 0 = -63*n + 68*n - 3*b + 6, 4*n - 2*b + 4 = 0. What is l in -1/5*l**2 - 1/5*l + 1/5*l**3 + n + 1/5*l**4 = 0?
-1, 0, 1
Let z(s) = -s**3 + 7*s**2 - 5*s - 4. Let t be z(6). Suppose 5*a = -5*v + 3*v + 6, 2*a = -t*v. Find l, given that a + 89*l - 2*l**2 - 89*l = 0.
-1, 1
Factor 2/11*h**2 + 30/11 + 16/11*h.
2*(h + 3)*(h + 5)/11
Let i(z) be the second derivative of -z**4/6 - z**3 + 10*z**2 - 9*z. Find g such that i(g) = 0.
-5, 2
Let g(t) be the second derivative of -t**8/1008 + 2*t**7/315 - t**6/72 + t**5/90 - 7*t**2 - 7*t. Let a(p) be the first deriva