et f be h/(-4)*-2 + 3. What is w in 2 + 5*w**5 + 10*w**4 + 3*w - 3*w**5 - 4*w + 20*w**f + 11*w + 20*w**3 = 0?
-1
Suppose -23 = p - 22. Let n be 36/(-126) - (59/(-35) - p). Factor -n*s**3 + 2/5*s + 0 + 0*s**2.
-2*s*(s - 1)*(s + 1)/5
Let k = 740/11 + -1469/22. What is w in 4*w - 8 - k*w**2 = 0?
4
Let q(a) be the second derivative of -a**5/330 - a**4/44 + 4*a**3/33 + 7*a**2 - a. Let w(j) be the first derivative of q(j). Factor w(x).
-2*(x - 1)*(x + 4)/11
Factor -31*o**3 - 60*o**2 + 349*o**2 - 3*o**3 + o**4.
o**2*(o - 17)**2
Let c(n) be the first derivative of 5*n**4/4 + 100*n**3/3 - 215*n**2/2 + 110*n + 211. What is r in c(r) = 0?
-22, 1
Let 108*v + 15*v**3 - 2*v**2 - 3*v**4 - 5*v**2 + 19*v**2 + 84*v**2 = 0. What is v?
-2, 0, 9
Suppose -6*j = -12*j + 18. Let p(s) be the first derivative of 0*s**2 - 4/3*s**j + 0*s - 1. Let p(b) = 0. Calculate b.
0
What is y in 1/2*y**2 - 11/8*y**4 + 0 - 1/8*y**5 - 3*y**3 + 4*y = 0?
-8, -2, 0, 1
Let h(n) be the third derivative of -n**6/120 - n**5/5 + 9*n**4/8 - 7*n**3/3 + 17*n**2. Factor h(t).
-(t - 1)**2*(t + 14)
Factor -3*z**3 - 5*z**3 - 14400*z - 360*z**2 - 192000 + 5*z**3.
-3*(z + 40)**3
Suppose 0 + 0*j + 1/7*j**3 + 0*j**2 = 0. Calculate j.
0
Let k(j) be the first derivative of 0*j**2 + 0*j + 2/33*j**3 - 3/22*j**4 - 45. Let k(i) = 0. Calculate i.
0, 1/3
Let w(i) be the second derivative of i**4/60 - 13*i**3/15 + 169*i**2/10 - 25*i. Suppose w(o) = 0. What is o?
13
Factor 4/5*k - 4/5*k**3 + 2/5*k**2 - 2/5*k**4 + 0.
-2*k*(k - 1)*(k + 1)*(k + 2)/5
Let b be 3/((-39)/12 - -4). Factor 8*m**3 + 0*m**b + 5*m**4 - 24*m**2 + m**5 + 2*m**4 + 8*m**2.
m**2*(m - 1)*(m + 4)**2
Let c(j) be the first derivative of j**7/140 - 3*j**6/80 + j**5/20 + 5*j**2/2 + 4. Let q(u) be the second derivative of c(u). Find w, given that q(w) = 0.
0, 1, 2
Suppose 3*k + k - 44 = -2*b, 3*k - 33 = b. Suppose 3*x - k - 1 = 0. Suppose 0*f - 2*f**3 - 2*f + x*f**3 = 0. What is f?
-1, 0, 1
Let b be 11/4 + 0 + -2. Let m(z) = z**3 - 6*z**2 + 3*z + 20. Let r be m(4). Solve -b*y**5 - 3/2*y**4 + r*y**3 + 0 + 3/2*y**2 + 3/4*y = 0 for y.
-1, 0, 1
Let p = -81 + 71. Let w be (-3)/((-25)/p + -4). Factor -10/3*m**3 - 4/3 - 14/3*m - 6*m**w - 2/3*m**4.
-2*(m + 1)**3*(m + 2)/3
Let b(r) be the second derivative of -1/360*r**5 - 2*r**2 + 1/144*r**4 + 0 - 5*r + 0*r**3. Let t(f) be the first derivative of b(f). Factor t(o).
-o*(o - 1)/6
Let i = 251 - 244. Let s(c) be the first derivative of -3/4*c**4 + 0*c**2 - 3/2*c**6 + 0*c - 3*c**5 + i + c**3. Factor s(y).
-3*y**2*(y + 1)**2*(3*y - 1)
Suppose -3 - 3 = -2*w, -6 = -k - w. Suppose -12 = -r - 4*v, -k*r = -2*r - 5*v + 15. Suppose r - 4 - 6*o - 3*o**2 + o**2 = 0. What is o?
-2, -1
Let g(c) be the second derivative of -1/50*c**5 + 0 + 0*c**2 + 0*c**3 - 1/15*c**4 + 4*c. Factor g(t).
-2*t**2*(t + 2)/5
Suppose -3*s + n = -10, 0 = -n + 1 + 1. Suppose 2*p = p + 2*z + 4, s*p - 10 = 2*z. Factor 1/4*j**4 - 3/4*j**p - 1/2*j**3 + 0 + 0*j.
j**2*(j - 3)*(j + 1)/4
Let i(j) = -6*j**2 - 117*j - 111. Let g(x) = 7*x**2 + 116*x + 109. Let w(n) = 3*g(n) + 4*i(n). Find k such that w(k) = 0.
-39, -1
Let b(k) = 2*k + 2. Let u be b(0). Factor u*a**2 - 10*a**2 + 5*a**2.
-3*a**2
Let y(q) be the first derivative of 682*q**5 + 6035*q**4/4 + 1870*q**3/3 - 725*q**2/2 + 30*q - 662. Suppose y(g) = 0. What is g?
-1, 3/62, 2/11
Let p(w) be the first derivative of w**7/9 + 4*w**6/15 + w**5/10 - w**4/9 + 3*w - 7. Let n(v) be the first derivative of p(v). Suppose n(u) = 0. What is u?
-1, 0, 2/7
Let q(j) = j**3 - 4*j**2 + 3. Let h be q(4). Suppose h*w + w - 52 = 0. Factor w*m**3 + 14*m**3 + 24 + 36*m + 18*m**2 - 24*m**3.
3*(m + 2)**3
Factor 0 - 17/2*g**2 - 1/4*g**3 + 0*g.
-g**2*(g + 34)/4
Let w(y) be the first derivative of -2*y**3/27 + 5*y**2/9 + 28*y/9 - 119. Find f such that w(f) = 0.
-2, 7
Suppose 6*f = 5*f + 6. Solve -f*t - 26*t**3 + 12*t**4 + 36*t - 9*t - 13*t = 0.
-1/2, 0, 2/3, 2
Let i = 52 - 49. Factor 49*z**4 + 3*z**3 + 8*z - 4*z**2 - 45*z**4 - 11*z**i.
4*z*(z - 2)*(z - 1)*(z + 1)
Let g be ((216/(-126))/(-2))/(10/28). Factor 4/5 + g*o**2 - 12/5*o - 4/5*o**3.
-4*(o - 1)**3/5
Let q(w) be the first derivative of -2*w**6/15 + w**5/5 + w**4/3 - 2*w**3/3 + 27*w + 21. Let o(g) be the first derivative of q(g). Find d, given that o(d) = 0.
-1, 0, 1
Suppose -m = -n + 1, -2*n + 24 = m + 7. Factor 1 + 14*l + 5*l - 23*l + n*l + l**2.
(l + 1)**2
Let a(y) = -y**3 + 8*y**2 + 8*y + 4. Let b be a(9). Let k be (-8)/(-10) + (24/b)/(-4). Factor 0*x + 2/11*x**4 + 0*x**k + 0*x**3 + 0.
2*x**4/11
Let w be (-255)/272*162/(-5). Solve 3/2 + w*j**2 + 27/2*j = 0.
-2/9
Let h(j) be the second derivative of 1/80*j**5 + 0 - 1/24*j**4 + 25*j + 1/24*j**3 + 0*j**2. Suppose h(q) = 0. What is q?
0, 1
Let g(v) be the third derivative of 0*v - 1/36*v**4 - 1/270*v**5 + 0 + 2*v**2 + 0*v**3. Find r such that g(r) = 0.
-3, 0
Let h(a) = 4*a**3 - 25*a**2 + 41*a - 11. Let j(f) = -5*f**3 + 26*f**2 - 41*f + 8. Let i(d) = 4*h(d) + 3*j(d). Factor i(n).
(n - 20)*(n - 1)**2
Let l(n) be the second derivative of 13*n + 22/9*n**6 - 23/9*n**4 + 8/3*n**2 + 50/63*n**7 - 16/9*n**3 + 19/15*n**5 + 0. Factor l(v).
4*(v + 1)**3*(5*v - 2)**2/3
Let p = 20 + -18. Factor 6*b + 7 - 6*b**3 + 0*b - 2*b**4 - 3 - 2*b**p + 0*b.
-2*(b - 1)*(b + 1)**2*(b + 2)
Let o = 5751/7652 - 3/1913. Factor 1/4*c**2 - 1 + o*c.
(c - 1)*(c + 4)/4
Let j(o) = o**2 + 1. Let v be 2*(-4 - (-177)/6). Let r(m) = 8*m**2 + 9. Let i(p) = v*j(p) - 6*r(p). What is c in i(c) = 0?
-1, 1
Suppose 4/9*u + 0 + 2/9*u**2 = 0. What is u?
-2, 0
Let f be (-1 - (-9)/7)*(-7)/(-12). Let c(k) be the second derivative of 5*k + k**2 - 1/12*k**4 - f*k**3 + 0. Factor c(o).
-(o - 1)*(o + 2)
Solve 34*l**2 - 3*l**4 + 3*l**3 + l**2 + 0*l**3 - 36*l - 11*l**2 = 0 for l.
-3, 0, 2
Let z(y) be the second derivative of -y**7/14 - y**6 - 93*y**5/20 - 11*y**4/2 + 16*y**3 + 48*y**2 + y + 16. What is k in z(k) = 0?
-4, -2, -1, 1
Let u(r) = -14*r**4 - 6*r**3 + 2*r**2 + r + 7. Let q(z) = 13*z**4 + 7*z**3 - z**2 - z - 6. Let x(o) = 7*q(o) + 6*u(o). Factor x(f).
f*(f + 1)**2*(7*f - 1)
Let c(i) be the first derivative of 12*i**5/65 + 5*i**4/26 - 12*i**3/13 - 3*i**2/13 + 20*i/13 - 108. Find z, given that c(z) = 0.
-2, -5/6, 1
Let z(j) be the first derivative of j**4/8 - 5*j**3/6 + 7*j**2/4 - 3*j/2 + 107. Solve z(o) = 0.
1, 3
Suppose 5*u - 114 = 6. Suppose z + z - u = 0. Determine t so that -30*t**5 - 22*t**4 - 60*t**3 - z*t**2 - 47*t**4 + 9*t**5 = 0.
-2, -1, -2/7, 0
Let y(c) = 312*c - 6084. Let z(b) = b**2. Let i(u) = y(u) - 4*z(u). Suppose i(f) = 0. Calculate f.
39
Suppose -2*b = -214 + 204. Suppose 0 = 5*d + h - 12, -2*h + 3*h + 8 = b*d. Factor 5/2*l - d*l**2 - 1/2.
-(l - 1)*(4*l - 1)/2
Let a(u) = u**4 - u**3 - u**2 + 2*u. Let p(f) = f**5 - 46*f**4 + 1008*f**3 - 8794*f**2 + 28573*f. Let w(d) = 6*a(d) - p(d). Find v such that w(v) = 0.
0, 13
Let s(l) be the second derivative of -1/10*l**4 + 0 + 2/15*l**3 - 11*l + 1/50*l**5 + 0*l**2. Factor s(c).
2*c*(c - 2)*(c - 1)/5
Let t = -28 + 42. Let u(f) = -f**3 + 13*f**2 + 15*f - 10. Let a be u(t). Solve 4*r - 6*r + 16*r**5 - 4*r**2 + 2*r + a*r**4 - 16*r**3 = 0.
-1, -1/4, 0, 1
Let g = 14729/3 + -4909. Suppose -g + 1/3*z**2 + 1/3*z = 0. What is z?
-2, 1
Let s(l) be the third derivative of -l**5/60 + l**4/12 + 4*l**3 + 3*l**2 - 9. Suppose s(z) = 0. Calculate z.
-4, 6
Let r be (1*-1)/(4 - 20/4). Let p be r/(7/((-21)/(-6))). Factor 0*t**2 - 1/2*t**4 + 0*t + p*t**3 + 0.
-t**3*(t - 1)/2
Let d = -7288033/45933 + -1/15311. Let h = d + 159. Factor 0 + 2/3*v - 1/3*v**3 + h*v**2.
-v*(v - 2)*(v + 1)/3
Let u = -149888/5 - -29979. Factor -6/5 - 1/5*f**2 + u*f.
-(f - 6)*(f - 1)/5
Let u = 9 - 9. Let v = u + 2. Suppose 4*j**2 + 0*j - j**2 - 2 - 4*j**v + 3*j = 0. What is j?
1, 2
Let c(d) be the third derivative of -5/2352*d**8 + 0*d + 0*d**4 - 2/105*d**6 - 17/1470*d**7 + 0*d**3 - 1/105*d**5 + d**2 + 0. Determine z, given that c(z) = 0.
-2, -1, -2/5, 0
Let j(n) be the first derivative of -2*n**6/3 + 8*n**5/5 - 8*n**3/3 + 2*n**2 - 147. What is o in j(o) = 0?
-1, 0, 1
Let s(a) be the third derivative of -1/420*a**6 + 0 + 0*a + 1/420*a**5 + 1/84*a**4 + 0*a**3 - 1/1470*a**7 + 13*a**2. Suppose s(c) = 0. Calculate c.
-2, -1, 0, 1
Let d(w) = -8*w**2 + 19*w + 139. Let v(k) = 52*k**2 - 124*k - 904. Let g(l) = -32*d(l) - 5*v(l). Factor g(i).
-4*(i - 6)*(i + 3)
Let v(z) be th