*y**2. Let i(n) = 3*n**5 - 80*n**4 - 281*n**3 - 149*n**2. Let x(p) = 7*h(p) + 4*i(p). Solve x(j) = 0 for j.
-8, -1/2, 0
Let r(t) = -3*t**2 - 5. Let l(m) = -3*m**2 - 4. Suppose -25 = 3*k - 13. Let s(d) = k*r(d) + 5*l(d). Factor s(v).
-3*v**2
Let r(t) = t**2 + 2*t - 20. Let z be r(4). Solve -25 - 10*b - 2*b**2 + 5*b**2 - z*b**2 = 0.
-5
Factor -47/2*m**2 - 42*m + 1/2*m**4 - 22 - 3*m**3.
(m - 11)*(m + 1)*(m + 2)**2/2
Let g(k) be the first derivative of k**5/5 + 11*k**4/2 + 133*k**3/3 + 156*k**2 + 252*k - 674. Factor g(z).
(z + 2)*(z + 3)**2*(z + 14)
Factor 14*u - 3*u**3 - 23*u - 9*u**2 + 3*u.
-3*u*(u + 1)*(u + 2)
Factor -41 + 13*i**2 - 27 + i**2 - 4 + 248*i.
2*(i + 18)*(7*i - 2)
Let l(b) be the first derivative of 0*b + 0*b**2 + 0*b**3 + 0*b**4 + 3/5*b**5 - 1/2*b**6 - 8. Factor l(h).
-3*h**4*(h - 1)
Suppose -j + 9/4*j**2 - 3/2*j**3 + 0 + 1/4*j**4 = 0. What is j?
0, 1, 4
Let x(p) = 3*p**3 + p**2 - 112*p + 111. Let q be x(1). Find d, given that 0*d - 5/2*d**q - 5*d**2 + 0 = 0.
-2, 0
Let m be (-2)/(-10) + 11 + 52/(-5). Factor 1/5*d**5 + 0*d**2 + 4/5*d**4 + 0 + m*d**3 + 0*d.
d**3*(d + 2)**2/5
Let u(c) = -c**5 + c**3 + c**2. Let i(r) = -r**5 + r**4 - 6*r**3 - 10*r**2. Let q(m) = i(m) - 2*u(m). Factor q(o).
o**2*(o - 3)*(o + 2)**2
Suppose -12/5 + 2/25*j**3 - 56/25*j**2 - 118/25*j = 0. Calculate j.
-1, 30
Suppose -66 = 2*i - 5*i. Suppose 250 + i*u + u**2 + 74 + 3*u**2 + 50*u = 0. What is u?
-9
Let v = 17 - 14. Find m, given that 12*m**2 + m**2 + v*m - 7*m**2 + 2 - 5*m**2 = 0.
-2, -1
Let c(p) be the first derivative of 2*p**6/15 - 7*p**5/5 + 17*p**4/3 - 34*p**3/3 + 12*p**2 + 40*p + 10. Let y(l) be the first derivative of c(l). Factor y(z).
4*(z - 3)*(z - 2)*(z - 1)**2
Factor 4*d**3 + 16 + 28*d - d**3 - d**3 + 17*d**2 - 3*d**2.
2*(d + 1)*(d + 2)*(d + 4)
Let b(a) be the second derivative of -a**6/840 - a**5/210 + a**4/42 + 11*a**3/6 + 26*a. Let d(m) be the second derivative of b(m). Factor d(z).
-(z + 2)*(3*z - 2)/7
Let q(b) be the third derivative of 1/16*b**4 - 1/18*b**3 + 8*b**2 + 0*b + 0 - 1/36*b**5. Factor q(v).
-(2*v - 1)*(5*v - 2)/6
Let d(o) = 40*o**4 - 11*o**3 - 165*o**2 + 64*o + 5. Let t(a) = 60*a**4 - 16*a**3 - 248*a**2 + 96*a + 8. Let c(z) = -8*d(z) + 5*t(z). Let c(v) = 0. What is v?
-2, 0, 2/5, 2
Let z(m) be the second derivative of -m**5/60 - 2*m**4/9 - 2*m**3/3 - 29*m. Factor z(d).
-d*(d + 2)*(d + 6)/3
Let b(h) be the third derivative of h**7/210 + 11*h**6/240 + h**5/6 + h**4/4 + 6*h**2 - 4. Factor b(m).
m*(m + 2)**2*(2*m + 3)/2
Let p(l) be the first derivative of -5*l**4/4 + 25*l**3/3 - 35*l**2/2 + 15*l + 171. Factor p(g).
-5*(g - 3)*(g - 1)**2
Determine o so that -17/2*o - 6 + 1/4*o**3 - 9/4*o**2 = 0.
-2, -1, 12
Let o = 197397/37960 + -1/7592. Determine j, given that o*j - 1/5*j**2 - 169/5 = 0.
13
Let b(f) = f**5 - 14*f**4 + 12*f**3 - 10*f**2 + 3*f - 8. Suppose -33 = v + 2*v. Let h = v + 8. Let l(n) = n**4 + 1. Let m(i) = h*b(i) - 24*l(i). Factor m(x).
-3*x*(x - 3)*(x - 1)**3
Suppose 0*w - 4*w + 40 = 0. Solve 12*q**4 + 10*q**3 + 5*q**5 + 3*q**4 - 188*q - 5 + 173*q - w*q**2 = 0.
-1, 1
Suppose -4 = 3*r + 8. Let z = 1 - r. Solve -36*q**2 - 5 - 40 + q**3 - z*q**3 - 63 - 108*q = 0.
-3
Let n = 124/177 + -2/59. Let w(y) be the first derivative of n*y + 2/9*y**3 - 2/3*y**2 + 2. Factor w(t).
2*(t - 1)**2/3
Let j(p) = -p**3 - 2*p**2 + p + 2. Let b(v) = -v**4 - 4*v**3 - 8*v**2 - 11*v - 6. Let x(f) = 2*b(f) + 6*j(f). Factor x(y).
-2*y*(y + 1)*(y + 2)*(y + 4)
Let m(o) be the third derivative of o**5/420 + 13*o**4/42 + 338*o**3/21 + 38*o**2. Factor m(d).
(d + 26)**2/7
Let s = 371/1380 - 1/460. Factor 14/15*f**3 - s + 2/5*f + 8/5*f**2.
2*(f + 1)**2*(7*f - 2)/15
Let i(g) be the first derivative of -3*g**5/20 + 9*g**3/4 - 577. Factor i(m).
-3*m**2*(m - 3)*(m + 3)/4
Suppose 0 = 5*i - 1 - 14. Suppose -4*s**2 + 6*s**i - s**5 - 4*s**5 + 3*s**5 = 0. What is s?
-2, 0, 1
Let t = -11030 - -11032. Suppose -2/11*i**t - 4/11*i + 0 + 2/11*i**3 = 0. Calculate i.
-1, 0, 2
Let g(n) = n**3 + 2*n**2 + 1. Let o be g(-2). Let s be (1 + o)/(1*(-3 - -10)). Let 2/7*d - 4/7*d**4 - 4/7*d**3 - 4/7 + 8/7*d**2 + s*d**5 = 0. What is d?
-1, 1, 2
Let g(p) = -p**3 + 12*p**2 - 41*p + 33. Let h be g(5). Let c(i) be the first derivative of -3*i**2 + 1/3*i**h - 3 + 9*i. Determine o, given that c(o) = 0.
3
Let s = 1607 - 1605. Suppose 0*k**4 - 8/3*k**3 + 0 + 0*k**s + 4/3*k**5 + 4/3*k = 0. Calculate k.
-1, 0, 1
Let x(l) = l - 26. Let a be x(12). Let p be (-60)/a - (-16)/(-56). Factor 2*t**2 - 4*t + 0*t + p*t**3 - 4 + 2*t**2 + 0*t.
4*(t - 1)*(t + 1)**2
Let v(r) be the third derivative of -1/240*r**6 + 0*r**3 + 0*r**5 + r**2 + 1/48*r**4 + 0*r + 0. Let v(y) = 0. What is y?
-1, 0, 1
Suppose -17 = 4*w - 0*i - 5*i, 0 = 5*w - 3*i + 5. Suppose -5*k = -155 + 25. Solve -24*y - 44*y**2 - 8 - k*y**w - 28*y**2 - 32*y = 0.
-2/7
Let t(i) = 3*i**4 - 26*i**3 - 56*i**2 + 259*i + 192. Let k(b) = -16*b**4 + 130*b**3 + 284*b**2 - 1294*b - 960. Let d(f) = 3*k(f) + 14*t(f). Solve d(o) = 0.
-3, -2/3, 4
Let k(f) = f**4 + 3*f**3 - 4*f**2 + 2*f. Let n(z) = 3*z**4 + 9*z**3 - 12*z**2 + 7*z. Let d(t) = -14*k(t) + 4*n(t). Find y such that d(y) = 0.
-4, 0, 1
Suppose 46 = -9*u + 64. Let f(y) be the first derivative of 0*y + 1/14*y**4 + 0*y**3 - 10 - 1/7*y**u. Factor f(n).
2*n*(n - 1)*(n + 1)/7
Factor 0*r**4 - 8553*r**3 + 12*r - 20*r**2 + 4*r**4 + 8557*r**3.
4*r*(r - 1)**2*(r + 3)
Let k = 349 + -346. Let s(q) be the third derivative of 0*q - 2/75*q**5 - 1/300*q**6 + 5*q**2 - 1/20*q**4 + 0 + 0*q**k. Factor s(v).
-2*v*(v + 1)*(v + 3)/5
Let z = 839 + -834. Let g(o) be the first derivative of 1/15*o**6 - 7 - 8/25*o**z + 0*o**2 + 0*o - 4/15*o**3 + 1/2*o**4. Factor g(c).
2*c**2*(c - 2)*(c - 1)**2/5
Let l = 7 + -1. Solve -l - 8*t**2 + t - 5*t + 10*t**2 = 0.
-1, 3
Let f(m) be the third derivative of m**6/360 - 7*m**5/90 + 65*m**4/72 - 50*m**3/9 + 85*m**2. Determine r so that f(r) = 0.
4, 5
Let s(x) be the third derivative of x**6/480 + x**5/48 - x**4/24 - 5*x**3/6 - 163*x**2. Factor s(g).
(g - 2)*(g + 2)*(g + 5)/4
Let v(i) be the first derivative of -i**8/112 + i**7/70 + i**6/40 - i**5/20 - 2*i**2 + 11. Let k(a) be the second derivative of v(a). What is j in k(j) = 0?
-1, 0, 1
Let q(n) be the second derivative of -n**5/60 - n**4/3 - 11*n**3/18 - 313*n. What is z in q(z) = 0?
-11, -1, 0
Let a = -15 + 20. Factor 24*g**2 + 4 + 2 - 3*g**5 - 21*g - 6*g**3 + 2*g**a + 4*g**5 - 6*g**4.
3*(g - 1)**4*(g + 2)
Let -1 + 5/2*s - 2*s**2 + 1/2*s**3 = 0. What is s?
1, 2
Suppose -2*l = a - 6, 3*a + 2*l - 5 = 5. Factor 17*g**4 - 9 + 31*g**3 + 19*g**4 - 44*g**a + 44*g - 91*g**3 + 1.
4*(g - 2)*(g + 1)*(3*g - 1)**2
Let d be ((-4)/(84/9))/((-5)/35). Let -19*p**2 - 173*p**d - p - 147*p**5 - 3*p - 280*p**4 - 25*p**2 = 0. Calculate p.
-1, -1/3, -2/7, 0
Let y(k) be the third derivative of 2*k**7/945 - 7*k**6/180 + k**5/27 - 365*k**2. Factor y(h).
2*h**2*(h - 10)*(2*h - 1)/9
Let s(i) be the second derivative of i**4/12 - 4*i**3/3 + 41*i. Factor s(b).
b*(b - 8)
Let a(d) be the first derivative of -9*d**4/2 + 26*d**3/3 - 40*d**2/9 + 8*d/9 + 186. Factor a(s).
-2*(s - 1)*(9*s - 2)**2/9
Let m(x) be the third derivative of -3*x**8/32 - 3*x**7/70 + 7*x**6/60 + x**5/15 + 70*x**2 + 2. Determine l, given that m(l) = 0.
-2/3, -2/7, 0, 2/3
Let a be ((-9)/(-15) - (-253)/45) + -6. Let 0*t**4 + 0 + 2/9*t**3 + 0*t + 0*t**2 - a*t**5 = 0. What is t?
-1, 0, 1
Solve -80*m + 694*m**3 - 690*m**3 + 72 + 16*m**4 - 104 - 56*m**2 + 4*m**5 = 0.
-2, -1, 2
Let 30 - 30 - 3*i**3 + 104*i + 2*i**4 + 61*i**3 + 160*i**2 = 0. What is i?
-26, -2, -1, 0
Suppose -2/3*o - 1/6*o**2 + 0 = 0. Calculate o.
-4, 0
Let t(k) be the second derivative of -k**5/4 - 185*k**4/12 - 175*k**3/3 - 300*k. Factor t(a).
-5*a*(a + 2)*(a + 35)
Factor -9*o - 232 - 5*o - 8*o**2 + 226.
-2*(o + 1)*(4*o + 3)
Let w(x) be the first derivative of -x**3/18 - 13*x**2/12 - 2*x + 78. Factor w(j).
-(j + 1)*(j + 12)/6
Factor 1/4*g**2 + 0 - 13/2*g.
g*(g - 26)/4
Let k(g) be the third derivative of g**7/2520 - g**6/360 - g**4 + 10*g**2. Let s(d) be the second derivative of k(d). Factor s(x).
x*(x - 2)
Factor -11/4*k**2 + 0 - 5/4*k - 7/4*k**3 - 1/4*k**4.
-k*(k + 1)**2*(k + 5)/4
Let u(v) be the first derivative of -17*v**6/3 + 20*v**5 - 31*v**4/2 - 4*v**3/3 + 55. What is k in u(k) = 0?
-1/17, 0, 1, 2
Let b(n) = -n**3 + 16*n**2 + 3*n - 15