*s - 25*s + 7*s**2 + 22*s**2 + 3*s**3 + 54.
3*(s + 2)*(s + 3)**2
Let l(d) = -3*d**2 + 12*d - 15. Let i(k) = k**2 - 4*k + 7. Let b(a) = 10*i(a) + 4*l(a). Suppose b(j) = 0. What is j?
-1, 5
Let v(u) be the third derivative of -9*u**2 + 0*u + 0*u**3 + 1/12*u**6 + 1/4*u**4 + 0 + 1/105*u**7 + 7/30*u**5. Find z, given that v(z) = 0.
-3, -1, 0
Let t(p) = 7*p**5 - 5*p**4 - 16*p**3 + 14*p**2 - 6*p. Let s(q) = 6*q**5 - 4*q**4 - 15*q**3 + 13*q**2 - 5*q. Let w(v) = -6*s(v) + 5*t(v). Factor w(y).
-y**2*(y - 2)*(y - 1)*(y + 4)
Suppose 4 = 6*k - 5*k. Let -354*j**3 - 196*j**k + 204*j**2 + 32 - 240*j + 284*j**2 + 270*j**3 = 0. What is j?
-2, 2/7, 1
Let h = 87193/80977 - -1/6229. Factor -2/13*k**5 + 0 + 10/13*k**4 - h*k**3 + 0*k + 6/13*k**2.
-2*k**2*(k - 3)*(k - 1)**2/13
Factor -7*v**4 + 7*v**3 - 10*v**2 + 4*v**4 + 39*v**2 + 55*v**2 + 2*v**3.
-3*v**2*(v - 7)*(v + 4)
Let 9/4*z**2 + 9/2 + 33/4*z = 0. Calculate z.
-3, -2/3
Let m(p) be the third derivative of -3*p**6/20 + 8*p**5/5 - 13*p**4/12 - 10*p**3/3 + 8*p**2 + 11. Let m(d) = 0. What is d?
-1/3, 2/3, 5
Let c(g) be the second derivative of g**4/4 + 31*g**3/6 + 5*g**2 + 103*g. Factor c(w).
(w + 10)*(3*w + 1)
Let b(o) be the first derivative of -o**3/15 - 2*o**2/5 + 9*o - 94. Suppose b(f) = 0. What is f?
-9, 5
Factor -u + 1/5*u**2 + 4/5.
(u - 4)*(u - 1)/5
Factor 1/4*q**3 + 0 + q - q**2.
q*(q - 2)**2/4
Let c(f) be the first derivative of -f**6/40 - f**5/10 + 7*f**2/2 + 8. Let z(u) be the second derivative of c(u). What is b in z(b) = 0?
-2, 0
Suppose -f + 38 = 2*y + 16, 3*f + 4*y - 48 = 0. Factor 4/7*r - 2/7 + 0*r**2 + 2/7*r**f - 4/7*r**3.
2*(r - 1)**3*(r + 1)/7
Let s(o) be the second derivative of o**9/12096 - o**8/6720 - 2*o**3 + 4*o. Let g(p) be the second derivative of s(p). Suppose g(l) = 0. What is l?
0, 1
Let b(h) be the first derivative of h**6/3 + 4*h**5/5 - 3*h**4/2 - 16*h**3/3 - 4*h**2 + 6. Find m, given that b(m) = 0.
-2, -1, 0, 2
Factor -207*p**3 + 97*p**3 + 3*p**2 + 2*p + p**4 - 2*p + 107*p**3 - p.
p*(p - 1)**3
Let z(a) be the third derivative of 0 - 1/315*a**7 - 5*a**2 - 1/12*a**4 - 1/90*a**5 + 1/60*a**6 + 2/9*a**3 + 0*a. Determine v, given that z(v) = 0.
-1, 1, 2
Let t(n) be the second derivative of n**5/15 - 8*n**3/3 + n**2 - 5*n + 2. Let x(w) be the first derivative of t(w). Factor x(g).
4*(g - 2)*(g + 2)
Let p(l) be the third derivative of 0 - 1/1680*l**8 + 24*l**2 + 1/200*l**6 - 1/150*l**5 + 0*l**4 + 0*l**3 + 0*l**7 + 0*l. Find y, given that p(y) = 0.
-2, 0, 1
Let y(f) be the second derivative of f**7/84 + f**6/12 + f**5/20 - 7*f**4/12 - f**3/4 + 9*f**2/4 - f + 17. Solve y(q) = 0 for q.
-3, -1, 1
Let c(m) be the second derivative of -m**5/30 - 5*m**4/18 + 25*m**3/9 + 125*m**2/3 - 10*m - 4. Factor c(a).
-2*(a - 5)*(a + 5)**2/3
Determine t, given that 0 - 1/6*t**4 + 0*t - 1/2*t**2 + 2/3*t**3 = 0.
0, 1, 3
Let c(l) be the first derivative of -3*l**5/5 - 3*l**4/2 + 7*l**3 - 6*l**2 + 7. Let c(n) = 0. What is n?
-4, 0, 1
Let i(m) be the third derivative of 11/140*m**6 - 25*m**2 + 3/392*m**8 + 0*m**3 + 29/735*m**7 + 1/14*m**5 + 1/42*m**4 + 0*m + 0. Let i(g) = 0. Calculate g.
-1, -2/9, 0
Factor -2/5*y**3 - 2/5*y**4 + 18/5*y**2 + 18/5*y + 0.
-2*y*(y - 3)*(y + 1)*(y + 3)/5
Let y be 0/2 - (10/30)/(-1). Let i(k) be the first derivative of 2/9*k**3 + 0*k - 1/24*k**4 + 5 - y*k**2. Suppose i(s) = 0. Calculate s.
0, 2
Let z(a) be the third derivative of a**5/15 - 5*a**4/3 - 22*a**3/3 - 40*a**2. Find x such that z(x) = 0.
-1, 11
Let m(u) = u**3 - 21*u**2 - 145*u + 392. Let f be m(26). Factor -3/2 - i + 1/2*i**f.
(i - 3)*(i + 1)/2
Let a(l) = -l**3 + 3*l**2 - l + 5. Let n be a(3). Factor -8*r + 2*r**2 - 15*r**n + 11*r**3 + r**2 - 15*r**3.
-4*r*(r + 1)*(r + 2)
Suppose 0 = b + 5*w - 8, 0 = b - 0*w - 2*w - 1. Suppose -7*c = b*c - 40. Determine x so that 3/2*x**2 + 2*x + 1/2 - 2*x**c - 2*x**3 = 0.
-1, -1/2, 1
Suppose 13*l - 35 = 8*l. Factor 4*p**3 + 3*p**2 + 2*p**3 + 8*p - 4*p + l*p**2.
2*p*(p + 1)*(3*p + 2)
Let k = -15 - -12. Let g be (3 - 12)/3 - k. Suppose s + g + 2 + 0*s**2 - s**2 = 0. Calculate s.
-1, 2
Let o(m) be the first derivative of m**3 - 55*m**2/2 - 38*m + 56. Factor o(l).
(l - 19)*(3*l + 2)
Let j(q) = 4*q**2 - 96*q + 576. Let m(a) = -2*a**2 + 48*a - 288. Let s(y) = 6*j(y) + 11*m(y). Let s(u) = 0. What is u?
12
Let o(m) be the first derivative of 0*m - 2/5*m**3 - 24/25*m**5 - 3/10*m**6 - 21/20*m**4 + 12 + 0*m**2. Solve o(c) = 0.
-1, -2/3, 0
Suppose 33 = -3*s - 3*a, 6*s - 10*s - 3*a = 47. Let b = s - -14. Factor 6/5*l**5 + 12/5*l**3 - 16/5*l**4 + 0*l**2 + b - 2/5*l.
2*l*(l - 1)**3*(3*l + 1)/5
Suppose -16 = 2*g - 4*t, -4*g + 12 = -19*t + 22*t. Factor -3*i + 0 + g*i**2 + 3/4*i**3.
3*i*(i - 2)*(i + 2)/4
Let p(r) = -r + 16. Let d be p(12). Solve -10*w**3 - 12 + 5*w - w**4 - d*w**4 + 5*w**5 + 10*w**2 + 7 = 0 for w.
-1, 1
Let k be (-16)/10 - 10/25. Let l be k*(-12)/8*1. Factor 4*h**3 + h + 2 - 3*h**3 - l*h - h.
(h - 1)**2*(h + 2)
Let i = -4 + 7. Let l be i/(0 - -3) - -5. What is f in 3*f + f**2 - f + 3*f**2 + 4 + l*f = 0?
-1
Let n be 15*(4 - (-11)/(-3)). Suppose -n*w = 3*t + 9, 2*t - w + 0*w = 7. Factor 1/4*z**t + 1/4*z**3 - 1/4*z - 1/4.
(z - 1)*(z + 1)**2/4
Let x = 1650 - 894. Let f be 2/((-4)/10 + x/90). Factor -f - 1/4*u + 1/4*u**3 + 1/4*u**2.
(u - 1)*(u + 1)**2/4
Let i(c) = 5*c**2 + 8*c + 4. Let g be (-3)/(10 + -1)*-12. Let q(z) = 0*z - 7*z + 0*z - g*z**2 - 4. Let l(f) = -3*i(f) - 4*q(f). Let l(w) = 0. What is w?
-2
Let l be -4 - ((-5)/1 + -1). Let y(r) = -2*r**5 + 4*r**4 + 6*r**3 - 6*r + 2. Let q(o) = o**4 + o**2 - o + 1. Let p(m) = l*q(m) - y(m). Factor p(h).
2*h*(h - 2)*(h - 1)*(h + 1)**2
Let o be 2/15 - 57596/(-16830). Solve -8/9*q + o*q**2 + 0 + 2/9*q**3 - 8/9*q**4 = 0.
-2, 0, 1/4, 2
Let i(n) be the first derivative of -n**6/60 - n**5/20 + n**4/24 + n**3/6 + 28*n - 24. Let y(g) be the first derivative of i(g). Factor y(v).
-v*(v - 1)*(v + 1)*(v + 2)/2
Let a(u) be the second derivative of -u**4/24 - u**3/3 - 101*u. Suppose a(m) = 0. What is m?
-4, 0
Let o(h) be the first derivative of -3*h**4/4 - 99*h**3 - 7497*h**2/2 - 7203*h - 417. Factor o(g).
-3*(g + 1)*(g + 49)**2
Let v be (-7 + 6 - 3)*1/(-1). Determine m so that 10/3 + 2/3*m**2 + v*m = 0.
-5, -1
Let q = -2590 - -2654. Factor -4/9*p**2 - 32/3*p - q.
-4*(p + 12)**2/9
Let v(q) = -q**3 + 5*q**2 + 7*q. Let s be v(6). Factor 5*l**4 + 7 - s*l**3 - 5*l + 1 - 15*l**2 + 2 + 11*l**3.
5*(l - 1)**2*(l + 1)*(l + 2)
Let z(b) = 4*b**3 + 117*b**2 - 226*b - 3. Let x(h) = 11*h**3 + 233*h**2 - 454*h - 7. Let l(f) = 3*x(f) - 7*z(f). Determine a so that l(a) = 0.
0, 2, 22
Suppose -20 = 4*g, 6 - 25 = -2*y + 3*g. Factor -18 + 12*k**y - 2*k - 25*k - 42*k.
3*(k - 6)*(4*k + 1)
Suppose -5*q - 2 = -17. Let o(f) be the first derivative of 2*f**2 + 2*f + q - 7/12*f**6 - 23/6*f**3 + 19/10*f**5 - 1/8*f**4. Suppose o(b) = 0. Calculate b.
-1, -2/7, 1, 2
Let d(f) be the second derivative of f**5/5 + f**4/3 - 12*f - 4. Let d(q) = 0. Calculate q.
-1, 0
Let b(n) = -n**2 + 32*n + 17. Let r(l) = -9*l**2 + 258*l + 135. Let u(s) = 33*b(s) - 4*r(s). Let u(m) = 0. What is m?
-7, -1
Let 3*g**2 + 20*g + 40 - 21*g**2 - 32*g**2 + 5*g**5 - 25*g**3 + 5*g**4 + 5*g**4 = 0. Calculate g.
-2, -1, 1, 2
Let t(j) be the first derivative of 0*j - 2/15*j**5 - 7 + 2/3*j**3 - 2/3*j**2 + 0*j**4. Find b such that t(b) = 0.
-2, 0, 1
Let z(l) be the third derivative of l**5/60 + l**4/3 - 7*l**3/6 - 3*l**2. Let o be z(-9). Solve 4*r + 5*r**o + 4*r - 12*r**3 - 2*r - 4*r = 0.
-1/4, 0, 2/3
Factor 11*z - 39*z**2 - 16*z**2 + 10*z**3 - 7*z + 21*z.
5*z*(z - 5)*(2*z - 1)
Let i = -26 - -18. Let w be (-48)/i + -2*1. Let 3*n**2 - 6*n**4 - 1 + 3*n**w + 1 = 0. Calculate n.
-1, 0, 1
Let x be 8/(-360)*(204/112 - 2). Let w(u) be the second derivative of 0*u**3 - 5*u + x*u**7 + 0 + 0*u**2 - 1/180*u**6 + 1/72*u**4 - 1/120*u**5. Factor w(b).
b**2*(b - 1)**2*(b + 1)/6
Let j(b) be the third derivative of -1/3*b**4 + 8/15*b**3 + 0*b + 1/840*b**8 + 7/75*b**5 + 35*b**2 - 4/525*b**7 + 0 + 1/300*b**6. Solve j(a) = 0.
-2, 1, 2
Suppose -4*j + 83 = -h, 2*h - 86 = -3*j - 2*h. Determine d, given that 13*d - 6*d**2 + 3*d**3 + 6 - j*d + 6*d = 0.
-1, 1, 2
Suppose 0 = 5*j + 2*i - 10, -5*j - 2*i = -4*i - 30. Factor -13 + 19 + 128*p - 4*p**j - 25*p**3 + 4 + 22 - 6*p**2.
-(p - 2)*(p + 4)**2*(4*p + 1)
Let p be (-32)/(-15) - (3 + 64/(-20)). Let h(t)