2.
-(r - 3)*(r + 1)/3
Let v = -43 - -646/15. Let x(q) be the first derivative of 1/10*q**4 + 0*q**2 + 1/25*q**5 + 0*q + 4 + v*q**3. Suppose x(y) = 0. Calculate y.
-1, 0
Let u = 14 - 12. Factor -5*y - 3*y**2 + u*y + 6*y**2.
3*y*(y - 1)
Let m(c) be the first derivative of c**4/4 - 3*c**2/2 + 2*c + 1. Find s such that m(s) = 0.
-2, 1
Let u be 10/8 - (-1)/(-4). Let s be (u + 0)/((-5)/(-25)). Suppose -10*l**4 - 18*l**4 + 16*l**s - 2*l**2 + l**3 + 13*l**3 = 0. Calculate l.
0, 1/4, 1/2, 1
Solve 0*m**2 - 4*m**2 + 4*m - 3 - 4*m**2 + 7*m**2 = 0 for m.
1, 3
Let q(j) = -j - 4. Let m be q(-9). Find v, given that -4*v**5 + 2*v**m + 2*v**4 - 3*v**2 + 3*v**2 = 0.
0, 1
Let w be 3 + (2 + 0)/2. Let m(b) = b**2 - 4*b + 3. Let i be m(4). Factor -i*j - 2*j - 4 + w*j**2 - 5*j**2 + 9*j.
-(j - 2)**2
Let z(o) be the third derivative of 1/30*o**5 + 1/3*o**3 + 2*o**2 + 5/24*o**4 + 0 + 0*o. Factor z(i).
(i + 2)*(2*i + 1)
Let l(z) be the second derivative of 0 - 1/3*z**3 - 1/15*z**6 - 1/2*z**4 + 3*z + 0*z**2 - 3/10*z**5. Factor l(d).
-2*d*(d + 1)**3
Suppose -11*w + 10*w = -56. Determine m, given that 5*m**4 - 24*m**2 - 8 - 15*m**3 + 48*m + w + 3*m**5 - 9*m**3 - 2*m**4 = 0.
-2, -1, 2
Let t(y) be the second derivative of -y**7/84 - y**6/10 - 9*y**5/40 - y**4/6 + y - 15. Factor t(d).
-d**2*(d + 1)**2*(d + 4)/2
Let d be -23*(-2)/(-4)*-2. Suppose 4*h = d - 7. Factor 2*l - l**4 + 2*l**2 - 4*l**2 + 3*l**h - 2*l**3.
2*l*(l - 1)**2*(l + 1)
Let g(v) be the first derivative of v**5 + 25*v**4/4 + 35*v**3/3 + 15*v**2/2 - 14. Suppose g(i) = 0. What is i?
-3, -1, 0
Factor 25*j**2 + 8*j**3 - 14*j**3 + 15 + 35*j + 11*j**3.
5*(j + 1)**2*(j + 3)
Let q(j) be the first derivative of -22/27*j**3 - 14/45*j**5 + 0*j + 2/9*j**2 + 4 + 8/9*j**4. Factor q(d).
-2*d*(d - 1)**2*(7*d - 2)/9
Let n(x) = 5*x**2 - 38*x + 82. Let z(s) = -110*s**2 + 835*s - 1805. Let b(w) = 45*n(w) + 2*z(w). Find q such that b(q) = 0.
4
Let u(b) = -5*b**2 - 3*b. Let h(k) = -6*k**2 - 2*k. Let a(o) = 3*h(o) - 4*u(o). Factor a(w).
2*w*(w + 3)
Suppose 3 = 4*h - 1. Let x be (h - 2 - -2)*2. Factor -2*z + 0*z + x*z**5 - 4*z**2 + 0*z + 4*z**4.
2*z*(z - 1)*(z + 1)**3
Let i = -5 - 4. Let s be i/(-1 + 4)*-1. Factor 3*z**3 + 8*z**s - 3*z**4 - 3*z**2 - 5*z**3.
-3*z**2*(z - 1)**2
Let s(d) be the third derivative of -d**7/70 + d**6/40 + 3*d**5/20 - d**4/8 - d**3 - 11*d**2. Suppose s(y) = 0. Calculate y.
-1, 1, 2
Let j(z) = -z**2 + 5*z + 8. Let b be j(6). Determine t so that -5*t - 3*t**2 + 7*t**2 - 2*t**3 - 2*t**4 + 6*t - b + t**5 = 0.
-1, 1, 2
Let u(c) = -45*c**2 - 175*c - 40. Let v(x) = 67*x**2 + 262*x + 60. Let j(i) = -7*u(i) - 5*v(i). Suppose j(p) = 0. Calculate p.
-4, -1/4
Let f(k) = -2*k**5 + k**4 + 2*k**3 - 2*k**2 + k + 1. Let a(p) = -p**4 + p + 1. Let u(i) = 2*a(i) - 2*f(i). Let u(v) = 0. What is v?
-1, 0, 1
Find k, given that 0*k - 1/5*k**2 + 0 + 1/2*k**3 = 0.
0, 2/5
Let m(s) be the first derivative of -s**6/12 + 3*s**5/10 - s**4/4 + 42. Solve m(n) = 0 for n.
0, 1, 2
Let x(k) be the first derivative of -k**6/39 - 2*k**5/65 + 10. What is s in x(s) = 0?
-1, 0
Find v such that 8*v - 4*v**2 + 12*v - 28*v + 12*v = 0.
0, 1
Let r(s) be the second derivative of s**4/42 - s**3/7 + 2*s**2/7 + 4*s. Determine g so that r(g) = 0.
1, 2
Suppose 0 = 90*g - 34*g - 112. Factor 15/2*u**g - 21/2*u + 3.
3*(u - 1)*(5*u - 2)/2
Let y(g) be the third derivative of -g**5/180 - g**4/24 + 2*g**3/9 + 2*g**2. Factor y(j).
-(j - 1)*(j + 4)/3
Factor -3*t + 0*t + 6*t**2 + t + 2*t**3 - 6.
2*(t - 1)*(t + 1)*(t + 3)
Let v(k) = k**2 - 11*k + 31. Let z be v(7). Determine u, given that 7/2*u**2 + 0 + u + 5/2*u**z = 0.
-1, -2/5, 0
Let y(f) be the third derivative of -f**6/780 + 2*f**5/195 - f**4/52 - 7*f**2. Find b, given that y(b) = 0.
0, 1, 3
Let u be 39/21 + (-3)/(-21). Factor 0*z**3 + 4*z**u + 2*z + z**3 + 8*z - 6*z.
z*(z + 2)**2
Let n be 360/648 + 1/3. Solve 0 + 2*w**3 + n*w**5 - 4/9*w**2 + 0*w - 8/3*w**4 = 0.
0, 1/2, 2
Let o = 61 + -58. Factor -1/3*u + 1/3*u**o + 0 + 0*u**2.
u*(u - 1)*(u + 1)/3
Let o(u) = 6*u**2 - 7*u + 5. Let q(n) = -3*n**2 + 4*n - 2. Let m(h) = -h + 2. Let k be m(0). Let t(x) = k*o(x) + 5*q(x). Suppose t(g) = 0. Calculate g.
0, 2
Let w(r) be the second derivative of -r**5/4 + 5*r**4/6 + 11*r. Find v, given that w(v) = 0.
0, 2
Let b = 6414/7 - 914. Let k = 128267/7 + -18281. Factor b*x + 250/7*x**4 + k*x**3 + 120/7*x**2 + 0.
2*x*(5*x + 2)**3/7
Let y = 79/4 - 37/2. Let r(i) be the first derivative of y*i**4 + 0*i + 2 - 1/5*i**5 + 1/3*i**3 - 1/2*i**6 - i**2. Find v, given that r(v) = 0.
-1, 0, 2/3, 1
Suppose -5*n = r - 16, -2*r = -5*n + 2 + 11. Let s be (-2)/(-8) + 14/8. Factor 3*f**3 - f**s + f**n - 5*f**3.
-f**2*(f + 1)
Let d = -244312/3 + 82218. Let j = -770 + d. Factor -16/3*b**2 - 14/3*b + j*b**3 - 2/3.
2*(b - 1)*(4*b + 1)**2/3
Let f(u) = u**2 + 7*u - 6. Let y be f(-8). Let b(g) = 2*g**2 - 2*g - 2. Let k be b(y). Factor -2/3*i + 4/9 + 2/9*i**k.
2*(i - 2)*(i - 1)/9
Let t(a) be the third derivative of -2*a**7/35 - 3*a**6/10 + 3*a**5/20 + a**4 - 3*a**3/2 - 8*a**2. Find w such that t(w) = 0.
-3, -1, 1/2
Let c(x) be the third derivative of x**5/40 - 15*x**2. Factor c(m).
3*m**2/2
Suppose 3 = h - 0. Suppose -20*j - 3*j**4 - 5 - 16*j - 18*j**h + 0*j - 39*j**2 - 7 = 0. Calculate j.
-2, -1
Let i be ((-12)/(-15) - 1)/((-17)/170). Factor 1/3*g**i + 0 + 0*g + 0*g**3 - 1/3*g**4.
-g**2*(g - 1)*(g + 1)/3
Let r(n) = n**2 + n - 5. Let c be r(-6). Let l be ((-6)/c)/(3/(-10)). Solve 6/5*h + 2/5*h**2 + l = 0.
-2, -1
Suppose d - 5*t = -3, -3*d - 3*t + 298 = 289. Solve -4/3 - 10/3*a + 2*a**d = 0 for a.
-1/3, 2
Let d(s) = -s**2 - 12*s + 3. Let o be d(-12). Let q be 2 - ((0 - -2) + 0). Factor -1/5*u**o + q*u + 0 + 2/5*u**2.
-u**2*(u - 2)/5
Determine h so that -3/4*h**2 + 0 - 3/4*h = 0.
-1, 0
Let f(b) be the first derivative of 3*b**5/5 - 3*b**4/2 - b**3 + 3*b**2 + 11. Solve f(s) = 0.
-1, 0, 1, 2
Let n = 17/4956 - -1/118. Let r(f) be the third derivative of 0 + 0*f**5 + n*f**4 - 1/420*f**6 + 0*f + 0*f**3 + f**2. Determine u so that r(u) = 0.
-1, 0, 1
Determine h, given that -16/17 - 40/17*h - 36/17*h**2 - 2/17*h**4 - 14/17*h**3 = 0.
-2, -1
Let n(b) = 2*b**3 + 2*b**2 - 22*b + 12. Let o(x) = -5*x**3 - 5*x**2 + 45*x - 25. Let p(a) = 5*n(a) + 3*o(a). Solve p(s) = 0 for s.
-3, 1
Let m be 7*(-1 - (-27)/21). Let t(u) = -3*u**2 - 13*u + 4. Let j(k) = -k**2 - 4*k + 1. Let i(f) = m*t(f) - 7*j(f). Factor i(c).
(c + 1)**2
Let v = 0 + -5. Let s(a) = a**3 + 4*a**2 - 6*a - 1. Let l be s(v). Factor -2/3*z**5 + 0*z**l + 0 - 2/3*z + 0*z**2 + 4/3*z**3.
-2*z*(z - 1)**2*(z + 1)**2/3
Let y(n) be the second derivative of -n**9/5040 + n**7/420 - n**5/40 - n**4/12 + 2*n. Let b(g) be the third derivative of y(g). Factor b(o).
-3*(o - 1)**2*(o + 1)**2
Let u = 9/4 + -7/4. Let f = u + 1/6. Factor 2/9*h**2 - f*h + 4/9.
2*(h - 2)*(h - 1)/9
Let i(o) be the first derivative of -1/6*o**4 + 0*o**2 + 1/15*o**5 + 0*o + 0*o**3 - 2 + 1/6*o**6. Factor i(h).
h**3*(h + 1)*(3*h - 2)/3
Let k = 394/7 + -56. Let b(m) = m**3 - 8*m**2 - 12*m + 29. Let w be b(9). What is z in 0*z + 0 + k*z**w = 0?
0
Let i(l) be the third derivative of 0*l - 25/112*l**8 - 2*l**2 - 1/2*l**4 + 3/7*l**7 - 3/5*l**5 + 0 + 0*l**3 + 11/40*l**6. Let i(r) = 0. What is r?
-2/5, 0, 1
Let q be 12/(-14)*(-77)/44. Find x, given that -3/2*x - 1/2*x**3 - 1/2 - q*x**2 = 0.
-1
Let r(f) be the first derivative of f**4/42 - 4*f**2/7 - 4*f + 1. Let s(j) be the first derivative of r(j). Factor s(t).
2*(t - 2)*(t + 2)/7
Let z(s) be the first derivative of -3*s**4/4 - 12*s**3 - 54*s**2 - 8. Solve z(b) = 0.
-6, 0
Let k(g) = g**2 - 1. Let o(j) = -j**2 + 5*j + 8. Let h be o(6). Let w be k(h). Factor -4 + 10*b**2 - 2*b**w + 6 + 6 - 16*b.
-2*(b - 2)**2*(b - 1)
Let d be (-22)/4 - (-4)/8. Let l(a) = -a - 5. Let t be l(d). Solve -6*m**2 + t + 2 - 4 - 6*m - 2*m**3 = 0.
-1
Determine l so that 31*l**3 - 24*l**2 + 128 - 16*l**3 + 0*l**2 - 19*l**3 = 0.
-4, 2
Suppose -4*o = o - 9*o. Factor -2/7*q**2 - 2/7*q + o.
-2*q*(q + 1)/7
Let c be (36/(-27))/(5/(-3)). Let r be (-1 - 0)/((-55)/44). Factor -2/5*z - r + 2/5*z**3 + c*z**2.
2*(z - 1)*(z + 1)*(z + 2)/5
Let t be (2 - 0) + (1 - -3). Let k(o) = -t*o - 6*o**2 + 2*o**2 - 1 + 5. Let h(c) = 11*c**2 + 17*c - 11. Let d(s) = 6*h(s) + 17*k(s). Factor d(x).
-2*(x - 1)*(x + 1)
Let k(l) = -3*l**3 - 6*l**2 - 7*l - 4. Let f = -5 - -1.