) = t*l(w) + 6*b(w). Factor d(m).
-4*m*(9*m - 2)
Let g(x) = -6*x**2 - x. Let t(s) = -7*s**2 - s. Let n(d) = -6*g(d) + 5*t(d). Let n(o) = 0. Calculate o.
-1, 0
Let b = -8 - -6. Let y be (-9)/54 + b/(-4). Factor -1/3*i**2 + 0*i - y*i**5 - i**3 - i**4 + 0.
-i**2*(i + 1)**3/3
Let x(g) be the second derivative of g**7/28 + g**6/8 + 3*g**5/20 + g**4/16 + 3*g. Factor x(q).
3*q**2*(q + 1)**2*(2*q + 1)/4
Suppose 9*g - 6 = 7*g. Let o(r) be the third derivative of 0*r - 1/210*r**7 + 0*r**g - 1/120*r**6 + 0*r**5 + 0*r**4 + 0 - 2*r**2. Let o(l) = 0. Calculate l.
-1, 0
Let q(u) = 4*u**2 + 18*u + 12. Let m(x) = -8*x**2 - 37*x - 24. Suppose 3*c - 20 = -5. Let z(h) = c*q(h) + 2*m(h). Solve z(y) = 0 for y.
-3, -1
Let m(f) = -3*f**5 + 2*f**4 + f**3 + f**2 - 3*f + 2. Let c(q) = 12*q**5 - 9*q**4 - 3*q**3 - 3*q**2 + 12*q - 9. Let p(o) = 5*c(o) + 21*m(o). Factor p(r).
-3*(r - 1)**2*(r + 1)**3
Let p(x) = -x + 2*x - 8*x**3 + 4*x - x**2. Let s(r) = -9*r**3 + 6*r. Let l(m) = -6*p(m) + 5*s(m). Factor l(k).
3*k**2*(k + 2)
Let b be 206/378 + (-2)/7. Let g(n) be the second derivative of 1/135*n**6 + 0 + b*n**3 + 1/18*n**5 + 2/9*n**2 + 1/6*n**4 - n. Suppose g(y) = 0. What is y?
-2, -1
Suppose -6 = -b - 0*b. Let o(l) = 2*l**4 - 9*l**3 + 11*l**2 + 11*l. Let x(t) = -t**4 + 5*t**3 - 6*t**2 - 6*t. Let k(a) = b*o(a) + 11*x(a). Factor k(n).
n**3*(n + 1)
Let i = 85 + -82. Factor 0 - 2/5*c**i + 4/5*c - 2/5*c**2.
-2*c*(c - 1)*(c + 2)/5
Let s(z) be the third derivative of 0*z**4 - 1/150*z**5 - 3*z**2 - 1/150*z**6 + 0*z**3 + 0 - 1/525*z**7 + 0*z. Suppose s(p) = 0. Calculate p.
-1, 0
Let r = 561/4 - 140. Let c(w) be the first derivative of 1/5*w**5 - 3 + 0*w**3 + 0*w + 0*w**2 + r*w**4. Factor c(o).
o**3*(o + 1)
Let b(l) = l**5 + l**4 - l**2 + l + 1. Let n(d) = -10*d**5 - 16*d**4 - 2*d**3 + 16*d**2 - 12*d - 12. Let x(r) = -12*b(r) - n(r). Let x(q) = 0. What is q?
-1, 0, 1, 2
Let o(n) = -6*n**2 - 6. Let z(q) = 7*q**2 + q + 6. Let i(k) = -6*o(k) - 5*z(k). Let p be i(4). Factor -a**4 + 4*a - 4*a**3 + 2*a**2 - 8*a**p + 7*a**4.
2*a*(a - 1)*(a + 1)*(3*a - 2)
Factor 4/7*t**4 + 0 - 4/7*t**2 + 4/7*t**5 - 4/7*t**3 + 0*t.
4*t**2*(t - 1)*(t + 1)**2/7
Let d(k) be the second derivative of -2/75*k**6 + 2/15*k**3 - k - 1/210*k**7 + 1/15*k**4 + 0 - 3/100*k**5 + 0*k**2. Suppose d(j) = 0. What is j?
-2, -1, 0, 1
Let d(k) = -k**2 - k. Let s(h) = 6*h - 10. Let w(m) = 2*d(m) - s(m). Solve w(b) = 0 for b.
-5, 1
Let g(r) be the first derivative of 0*r + 0*r**2 + 2 - 3/5*r**5 - 3*r**4 - 4*r**3. Factor g(c).
-3*c**2*(c + 2)**2
Let n(v) = -6*v - 21. Let r be n(-4). Let k(o) be the first derivative of -3 + 1/3*o**r - 1/2*o**2 - 2*o. Factor k(u).
(u - 2)*(u + 1)
Let v(u) be the third derivative of u**8/2520 - u**7/105 + u**6/10 - 3*u**5/5 + 9*u**4/4 - 27*u**3/5 - 5*u**2. Factor v(t).
2*(t - 3)**5/15
Let f(h) be the third derivative of h**8/112 + h**7/35 + h**6/40 + 3*h**2. Find d, given that f(d) = 0.
-1, 0
Let r(t) be the third derivative of t**5/100 + t**4/2 + 10*t**3 - 20*t**2. Factor r(c).
3*(c + 10)**2/5
Suppose r = 3*r - 10. Suppose -r*z = -4*z + q - 3, -4*z + 2*q = -6. Factor -2 + 3*k + z*k**2 + k**2 - 4*k**2.
-(k - 2)*(k - 1)
Let h = 302 + -300. Factor -1/2*b**h - 2 + 2*b.
-(b - 2)**2/2
Let z = 77/2 - 38. Factor 0*g - z*g**2 + 1/2.
-(g - 1)*(g + 1)/2
Factor 8*c + 17*c + 16*c**2 + 25*c**4 - 30*c**3 - 26*c**2 - 15 + 10*c - 5*c**5.
-5*(c - 3)*(c - 1)**3*(c + 1)
Let j(b) be the second derivative of b**4/150 - b**3/15 + 6*b**2/25 + 14*b - 2. Solve j(m) = 0 for m.
2, 3
Let q(m) be the first derivative of 4*m**3/33 + 3*m**2/11 - 19. Factor q(a).
2*a*(2*a + 3)/11
Find g, given that -9/5*g**2 + 13/5*g**3 - g**4 + 2/5 - 1/5*g = 0.
-2/5, 1
Solve -9*y**2 + 0*y - 13*y**2 - 2*y**3 + 24*y**2 + 4*y = 0 for y.
-1, 0, 2
Let s = 13 + -7. Suppose -o + d = -4, -o + d = 5*d + s. Factor -2/5 - 2/5*i**3 - 6/5*i - 6/5*i**o.
-2*(i + 1)**3/5
Suppose 3 = -2*y + r, 6*y - y = -r + 10. What is s in -1 + y + 0 - s**2 = 0?
0
Factor -1/6*f**2 + 1/3*f - 1/6.
-(f - 1)**2/6
Factor c**5 - 221/2*c**2 - 11/4*c**4 - 18 - 171/4*c**3 - 97*c.
(c - 9)*(c + 2)**3*(4*c + 1)/4
Let 16/3*k**4 - 8*k**3 + 5*k - 2/3 - 23/3*k**2 = 0. Calculate k.
-1, 1/4, 2
Suppose -4*u = -2*u. Suppose u*v - 3 = v. Let q(x) = -4*x**3 + x**2 + 4*x - 1. Let k(w) = 3*w**3 - w**2 - 3*w + 1. Let p(g) = v*k(g) - 2*q(g). Factor p(f).
-(f - 1)**2*(f + 1)
Let d = 325/28 - 43/4. Let m(h) be the first derivative of -h**2 - 3 + 4/7*h - d*h**3. Factor m(q).
-2*(q + 1)*(9*q - 2)/7
Let j(b) be the third derivative of b**5/60 - 7*b**4/24 + 37*b**2. Factor j(y).
y*(y - 7)
Let g(y) be the first derivative of 13/7*y**3 + 12/7*y + 24/7*y**2 + 9 + 9/28*y**4. Let g(s) = 0. Calculate s.
-2, -1/3
Let n(p) = -3*p**2 + 5*p + 5. Let u(c) = 4*c**2 - 7*c - 7. Let q = -23 + 18. Let s(k) = q*u(k) - 7*n(k). Find o such that s(o) = 0.
0
Let s(y) be the second derivative of -y**8/224 - 3*y**7/140 - 3*y**6/80 - y**5/40 - y**2/2 - 5*y. Let i(f) be the first derivative of s(f). Factor i(z).
-3*z**2*(z + 1)**3/2
Let i(f) be the third derivative of -f**5/140 - f**4/28 - f**3/14 - 17*f**2. Find t such that i(t) = 0.
-1
Suppose 0 = -0*o + 4*o - 12. Let s be (-69)/(-21) + 6/(-21). Factor o*a**2 + 3/2*a**s + 0 + 3/2*a.
3*a*(a + 1)**2/2
Let y(x) be the first derivative of 0*x**4 - 1/15*x**6 + 1/5*x**2 - 4/15*x**3 + 4/25*x**5 + 0*x - 2. Factor y(p).
-2*p*(p - 1)**3*(p + 1)/5
Let j(m) be the third derivative of 1/12*m**4 + 0 + 0*m + 1/210*m**7 + 0*m**5 - 1/6*m**3 - 1/60*m**6 + 4*m**2. Factor j(y).
(y - 1)**3*(y + 1)
Let -3*q - 4 - q**2 + 1 + 7 = 0. Calculate q.
-4, 1
Let h(g) = g**2 - g - 1. Let k(x) = 4*x**2 + 2*x - 14. Let m(s) = -6*h(s) + k(s). Determine q so that m(q) = 0.
2
Let v be (1 - -5)*(-1)/(-2). Suppose -v*w + w = 0. Factor w - 1/4*b**2 + 0*b.
-b**2/4
Factor -8/5*o**4 + 0*o - 2/5*o**2 - 2*o**3 + 0.
-2*o**2*(o + 1)*(4*o + 1)/5
Let c(l) be the first derivative of -2*l**6/3 + 7*l**5/5 + 3*l**4/2 - 7*l**3/3 - l**2 - 7. Solve c(v) = 0.
-1, -1/4, 0, 1, 2
Let q(l) = l + 1. Let i be q(2). Suppose 9 = 3*m + i. Factor -g**2 + 3*g**2 - m + 6*g + 6.
2*(g + 1)*(g + 2)
Factor -3/7*w**3 + 5/7*w**2 + 0 + 2/7*w.
-w*(w - 2)*(3*w + 1)/7
Let b(v) be the first derivative of -2*v**3/3 + v**2 + 12*v + 7. Find h, given that b(h) = 0.
-2, 3
Factor 2/13*h**4 - 2/13*h**2 - 2/13*h + 2/13*h**3 + 0.
2*h*(h - 1)*(h + 1)**2/13
Suppose -28*d = -26*d - 1538. Let a = d + -6913/9. Solve a*i + 0 + 2/9*i**3 + 8/9*i**2 = 0.
-2, 0
Let h(q) be the third derivative of -q**8/1680 - q**7/210 - q**6/75 - q**5/75 + 6*q**2 + 3. Determine x so that h(x) = 0.
-2, -1, 0
Let q(i) be the first derivative of 5*i**3/12 + 13*i**2/8 - 3*i/2 + 2. Factor q(y).
(y + 3)*(5*y - 2)/4
Let u be (-5)/(-18) - 7/(126/(-4)). Let w(c) be the first derivative of 2 + 0*c - 1/4*c**6 - u*c**3 + 3/10*c**5 + 3/8*c**4 + 0*c**2. Factor w(a).
-3*a**2*(a - 1)**2*(a + 1)/2
Factor 0 + 0*v + 5/2*v**3 - 5/2*v**2.
5*v**2*(v - 1)/2
Let z(q) be the first derivative of -3 + 0*q**2 - 1/16*q**4 - 1/12*q**3 + 0*q. Factor z(g).
-g**2*(g + 1)/4
Let s be (((-25)/90)/(-5))/(3/8). Let p(x) be the first derivative of 1/9*x**2 + 0*x - 3 - s*x**3 + 1/18*x**4. Factor p(b).
2*b*(b - 1)**2/9
Let l = -62 - -65. Factor 2/7*p + 2/7*p**l + 4/7*p**2 + 0.
2*p*(p + 1)**2/7
Suppose -w = -4*f + 12, -3*w - f = -3*f + 6. What is d in 0 + w*d**2 + 1/3*d - 1/3*d**3 = 0?
-1, 0, 1
Solve 13/2*n - 5/2*n**2 + 3 = 0.
-2/5, 3
Let l(v) = -8*v**2 + 12*v - 22. Let d(z) = -z**2 - 1. Let x(w) = -6*d(w) + l(w). Find m such that x(m) = 0.
2, 4
Let t(j) = 7*j**2 - 2*j - 2. Let m be t(2). Let b be -3 - (-3)/(18/m). Solve 1/3*n + 0*n**3 + 2/3*n**2 + 0 - b*n**4 - 1/3*n**5 = 0 for n.
-1, 0, 1
Determine c so that -4/3*c**2 + 8/3*c**3 + 0*c + 0 - 5/3*c**4 + 1/3*c**5 = 0.
0, 1, 2
Let b = -174935/99 - -1767. Let c = b + 1796/693. Find p such that 24/7*p - 8/7 - c*p**2 = 0.
2/3
Factor -18/7 - 24/7*b - 8/7*b**2.
-2*(2*b + 3)**2/7
Let g be (2 + -1)*(-1 + 5). Suppose 0 + 0*x**3 - x**g - 1/4*x + 3/4*x**2 = 0. Calculate x.
-1, 0, 1/2
Solve -3/2*z**3 + 3/2*z - 1 + 1/2*z**2 + 1/2*z**4 = 0.
-1, 1, 2
Let x be (-10)/(-25) - 2/30*-4. Determine o, given that 2/3*o**3 - 2/3*o - 2/3*o**2 + 0 + x*o**4 = 0.
-1, 0, 1
Let g(f) = 6*f**2 - 15*f + 12. Let m(w) = 7*w**2 - 16*w + 12. Let y(i) = 4*g(i) - 3*m(i). Factor y(r).
3*(r - 2)**2
Let q be 30/(-10)*(10/(-6) +