c. Let y(t) be the third derivative of d(t). Factor y(u).
-2*(u + 1)*(u + 2)**2/13
Let l(k) = -2*k**2 + 20*k - 16. Let d be l(9). What is q in 1 + 1/2*q**3 + 5/2*q + 2*q**4 - 6*q**d = 0?
-2, -1/4, 1
Suppose 0 = 3*j - 5*j + 100. Let g = -148/3 + j. Let -1/3*c**2 - g*c - 1/3 = 0. Calculate c.
-1
Let y(n) = -n**3 - 6*n**2 + n + 8. Let a be y(-6). Factor -2 - 1 - 2*d**a + 5.
-2*(d - 1)*(d + 1)
Suppose -r - 8 = -5*r. Let g = 4 - r. Find q such that g*q**5 + 0*q**5 + 6*q**3 + 5*q**4 + 2*q**2 + q**4 = 0.
-1, 0
Let b(r) be the second derivative of r**7/14 - r**6/10 - 3*r**5/20 + r**4/4 - 20*r. Solve b(m) = 0.
-1, 0, 1
Let x(r) be the second derivative of -r**4/32 - 3*r**3/16 + 10*r. Factor x(y).
-3*y*(y + 3)/8
Let z be (15/(-35))/((-2)/14). Factor 2/9*h - 2/9*h**z + 2/9*h**2 - 2/9.
-2*(h - 1)**2*(h + 1)/9
Let k(f) = -f**2 + 9*f + 10. Suppose -8*a = -3*a - 50. Let s be k(a). Factor 2/9*d**5 - 2/3*d**4 + 0*d + 2/3*d**3 - 2/9*d**2 + s.
2*d**2*(d - 1)**3/9
Let m(n) = -17*n**2 - 82*n + 20. Let u(a) = -16*a**2 - 83*a + 19. Let l(q) = 5*m(q) - 4*u(q). Determine i so that l(i) = 0.
-4, 2/7
Suppose 4*l - 3*p = 32, -p = -3*p + 8. Let z = -7 + l. Factor -2*d**5 + 5*d**z + d**3 + 5*d**5 + 2*d**5 - d**5.
d**3*(d + 1)*(4*d + 1)
Let i(d) be the third derivative of -d**9/3024 + d**8/840 - d**6/180 + d**5/120 - d**3/6 + d**2. Let q(c) be the first derivative of i(c). Factor q(l).
-l*(l - 1)**3*(l + 1)
Let m(z) be the first derivative of -z**6/420 - z**5/105 + z**4/84 + 2*z**3/21 + z**2/2 - 2. Let l(h) be the second derivative of m(h). Factor l(f).
-2*(f - 1)*(f + 1)*(f + 2)/7
Let y(s) be the second derivative of -s**4/132 + 5*s**3/22 + 6*s - 2. Find z, given that y(z) = 0.
0, 15
Let t(q) = q + 3. Let f be t(-4). Let g be (f/2)/((-6)/24). Suppose -3*k**3 - 20*k**2 - 7*k**3 + 14*k**4 + 4 + 10*k + 2*k**g = 0. What is k?
-1, -2/7, 1
Let l(w) be the first derivative of -3/8*w**2 + 1/16*w**4 - 1/6*w**3 + 0*w + 7. Find y, given that l(y) = 0.
-1, 0, 3
Let c(r) = -16*r**4 - 4*r**3 + 14*r**2 + 6*r + 2. Let q(s) = 49*s**4 + 12*s**3 - 42*s**2 - 19*s - 7. Let j(m) = 14*c(m) + 4*q(m). Factor j(v).
-4*v*(v - 1)*(v + 1)*(7*v + 2)
Let q(c) = -2*c. Let r(f) = -f**2 + f. Let w(y) = q(y) + r(y). Find t such that w(t) = 0.
-1, 0
Let i(s) = 2*s**2 - 9*s - 3. Let f be i(5). Factor -4*n**f + 6*n**2 - 2*n - 15 + 11.
2*(n - 2)*(n + 1)
Factor 0*w**2 + 2*w**2 + 0*w**2 - 6*w**2.
-4*w**2
Let x be (-5)/12*10/(-1750). Let t(j) be the third derivative of -2*j**2 + 1/84*j**4 + 0 + 0*j**5 + 0*j + 0*j**3 - x*j**6. Factor t(h).
-2*h*(h - 1)*(h + 1)/7
Let c be 1*(-3 + 0 - -2). Let w be (7 + -11)*c/9. Suppose -2/9*i - w + 2/9*i**2 = 0. What is i?
-1, 2
Let o(k) = -k**3 - 3*k - 6. Let b(l) = -l**3 - l**2 - 4*l - 5. Let j(i) = 6*b(i) - 5*o(i). Solve j(w) = 0.
-3, 0
Let m be 15/9*12/30. Determine n so that 0*n**3 - 2/9*n**4 + 16/9*n + m + 4/3*n**2 = 0.
-1, 3
Suppose 5*q + k - 81 = -k, 0 = 5*q + k - 78. Find p, given that -9*p**2 + 2 + q*p - 1 + 5 + 0 = 0.
-1/3, 2
Factor 0 + 3/7*k**3 - 1/7*k**4 + 1/7*k - 3/7*k**2.
-k*(k - 1)**3/7
Let j(k) be the first derivative of 2*k**5/55 - 5*k**4/22 + 6*k**3/11 - 7*k**2/11 + 4*k/11 - 14. Factor j(n).
2*(n - 2)*(n - 1)**3/11
Factor 0*j**2 + 4/9*j**3 + 2/9 - 4/9*j - 2/9*j**4.
-2*(j - 1)**3*(j + 1)/9
Let q be (-21)/(-40) - (-11)/(-88). Factor -4/5*d**3 - q*d**4 - 2/5 + 4/5*d**2 + 2/5*d + 2/5*d**5.
2*(d - 1)**3*(d + 1)**2/5
Let c(g) = 6*g**4 + 6*g**3. Let p(m) be the first derivative of -m**5/5 - m**4/4 - 5. Let h(x) = -2*c(x) - 11*p(x). Factor h(f).
-f**3*(f + 1)
Let w(d) = 7*d**2 - d + 10. Let j(k) be the third derivative of -k**5/60 - k**3/6 - 6*k**2. Let f(o) = 24*j(o) + 3*w(o). Suppose f(v) = 0. Calculate v.
-2, 1
Let p be (-18)/4*12/(-18). Let r(b) be the second derivative of -3*b + 1/12*b**4 - b**2 + 1/6*b**p + 0. Solve r(a) = 0.
-2, 1
Let x(b) be the third derivative of 0*b**4 + b**2 + 5/2184*b**8 + 0 + 1/195*b**5 + 0*b**3 - 2/1365*b**7 + 0*b - 1/156*b**6. Let x(g) = 0. What is g?
-1, 0, 2/5, 1
Let s(d) = -d + 1. Let j(p) = p - 1. Let v(l) = 3*j(l) + 2*s(l). Let a be v(2). Factor i + 4*i**3 + 0*i - i**4 - 6*i**2 - a + 3*i.
-(i - 1)**4
Suppose 37*t - 32*t + 1540 = 0. Let x be (-2)/(-8) + (-11)/t. Let x + 4/7*v + 2/7*v**2 = 0. What is v?
-1
Let f be (-20)/(-5) - -1 - (2 + 3). Find o such that f*o - 2/3*o**4 + 2/3*o**2 + 0 + 2/3*o**5 - 2/3*o**3 = 0.
-1, 0, 1
Let x(t) be the second derivative of -1/75*t**6 - 1/5*t**4 + 0 - 3*t + 2/25*t**5 + 4/15*t**3 - 1/5*t**2. What is u in x(u) = 0?
1
Let q be 1 + -1 - (-43 - -41). Factor -2/13*r**q + 8/13*r - 8/13.
-2*(r - 2)**2/13
Find n such that 46/19*n**3 - 8/19*n**4 - 46/19*n + 20/19*n**2 - 12/19 = 0.
-1, -1/4, 1, 6
Let m(p) be the first derivative of -1 + 1/6*p**3 + 0*p**2 + 3*p + 1/12*p**4. Let g(f) be the first derivative of m(f). Factor g(i).
i*(i + 1)
Let f(g) be the second derivative of -g**9/15120 + g**7/1260 - g**5/120 + g**4/4 - g. Let h(d) be the third derivative of f(d). Suppose h(a) = 0. What is a?
-1, 1
Let c(i) = 3*i - 2. Let r be c(5). Suppose 3*z - 2 = r. Let -3*f**3 + 5*f**3 + 3*f - z*f = 0. Calculate f.
-1, 0, 1
Let l be ((-12)/(-15))/(2/5). Suppose 4*c + l = -5*w - 5, 0 = -3*c - 3*w - 3. Factor 9/2*v**c - 6*v**3 - v + 5/2*v**4 + 0.
v*(v - 1)**2*(5*v - 2)/2
Let t(z) be the first derivative of z**4/2 - z**2 - 4. Factor t(l).
2*l*(l - 1)*(l + 1)
Let s(r) be the second derivative of r**7/840 + r**6/240 + 7*r**4/12 + 7*r. Let h(q) be the third derivative of s(q). Determine x so that h(x) = 0.
-1, 0
Factor 544/7*q**3 + 456/7*q**2 + 10/7 - 128/7*q**4 + 118/7*q.
-2*(q - 5)*(4*q + 1)**3/7
Suppose 4*t - 8 - 12 = 0. Let x be (1/t)/(3/10). Suppose 8/3*z**2 + x - 8/3*z = 0. Calculate z.
1/2
Let j(w) be the second derivative of w**8/392 - 8*w**7/735 + w**6/60 - w**5/105 + w**2/2 + 4*w. Let r(s) be the first derivative of j(s). Factor r(m).
2*m**2*(m - 1)**2*(3*m - 2)/7
Let d be (-4)/10 + 36/15. Factor -h**3 - 3*h**2 - d*h - 2*h + 4*h**2 + 3*h**2.
-h*(h - 2)**2
Let y(p) be the second derivative of p**6/120 - p**5/10 + p**4/2 - p**3/3 - p. Let g(f) be the second derivative of y(f). Suppose g(s) = 0. Calculate s.
2
Let l(w) = -2*w - 3. Let f be l(-4). Suppose 4*z + 8*c - 3*c + 1 = 0, 3*c + f = 2*z. Suppose z - 18*k**3 + 10*k + 3 + 8*k**3 - 4*k**2 = 0. Calculate k.
-1, -2/5, 1
Let c(o) be the third derivative of o**6/210 + 4*o**5/105 + 2*o**4/21 + 12*o**2. Factor c(p).
4*p*(p + 2)**2/7
Suppose 0 = 2*c - 5*c + 9. Solve -14*r + 6*r**c + 36*r**2 + 8*r**3 + 2*r**4 + 16 + 54*r = 0.
-2, -1
Let h be 6*(-2 + 5/2). Let v(c) be the third derivative of 1/60*c**5 + 2*c**2 + 0 + 1/120*c**6 - 1/24*c**4 - 1/6*c**h + 0*c. Factor v(r).
(r - 1)*(r + 1)**2
Suppose 3*i - 2*y + 11 + 8 = 0, 3*y = -5*i. Let b = -3 - i. Factor -10/7*d**2 + b - 4/7*d.
-2*d*(5*d + 2)/7
Let z(n) = 5*n**5 - 3*n**4 + n**3 + 3*n**2 + 6*n + 4. Let m(a) = -a**5 + a**4 - a**3 - a**2 - a - 1. Let r(x) = -4*m(x) - z(x). Factor r(f).
-f*(f - 1)**2*(f + 1)*(f + 2)
Let d(c) be the first derivative of -c**8/4200 + c**7/525 - c**6/180 + c**5/150 + c**3/3 + 1. Let x(j) be the third derivative of d(j). Let x(v) = 0. What is v?
0, 1, 2
Let w(n) = n + 1. Let z be w(2). Suppose -5*r - 4 = -2*x, -2*r + 6*x = z*x + 6. Factor r + 2/5*y**2 + 4/5*y.
2*y*(y + 2)/5
Let q = 57 - 169/3. Let a be 0*(-1 + (15/9 - 1)). Factor a*t - q*t**2 + 2/3*t**3 + 0.
2*t**2*(t - 1)/3
Let w(z) be the first derivative of -10*z**6/9 + 176*z**5/15 - 42*z**4 + 48*z**3 + 18*z**2 - 35. Factor w(y).
-4*y*(y - 3)**3*(5*y + 1)/3
Suppose -4*g - 137 + 137 = 0. Factor 0*o - 6/5*o**3 + g - 4/5*o**2.
-2*o**2*(3*o + 2)/5
Let q(k) be the first derivative of -k**4/10 + 2*k**3/15 + k**2/5 - 2*k/5 - 18. Solve q(i) = 0.
-1, 1
Let b(i) be the second derivative of -3*i**6/25 + 9*i**5/25 - 2*i**4/5 + 8*i**3/45 - 6*i. Find s such that b(s) = 0.
0, 2/3
Let g be 1 - ((-1)/2)/((-1)/(-6)). Let d(h) be the third derivative of 1/120*h**6 + 0*h + 0*h**5 + 2*h**2 + 0*h**3 + 0*h**g - 1/210*h**7 + 0. Solve d(r) = 0.
0, 1
Let b(q) be the second derivative of 0 + 4*q**2 + q - 25/6*q**4 + 0*q**3. Find a, given that b(a) = 0.
-2/5, 2/5
Let b(u) be the third derivative of 0*u + 0*u**3 - 1/231*u**7 - 3/110*u**5 + 0 + 1/55*u**6 + 1/66*u**4 + 4*u**2. Factor b(j).
-2*j*(j - 1)**2*(5*j - 2)/11
Solve 2*y**2 - 3*y**3 + 9*y + 6*y**3 - 3 - 11*y**2 = 0 for y.