5. Let b(d) = 23*d**4 - 218*d**3 + 788*d**2 - 982*d + 397. Let a(q) = 5*b(q) + 8*l(q). Factor a(v).
-5*(v - 9)*(v - 3)*(v - 1)**2
Let z = 3146/119 - 413/17. Suppose 6/7 + 12/7*b**2 + z*b + 3/7*b**3 = 0. What is b?
-2, -1
Suppose 7 = 82*a - 75*a. Let g(m) = -m**3 + 3*m**2 + 4*m + 2. Let z be g(4). Factor 2*s**z - 2*s - 2 - s**2 - a.
(s - 3)*(s + 1)
Let c(m) be the first derivative of 0*m - 39/4*m**4 + 10 + 12/5*m**5 + 11*m**3 - 3*m**2. What is x in c(x) = 0?
0, 1/4, 1, 2
Let k(m) be the third derivative of 28*m**2 + 0*m + 0*m**4 + 1/2100*m**7 + 0*m**3 + 0 + 1/600*m**5 - 1/600*m**6. Determine w so that k(w) = 0.
0, 1
Let b be 1/(-4) - 196/(-16). Factor -9*a**4 + 3*a**3 + b*a**4 + 9*a + 3*a**2 - 18*a**2.
3*a*(a - 1)**2*(a + 3)
Let c = -2959/3 + 989. Let a(n) be the first derivative of 0*n - 5*n**4 + 0*n**2 - c*n**3 - 12. Let a(q) = 0. Calculate q.
-2/5, 0
Let h be (3 + ((-9)/2 - -2))*18. Determine p so that -7*p**3 - 5*p**3 + h*p**3 = 0.
0
Suppose 0 = 8*u - 24 - 0. Suppose 16/5*z**2 - 18/5 + 2/5*z**4 + 12/5*z - 12/5*z**u = 0. What is z?
-1, 1, 3
Let k be 1 + -1 + -1 + 3. Let s = 3 - 1. Find q such that 2*q**3 - 4*q**2 + 2*q**s - 2*q**2 + 0*q**3 - k*q + 4 = 0.
-1, 1, 2
Let m(b) be the third derivative of -1/12*b**5 + 0 - 11*b**2 + 0*b**4 + 0*b + 0*b**3. Let m(r) = 0. What is r?
0
Let v(h) be the third derivative of -77*h**5/600 - 19*h**4/30 + h**3/15 - 946*h**2. Factor v(p).
-(p + 2)*(77*p - 2)/10
Let d(f) be the first derivative of -f**4/10 - 22*f**3/15 + f**2/5 + 22*f/5 + 177. Determine k so that d(k) = 0.
-11, -1, 1
Let d(r) be the second derivative of 1/45*r**5 + 0 - 1/135*r**6 - 2/27*r**3 - 6*r + 1/54*r**4 + 0*r**2. Factor d(a).
-2*a*(a - 2)*(a - 1)*(a + 1)/9
What is f in 8/7*f + 2/7*f**2 - 120/7 = 0?
-10, 6
Let p(v) be the third derivative of -13*v**7/630 + v**6/15 + 17*v**5/180 - v**4/3 - 2*v**3/9 + 24*v**2. Solve p(i) = 0.
-1, -2/13, 1, 2
Solve -6 + 56/9*q - 2/9*q**2 = 0 for q.
1, 27
Solve -884*s**3 + 0 + 6034/3*s**4 + 98/3*s**5 - 2984/3*s**2 - 496/3*s = 0.
-62, -2/7, 0, 1
Let z(i) = -11*i**3 - 9*i**4 + 10*i + 6*i + 3 - 7. Let d(r) = 10*r**4 + 10*r**3 - 15*r + 5. Let o(n) = 4*d(n) + 5*z(n). Factor o(f).
-5*f*(f - 1)*(f + 2)**2
Let s(g) be the first derivative of g**4/36 - 28*g**3/27 - 57. Suppose s(c) = 0. Calculate c.
0, 28
Let j(y) = -4*y**3 + 2*y**2 + 4*y + 22. Let z(g) = -3*g**3 + g**2 + 2*g + 21. Let q(v) = -5*j(v) + 6*z(v). Factor q(c).
2*(c - 2)**2*(c + 2)
Let x(k) be the third derivative of -k**8/504 + k**7/63 - k**6/20 + 7*k**5/90 - k**4/18 + 78*k**2. Solve x(v) = 0.
0, 1, 2
Let d = 6775/372 - 252/31. Let r = d + -47/6. Factor 0 + 3/4*f**2 + r*f - 2*f**3 - f**4.
-f*(f - 1)*(2*f + 3)**2/4
Let z(w) be the first derivative of 4*w**3/3 + 268*w**2 + 17956*w + 123. Factor z(m).
4*(m + 67)**2
Let a(i) be the third derivative of -i**7/42 + 3*i**6/8 + 4*i**5 + 65*i**4/6 + 4*i**2 - 9*i. Solve a(q) = 0.
-2, 0, 13
Let b(w) be the first derivative of w**6/360 + w**5/15 + 2*w**4/3 + 32*w**3/9 + 18*w**2 - 36. Let m(c) be the second derivative of b(c). Factor m(h).
(h + 4)**3/3
Let b(h) = -h**2 + h - 1. Let i(j) = 55 - 12*j**2 - 15 + 130*j - 118*j. Let k(x) = 8*b(x) - i(x). Factor k(q).
4*(q - 4)*(q + 3)
Let k(a) be the second derivative of -a**4/18 - 25*a**3/9 - 8*a**2 - 7*a + 5. Factor k(h).
-2*(h + 1)*(h + 24)/3
Let c be ((-16)/600)/(2 - (-2588)/(-1302)). Let o = 2/25 - c. Let -3/2*n**3 + 3/2*n**2 + 9/4*n - 3/4*n**5 - o*n**4 + 3/4 = 0. Calculate n.
-1, 1
Let g = 0 + 2. Find a such that -80*a**3 - 10*a + 35*a**4 + 21*a**g - 13*a**2 + 28*a**2 + 19*a**2 = 0.
0, 2/7, 1
Factor -3/4*c**2 - 9/4*c + 3.
-3*(c - 1)*(c + 4)/4
Let y(c) be the second derivative of -c**5/70 - 23*c**4/42 - 40*c**3/7 + 144*c**2/7 - 206*c. Factor y(j).
-2*(j - 1)*(j + 12)**2/7
Let h(d) = -10*d - 2. Let y be h(-1). Let b = 31 - y. Factor -19 - 24*x - 4*x**2 + 6 - b.
-4*(x + 3)**2
Let h = -7 - -7. Let i = 22 + -19. Factor -27*d**i + h*d**2 + 29*d**3 - 2*d**2.
2*d**2*(d - 1)
Let j(g) = g**2 - 11*g - 121. Let a be j(-7). Suppose 2*t = -3*t. Factor 2/11*r**4 + 2/11*r**3 + 0 + t*r - 2/11*r**2 - 2/11*r**a.
-2*r**2*(r - 1)**2*(r + 1)/11
Let q(g) be the second derivative of -g**7/105 + 17*g**6/75 - 103*g**5/50 + 239*g**4/30 - 8*g**3/3 - 80*g**2 + 60*g + 1. Let q(x) = 0. Calculate x.
-1, 4, 5
Let y(h) = -6*h**4 + 3*h**3 + 50*h**2 - 44*h. Let u(i) = i**4 - 2*i**3 - 2*i**2. Let c(b) = -5*u(b) - y(b). Determine t so that c(t) = 0.
-11, 0, 2
Let n(p) = -p**2 + 10*p - 7. Let i be n(9). Let r(l) = -22*l - 1009. Let h be r(-46). Factor 0*o**i + 2/3*o**4 + 1/6*o**5 + 2/3*o**h + 0*o + 0.
o**3*(o + 2)**2/6
Let g(h) = h**3 + h**2 + h. Let k(n) = -n**4 - 6*n**3 + 9*n**2 - 14*n. Let c(u) = -4*g(u) - k(u). Find l, given that c(l) = 0.
-5, 0, 1, 2
Suppose 33*y = 28*y + 10. Let i(v) = -5*v**2 - 2*v + 7. Let g(d) = 135*d**2 + 55*d - 190. Let a(x) = y*g(x) + 55*i(x). Factor a(n).
-5*(n - 1)*(n + 1)
Factor -97200/7 - 3/7*y**2 + 1080/7*y.
-3*(y - 180)**2/7
Factor -888*s**2 + 0*s**5 + 900*s**2 - s**5 + s**3 - 12*s**4.
-s**2*(s - 1)*(s + 1)*(s + 12)
Let s be 1/(-3 + 84/27). Suppose 0 = -2*a + s - 5. Let -2/3*z + 4/3 - 4/3*z**a + 2/3*z**3 = 0. Calculate z.
-1, 1, 2
Let y(m) be the second derivative of -m**6/15 + 3*m**5/5 + 5*m**4/2 + 8*m**3/3 + 200*m. Factor y(p).
-2*p*(p - 8)*(p + 1)**2
Let j(p) = 4*p**5 + 8*p**4 + 4*p**3 - 11*p**2 - 5*p + 21. Let k(c) = -5*c**5 - 9*c**4 - 4*c**3 + 10*c**2 + 6*c - 22. Let h(z) = 6*j(z) + 5*k(z). Factor h(o).
-(o - 2)**3*(o + 1)*(o + 2)
Let o(u) be the first derivative of u**3/3 + 28*u**2 + 784*u - 80. Determine d so that o(d) = 0.
-28
Let c be -2 + (-5)/((-25)/12). Let a = -1825 - -1825. Factor -2/5*l**3 + c*l + a + 0*l**2.
-2*l*(l - 1)*(l + 1)/5
Let x(j) = -4*j**2 + 4*j. Let t(p) = -4*p - 2 - 11*p**2 + 15*p**2 + 7 - 5. Let y = 10 - 5. Let d(c) = y*t(c) + 6*x(c). What is q in d(q) = 0?
0, 1
Let k(n) be the third derivative of n**5/12 - 35*n**4/12 + 20*n**3 - 58*n**2. Find u, given that k(u) = 0.
2, 12
Let k(p) be the third derivative of 1/840*p**8 + 1/60*p**4 + 0 + 4/525*p**7 + 0*p + 1/50*p**6 + 0*p**3 + 2/75*p**5 - 5*p**2. Solve k(v) = 0.
-1, 0
Suppose p = -q - 2*q + 100, 4*q = -3*p + 125. Find s such that 24*s**2 + 20 + 50*s**3 - 114*s**2 - 135*s + 90 + 5*s**5 + 25 + q*s**4 = 0.
-3, 1
Let l(t) be the second derivative of -t**5/180 + t**4/72 + t**3/3 - 2*t**2 + 25*t. Let z(j) be the first derivative of l(j). What is c in z(c) = 0?
-2, 3
Let c(w) = 3*w**4 - w**3 - 2*w**2 - 2. Let a(g) = -20*g**4 + 6*g**3 + 13*g**2 + 13. Let s(y) = 6*a(y) + 39*c(y). Let s(d) = 0. What is d?
-1, 0
Let y(g) be the first derivative of -g**6/120 - g**5/20 - g**4/16 + 6*g + 12. Let o(m) be the first derivative of y(m). Factor o(l).
-l**2*(l + 1)*(l + 3)/4
Suppose 4*z = z + 183. Factor 60*x**2 + 2*x - z*x**2 + x**3 - 4*x.
x*(x - 2)*(x + 1)
Suppose 5*n - 4*q - 162 = 0, 3*n - 3*q = -2*n + 159. Let l = 32 - n. Factor -21*z**3 + 6 + 17*z + 27*z**4 + 4*z + 8*z**2 - 20*z**2 - 21*z**l.
3*(z - 1)**2*(z + 1)*(9*z + 2)
Let j be (-1 + 11)*13/((-325)/210). Let g be (-2)/3 - (9 + 833/j). Factor 1/4*h**2 + 1/4*h**3 + 0 - 1/4*h - g*h**4.
-h*(h - 1)**2*(h + 1)/4
Let k(w) be the first derivative of 0*w + 0*w**2 + 2/5*w**5 - 19 - 2/3*w**3 + 1/2*w**4 - 1/3*w**6. Suppose k(f) = 0. What is f?
-1, 0, 1
Let f(i) = -2*i - 8. Let h be f(-6). Suppose 9*w**2 - 20 - w**4 + 6*w**h + 20*w**3 - 20*w - 6*w**2 + 12*w**2 = 0. What is w?
-2, -1, 1
Let x(w) be the second derivative of w**6/150 - 41*w**5/50 + 1597*w**4/60 + 574*w**3/5 + 882*w**2/5 + w + 111. Determine r, given that x(r) = 0.
-1, 42
Suppose -3*i = 4*x - 14, -i - 2*x - 2*x + 10 = 0. Suppose -2*o + o + i = 0. Factor 4*k**4 + 2*k**3 - 5*k**3 + 4*k - 4*k**o - k**3.
4*k*(k - 1)**2*(k + 1)
Let v(q) be the third derivative of 0 + 1/70*q**6 + 0*q**3 - 4/105*q**5 + 7*q**2 + 0*q + 1/588*q**8 - 2/21*q**4 + 8/735*q**7. Determine m, given that v(m) = 0.
-2, -1, 0, 1
Factor 11/5*d**2 + 8*d + 28/5 - 1/5*d**3.
-(d - 14)*(d + 1)*(d + 2)/5
Let o be 78 - 5/((-10)/6). Suppose -4*z + 3*r + 34 = -o, 60 = 3*z + 3*r. Factor z*w**3 - 20*w**2 - 2 - 10*w**4 - 5*w**3 + 6*w + 4*w + w**5 + w**5.
2*(w - 1)**5
Let y be (-3 - -3) + 1 + 2. Suppose -20 + 26 = 3*m. Solve 9 + b**m + 2*b**2 + b**3 + 15*b - 4*b**y = 0.
-1, 3
Let h = 829 + -3315/4. Find r such that h - 1/4*r + 1/4*r**3 - 1/4*r**2 = 0.
-