u(h).
-(h - 1)**2
Let b(j) = -21*j**2 - 271*j - 1679. Let g(h) = h**2 - 2*h + 11. Let i be g(0). Let r(v) = -4*v**2 - 54*v - 336. Let o(z) = i*r(z) - 2*b(z). Factor o(k).
-2*(k + 13)**2
Suppose 280 = 250*h - 180*h. Solve 0 - 32/5*x - 16*x**2 - 2/5*x**5 - 66/5*x**3 - 4*x**h = 0.
-4, -1, 0
Solve -30 + 137/3*n - n**2 = 0.
2/3, 45
Let i(k) be the first derivative of k**6/39 + 18*k**5/65 + 12*k**4/13 + 32*k**3/39 + 8. Factor i(h).
2*h**2*(h + 1)*(h + 4)**2/13
Suppose 2*v - 7*v + 55 = 0. Suppose -2*n = y + n + v, -3*y - 3*n - 3 = 0. Factor -2*g + 7*g**2 + 5*g**2 - g + y*g**4 - 16*g**4 + 3*g**3.
-3*g*(g - 1)*(g + 1)*(4*g - 1)
Let f(g) be the second derivative of g**4/102 - 7*g**3/51 - 8*g**2/17 + 13*g - 15. Solve f(v) = 0.
-1, 8
Let n be -4 + 4 - -4566 - -1. Factor -4060 + 0*t**2 + 2*t**2 + 78*t + n + t**2.
3*(t + 13)**2
Let r(v) be the first derivative of -4/5*v**3 - 26 + 1/10*v**4 - 16/5*v + 12/5*v**2. Determine y, given that r(y) = 0.
2
Let p(d) be the third derivative of 16/15*d**3 + 0 + 0*d + 1/300*d**6 + 1/525*d**7 - 2/25*d**5 - 14*d**2 + 1/15*d**4. Factor p(t).
2*(t - 2)**2*(t + 1)*(t + 4)/5
Let f(o) be the second derivative of -o**6/15 + 9*o**5/10 - 5*o**4/2 - 25*o**3/3 + 25*o + 1. Factor f(i).
-2*i*(i - 5)**2*(i + 1)
Factor -13/2*c + 0 - 1/2*c**2.
-c*(c + 13)/2
Let q(k) = -k**2 + 10*k + 5. Let j(o) = o. Let t(d) = -30*d - 5. Let p(f) = -20*j(f) - t(f). Let n(m) = -6*p(m) + 5*q(m). Factor n(a).
-5*(a + 1)**2
Let x(t) be the first derivative of -t**3/3 - 81*t**2/2 - 71*t + 39. Let w(a) = a**2 + 41*a + 36. Let c(o) = 9*w(o) + 4*x(o). Factor c(u).
5*(u + 1)*(u + 8)
Let o(q) be the second derivative of 5*q**6/24 + 7*q**5/16 + 11*q**4/48 + q**3/24 - 64*q. Factor o(x).
x*(x + 1)*(5*x + 1)**2/4
Let o = 315 + -313. Find c, given that -1/7*c**o + 1/7*c + 1/7 - 1/7*c**3 = 0.
-1, 1
Let l(g) be the third derivative of 5/12*g**4 + 4*g**2 + 0 + 0*g - 3/2*g**3 - 1/60*g**5. What is u in l(u) = 0?
1, 9
Let z(w) = 5*w**2 - 10*w + 3. Let a be z(2). Solve -2/9*b**a + 2/9 + 2/9*b - 2/9*b**2 = 0.
-1, 1
Let o(a) be the first derivative of a**6/9 + 22*a**5/15 + 9*a**4/2 - 22*a**3/9 - 28*a**2/3 + 85. Determine n, given that o(n) = 0.
-7, -4, -1, 0, 1
Let v = -37772/5 - -7558. Solve 3/5 + v*f + 27/5*f**2 = 0.
-1/3
Let p(n) = 8*n**4 - 328*n**3 + 6716*n**2 - 4*n. Let m(j) = -7*j**4 + 328*j**3 - 6718*j**2 + 3*j. Let x(t) = -4*m(t) - 3*p(t). Suppose x(z) = 0. Calculate z.
0, 41
Let p(z) be the first derivative of -40/3*z**3 - 9 - z**4 + 0*z - 50*z**2. Factor p(k).
-4*k*(k + 5)**2
Factor 15/2*m - 3/2*m**2 + 21.
-3*(m - 7)*(m + 2)/2
Factor -606/7*c**2 - 3/7*c**3 - 1203/7*c - 600/7.
-3*(c + 1)**2*(c + 200)/7
Let h = 242 + -50819/210. Let c(n) be the third derivative of 2*n**2 + 0*n + 1/6*n**3 - 1/30*n**5 + h*n**7 + 0*n**4 + 0 + 0*n**6. Let c(u) = 0. What is u?
-1, 1
Let x = -8434 + 42171/5. Factor -x*r**2 + 2/5*r + 3/5.
-(r - 3)*(r + 1)/5
Let x = 1013 + -10121/10. Let k(z) be the first derivative of -1/5*z**3 - x*z**2 - 6/5*z + 7. Determine d, given that k(d) = 0.
-2, -1
Let n be (-35)/(-10)*2 + -4. Let b be (-2)/(-4) + (1 - 1). Factor 3/2*a**n - b*a**2 + 0*a - 3/2*a**4 + 0 + 1/2*a**5.
a**2*(a - 1)**3/2
Let f(d) = 14*d**2 - 117*d + 280. Let l(u) = 5*u**2 - 39*u + 92. Let b(t) = -4*f(t) + 11*l(t). Factor b(v).
-(v - 36)*(v - 3)
Let s be 26/14 - 20/(7 - -13). Let a(q) be the first derivative of s*q - 7 - 9/14*q**2 + 1/7*q**3. Factor a(k).
3*(k - 2)*(k - 1)/7
Let z(k) be the second derivative of k**8/13440 + k**7/15120 - k**6/540 + k**5/180 + 3*k**4/4 - 8*k. Let f(p) be the third derivative of z(p). Factor f(c).
(c - 1)*(c + 2)*(3*c - 2)/6
Let z(j) be the first derivative of -j**6/360 + j**5/160 + j**4/96 + 16*j**3/3 + 14. Let p(d) be the third derivative of z(d). Solve p(a) = 0.
-1/4, 1
Suppose -24 - 4*f**3 - 19*f + 10*f + 2*f**4 - 47*f - 38*f**2 = 0. What is f?
-2, -1, 6
Let u(j) be the second derivative of -2*j**6/15 + 14*j**5/5 - 20*j**4 + 208*j**3/3 - 128*j**2 - 81*j. Factor u(p).
-4*(p - 8)*(p - 2)**3
Let j = -75 + 78. Suppose 21*n**5 - 12*n**4 + 9*n**j + 6*n**2 + 0*n**4 - 24*n**4 = 0. What is n?
-2/7, 0, 1
Factor 243/4 + 39*m**2 - 189/2*m + 1/4*m**4 - 11/2*m**3.
(m - 9)**2*(m - 3)*(m - 1)/4
Let c(z) = 7*z**2 + 7*z + 3. Let u(o) = 11*o**2 + 11*o + 5. Let n(l) = 8*c(l) - 5*u(l). Let t(q) = -14*q + 12. Let k(v) = -4*n(v) - 2*t(v). Factor k(w).
-4*(w - 5)*(w - 1)
Let z be (-5)/7 - -1 - 3*598/(-483). Factor 3*t**2 + 1/2*t**3 - 2*t - z - 1/2*t**4.
-(t - 2)**2*(t + 1)*(t + 2)/2
Factor 48*x + x**2 + 9*x**2 - 4*x**2 - 11*x**2 + 3*x**2.
-2*x*(x - 24)
Let n(q) be the second derivative of -7*q**5/120 - 97*q**4/36 - 329*q**3/9 + 98*q**2/3 + 248*q. Factor n(b).
-(b + 14)**2*(7*b - 2)/6
Let t(p) be the second derivative of -p**4/84 + 79*p**3/42 + 50*p + 7. Factor t(u).
-u*(u - 79)/7
Factor -4/9*g**4 + 0 + 0*g**2 + 0*g - 4/3*g**3.
-4*g**3*(g + 3)/9
Let b(x) be the third derivative of -x**5/150 - 11*x**4/60 - 8*x**3/5 + 168*x**2. Factor b(d).
-2*(d + 3)*(d + 8)/5
Factor 1439*h**2 + 6*h**3 + 9*h**3 - 1564*h**2 - 155 - 361*h + 66*h.
5*(h + 1)**2*(3*h - 31)
Let x(w) be the second derivative of -2*w**3 - w**4 + 0*w**2 + 3*w - 1/14*w**7 + 9/20*w**5 + 1/5*w**6 + 0. Factor x(f).
-3*f*(f - 2)**2*(f + 1)**2
Solve 56*w + 6/7*w**5 + 0 + 526/7*w**3 + 128*w**2 + 100/7*w**4 = 0 for w.
-7, -2, -2/3, 0
Let j(f) be the first derivative of 23 - 5/2*f**2 + 0*f + 5*f**3 - 15/4*f**4 + f**5. Let j(c) = 0. What is c?
0, 1
What is b in -231*b**3 + 0*b**2 + 4*b**2 + 229*b**3 + 26*b + 20 = 0?
-2, -1, 5
Let h = 3362/26843 - 12/1579. What is g in 18/17 - 20/17*g + h*g**2 = 0?
1, 9
Suppose l + 4*r + 0 = -15, 2*r - 45 = 3*l. Let m(y) = 3*y**5 - y**4 + 4*y**3. Let n(x) = 7*x**5 - x**4 + 9*x**3. Let c(t) = l*m(t) + 6*n(t). Factor c(p).
-3*p**3*(p - 2)*(p - 1)
Factor -288/19 + 52/19*v**3 - 2/19*v**4 - 386/19*v**2 + 624/19*v.
-2*(v - 12)**2*(v - 1)**2/19
Let v be 1 - (-1 - 0/(-5))/(-1). Let n(f) be the third derivative of 0 - 6*f**2 - 1/42*f**4 - 1/105*f**7 - 4/105*f**6 - 11/210*f**5 + 0*f**3 + v*f. Factor n(l).
-2*l*(l + 1)**2*(7*l + 2)/7
Let h(f) = f**2 - 25*f - 28. Let c be h(27). Find w, given that 61*w**3 - 20*w + 0 + 0 - c*w**3 + 60*w**2 = 0.
-2, 0, 2/7
Let y(h) be the second derivative of -h**8/336 + 4*h**7/525 + h**6/150 - 3*h**2/2 - 5*h. Let c(r) be the first derivative of y(r). Factor c(z).
-z**3*(z - 2)*(5*z + 2)/5
Let c(m) be the first derivative of m**6/8 + m**5/10 - 5*m**4/8 - m**3 - 9*m**2 + 13. Let h(d) be the second derivative of c(d). What is y in h(y) = 0?
-1, -2/5, 1
Let h(k) be the third derivative of k**7/630 - 7*k**6/180 - 5*k**4/12 + 35*k**2. Let f(b) be the second derivative of h(b). Factor f(x).
4*x*(x - 7)
Let u be ((-2)/3)/((-2)/126). Let h be 45*4/u + -4. Solve 2/7 - h*a**3 - 6/7*a + 6/7*a**2 = 0 for a.
1
Let j(n) be the third derivative of -7*n**6/40 + 116*n**5/5 - 587*n**4/8 + 65*n**3 - 2*n**2 - 45*n. Factor j(y).
-3*(y - 65)*(y - 1)*(7*y - 2)
Determine h so that 116/5*h - 2/5*h**2 - 1682/5 = 0.
29
Let s = -6/1691 - -30468/8455. Factor -27/5 - 3/5*n**2 - s*n.
-3*(n + 3)**2/5
Let c(x) = -3*x**3 + 21*x**2 - 33*x + 8. Let f(k) = -2*k**3 + 14*k**2 - 22*k + 5. Suppose -6*i - 14 = 28. Let t(r) = i*f(r) + 5*c(r). Factor t(n).
-(n - 5)*(n - 1)**2
Let 8*g**2 + 234/5*g + 2/5*g**3 + 324/5 = 0. What is g?
-9, -2
Let w(u) = 4*u**2 + 22*u + 12. Let c be w(-5). Let m(g) be the second derivative of 4*g + 1/3*g**4 + 1/6*g**3 + 0 + 0*g**c. Factor m(r).
r*(4*r + 1)
Let n(v) = -11*v**2 + 91*v - 2299. Let m(b) = -9*b**2 + 92*b - 2300. Let k(r) = 5*m(r) - 4*n(r). Determine j so that k(j) = 0.
48
Let z(n) be the third derivative of -1/60*n**5 - 1/84*n**8 + 0 - 1/8*n**4 + 1/6*n**3 + 11*n**2 + 0*n**7 + 0*n + 7/120*n**6. Determine r, given that z(r) = 0.
-1, 1/2, 1
Let r(l) = -8 - 5*l - 4*l**2 + 9*l + 8*l. Let d(j) = -12*j**2 + 36*j - 24. Let y(t) = -2*d(t) + 7*r(t). Factor y(x).
-4*(x - 2)*(x - 1)
Solve -4*w**2 - 25548 + 1048 - 4*w**2 - 199*w - 501*w + 3*w**2 = 0 for w.
-70
Let r(t) be the second derivative of 2*t**7/63 - 4*t**5/15 + 2*t**4/9 + 2*t**3/3 - 4*t**2/3 - 64*t + 2. Let r(f) = 0. What is f?
-2, -1, 1
Factor 2/15*p**2 + 32/15 - 4/3*p.
2*(p - 8)*(p - 2)/15
Let c(k) = 179*k - 353. Let o be c(2). Determine x so that -16/7*x**4 + 2/7*x**o + 50/7*x**3 - 76/7*x**2 - 16/7 + 8*x = 0.
1, 2
Let j(b) be the thir