 - 1/2*r**5 - 25/2*r - 155/2*r**2 - 31/4*r**4 + 125/4 = 0.
-5, -1, 1/2
Let s(x) be the second derivative of -x**4/24 + 5*x**3/2 - 225*x**2/4 - 20*x. Let s(m) = 0. Calculate m.
15
Factor -248*t**2 - 31*t**3 + 45 - 18*t**2 + 26 + 49*t**3 + 192*t - 15.
2*(t - 14)*(t - 1)*(9*t + 2)
Let z(h) be the second derivative of -h**7/84 - h**6/10 + 3*h**5/10 + 53*h**4/12 + 23*h**3/4 - 45*h**2 - 2*h - 319. Solve z(i) = 0 for i.
-5, -3, 1, 4
Let v(r) = 3*r**2 - 7*r + 18. Let d(k) = -k**2 + k - 2. Let m(g) = -20*d(g) - 5*v(g). Suppose m(f) = 0. Calculate f.
-5, 2
Let r(g) = g**3 + 2*g**2 - 9*g + 3. Let a(v) = -2*v**3 - 4*v**2 + 10*v - 2. Let o(y) = -3*a(y) - 2*r(y). Determine l, given that o(l) = 0.
-3, 0, 1
Determine n so that 128*n + 139*n**4 - 137*n**4 + 58*n**3 + 160*n**2 - 24*n**3 = 0.
-8, -1, 0
Factor -4/3*f**4 - 16/9*f**3 + 64/9 + 32/3*f - 2/9*f**5 + 32/9*f**2.
-2*(f - 2)*(f + 2)**4/9
Suppose -2*v**2 + 50*v + 928 - 928 = 0. What is v?
0, 25
Suppose 22/13*d - 2/13*d**4 + 6/13*d**2 + 12/13 - 6/13*d**3 = 0. What is d?
-3, -1, 2
Suppose 2 + 1 = d. Suppose -5*v = 3*i - d, 4*i = -i + 5. Factor 3/7*n + v - 1/7*n**2.
-n*(n - 3)/7
Let g(q) = q**3 + q**2 - 1. Let i = -18 + 17. Let v(k) = -2*k**3 + 32*k**2 + 216*k + 436. Let c(w) = i*v(w) - 4*g(w). Suppose c(u) = 0. What is u?
-6
Suppose 10*t = 7*t, -2*k + 2*t = 0. Let l be ((-6)/8)/((-54)/32). Factor k*m**2 + 4/9*m**3 - 2/9 + 2/9*m**4 - l*m.
2*(m - 1)*(m + 1)**3/9
Let s(r) be the first derivative of 2*r**6/21 - 8*r**5/35 - 5*r**4/7 + 40*r**3/21 + 8*r**2/7 - 32*r/7 + 144. What is k in s(k) = 0?
-2, -1, 1, 2
Let z(v) = -2*v**2 - 21*v - 72. Let t(w) = -6*w**2 - 64*w - 216. Let h(k) = -k**2 + 6*k - 3. Let j be h(6). Let b(a) = j*t(a) + 8*z(a). Factor b(c).
2*(c + 6)**2
Let x(b) be the third derivative of -b**5/60 - 11*b**4/24 + 5*b**2 - b. Factor x(p).
-p*(p + 11)
Let z(o) = 364*o + 369. Let c be z(-1). Find r, given that -30/7*r**4 + 18/7 - 12/7*r + 4/7*r**c - 52/7*r**2 + 72/7*r**3 = 0.
-1/2, 1, 3
Let c be 3/6 - 5/(-2). Let v be 4/(-4)*-12*23/184. Factor 0 + 1/2*a**c - v*a**2 + 3/2*a**4 - a + 1/2*a**5.
a*(a - 1)*(a + 1)**2*(a + 2)/2
Let s(q) be the second derivative of -1/2*q**2 + 0 + 1/108*q**4 + 1/270*q**5 + 4*q + 0*q**3. Let d(m) be the first derivative of s(m). Factor d(i).
2*i*(i + 1)/9
Let s(z) = z**3 + 25*z**2 + 111*z + 1495. Let m be s(-23). Let -1/9*f**5 + 4/9*f**4 + 0*f + m + 0*f**2 - 4/9*f**3 = 0. Calculate f.
0, 2
Let x(w) = 15*w**5 + 38*w**4 + 7*w**3 - 5*w**2 - 11*w. Let u(m) = -8*m**5 - 20*m**4 - 4*m**3 + 2*m**2 + 6*m. Let k(v) = 11*u(v) + 6*x(v). Solve k(i) = 0.
-4, -1, 0, 1
Factor 17576/5 + 78/5*j**2 - 2028/5*j - 1/5*j**3.
-(j - 26)**3/5
Factor 8*l**2 - 4*l**3 + 9 - 10 - 4 + 4*l - 3.
-4*(l - 2)*(l - 1)*(l + 1)
Suppose 0 = 11*o - 9*o - 4. Suppose 44*t**2 - o*t**3 - t**3 - 38*t**2 = 0. Calculate t.
0, 2
Let z(f) be the third derivative of 243*f**7/14 - 2997*f**6/8 - 1035*f**5/2 - 1745*f**4/6 - 260*f**3/3 + f**2 - 110. Factor z(o).
5*(o - 13)*(9*o + 2)**3
Let f(b) be the third derivative of 0*b - 1/28*b**4 + 1/70*b**5 + 0 + 1/21*b**3 - 1/420*b**6 - 18*b**2. Factor f(n).
-2*(n - 1)**3/7
Let r be (-20)/(176/(-60)*9/6). Let c = r - 189/44. Factor -1/4 - c*j**2 - 1/2*j.
-(j + 1)**2/4
Let z be ((-2)/6)/((-7)/42). Let h be (-3)/z*(-16)/3. Factor h - 4*j + 12*j - 4 + 4*j**2.
4*(j + 1)**2
Solve -5/2*b**2 + 55/2*b - 25 = 0 for b.
1, 10
Let f(c) = -c**3 - 3*c**2 - c + 1. Let o be f(-3). Factor -2*b + 6*b**2 - b**3 + 2 - o*b - b**3.
-2*(b - 1)**3
Let l = 46303 + -46301. Find a such that -2*a**l + 1/2*a**4 - 2*a + 0 + 1/2*a**3 = 0.
-2, -1, 0, 2
Let o be (-28)/182 - (-132)/13. Let x = 13 - o. Solve 0 - 2 - x*b**2 - 6*b + 1 - 2 = 0 for b.
-1
Let w(k) be the second derivative of -k**4/12 - 5*k**3/24 + 13*k**2/4 - 217*k. Suppose w(c) = 0. What is c?
-13/4, 2
Let k be 2/11 + 66/(-363). Let p be (2/8)/(1/2). Factor 0 + k*t**2 + p*t**3 - 1/2*t.
t*(t - 1)*(t + 1)/2
Suppose 446 = -9*w + 1202. Suppose -w*k + 85*k = 3. Let -4 + 68/3*f - 13*f**2 - 49/3*f**4 - 56*f**k = 0. Calculate f.
-3, -1, 2/7
Let x(f) be the first derivative of 11 - 49/10*f**5 - 44/3*f**3 + 24*f**2 - 21*f**4 - 8*f. Find r such that x(r) = 0.
-2, 2/7
Suppose 7*x - 237 = 533. Let o = 115 - x. Factor 0*h**4 + 0*h**2 + 2/5*h**o + 0 + 0*h + 0*h**3.
2*h**5/5
Let x(b) = -7*b**2 + b - 1. Let f(h) = -116*h**2 - 28. Let w(q) = -f(q) + 16*x(q). What is k in w(k) = 0?
-3, -1
Let n(t) be the second derivative of -t**2 - 1/6*t**3 + 1/20*t**5 + 1/6*t**4 - 15*t + 0. Factor n(g).
(g - 1)*(g + 1)*(g + 2)
Let g(x) be the first derivative of x**7/420 + x**6/180 - x**5/60 - x**4/12 + 4*x**3/3 + 8. Let q(i) be the third derivative of g(i). Factor q(a).
2*(a - 1)*(a + 1)**2
Let z(j) be the second derivative of -j**5/4 - 35*j**4/12 + 28*j. Factor z(k).
-5*k**2*(k + 7)
Let b(t) be the third derivative of t**5/240 + t**4/12 + 5*t**3/8 - 2*t**2 - 49*t. Factor b(k).
(k + 3)*(k + 5)/4
Let s be (-7 - (-1)/(-1))*1/(-2). Factor 3*l**2 - 3*l**4 + l**s + 2*l**4 - 3*l**4 - 6*l + 6*l**3.
-3*l*(l - 2)*(l - 1)*(l + 1)
Let 3/7*c + 9/7*c**2 - 12/7 = 0. What is c?
-4/3, 1
Suppose 2*r - 10 = -4*q, -3*r + 4*q = -4 - 21. Let w = r + -27/4. Solve -w*b**3 + 0 + 1/2*b**2 + 0*b = 0.
0, 2
Let a(b) = -2*b + 26. Let q be a(16). Let c(s) = -4*s**2 - 20*s - 5. Let f(d) = -d**2 - 5*d - 1. Let w(x) = q*c(x) + 22*f(x). What is j in w(j) = 0?
-4, -1
Let t = 1812 + -1810. Suppose 0 + 0*n**3 - 2/3*n + n**t - 1/3*n**4 = 0. What is n?
-2, 0, 1
Suppose 52 + 53*a + 121*a - 228*a + 2*a**2 = 0. What is a?
1, 26
Let o(j) = -14*j. Let k be o(-1). Let r be k + (-3)/1 + -2. What is h in 4 + 8*h**2 - 4*h**2 - h + r*h = 0?
-1
Suppose 14*v**4 + 5*v**4 - 24*v**4 - 5*v**5 + 5*v**3 + 5*v**2 = 0. What is v?
-1, 0, 1
Suppose 2*n + 3 = -f - 5, 0 = f + 4*n + 16. Let o = f + 3. Factor -o*a**4 - 8*a**3 - a**3 + 0*a**4 - 3*a - 9*a**2.
-3*a*(a + 1)**3
Let h(m) = 15*m**2 - 43*m + 337. Let w(o) = 9*o**2 - 22*o + 169. Let g(u) = 4*h(u) - 7*w(u). Factor g(y).
-3*(y - 5)*(y + 11)
Suppose -23*c + 25 = -18*c. Find k such that 9*k**2 + c*k**4 - 7*k**2 - 12*k**2 + 5*k**3 = 0.
-2, 0, 1
Let r(t) = 3*t**2 + 30*t - 363. Let n(w) = -13. Let m(c) = -15*n(c) + r(c). Factor m(l).
3*(l - 4)*(l + 14)
Suppose 0 = -2*k + 2*a + 3 + 1, 5*a + 7 = 4*k. Find b such that -44*b**2 - 7*b**3 - 5*b**k - 40*b + 7*b**3 - 12 - 11*b**3 = 0.
-1, -3/4
Let k be (-5)/(-100) - ((-18)/99 + 25/(-44)). Factor -26/15*t**2 - 4/15*t**3 + 0 - k*t.
-2*t*(t + 6)*(2*t + 1)/15
Let y(j) be the third derivative of -j**5/60 + j**4/3 - j**3/2 + 24*j**2. Let k be y(7). Factor 2*q**k + 2/3*q**5 - 4/3*q**2 + 4/3*q**3 - 2*q - 2/3.
2*(q - 1)*(q + 1)**4/3
Let f(c) be the first derivative of c**6/450 - 2*c**5/75 + 2*c**4/15 - 5*c**3 + 38. Let y(t) be the third derivative of f(t). Determine l so that y(l) = 0.
2
Let s(m) = m**3 - 1. Let a(p) = -10*p**3 + 60*p**2 - 1994. Let g(x) = a(x) + 6*s(x). Find y such that g(y) = 0.
-5, 10
Let l(h) be the third derivative of h**7/420 - h**6/60 + h**5/40 - 28*h**2. Solve l(j) = 0 for j.
0, 1, 3
Suppose -55*b + 50*b - 6 = -3*h, 2*h = 5*b + 4. Factor -20/11*q - 2/11*q**h + 0.
-2*q*(q + 10)/11
Let n(t) = -t**3 - 23*t**2 + 3*t + 72. Let d be n(-23). Solve 0 - 3/2*f**4 - 6*f**5 + 3/2*f**2 + 0*f + 6*f**d = 0.
-1, -1/4, 0, 1
Let k(t) = 2*t**3 - 4*t**2 - 2. Let l(x) = 0*x**3 - 6 + 4*x**3 - 5*x**2 - 2*x**2 + 1. Let o(z) = -10*k(z) + 4*l(z). Factor o(v).
-4*v**2*(v - 3)
Factor 339*l + 160 + 156*l**2 + 204*l + 2*l**3 - 861*l.
2*(l - 1)**2*(l + 80)
Let d = 3336/3895 - 44/779. Factor 8/5*j**3 + 0 + 0*j + d*j**5 + 0*j**2 - 12/5*j**4.
4*j**3*(j - 2)*(j - 1)/5
Let s(p) = 10*p**4 - p**3 - 21*p**2 + p + 11. Let c = -188 - -199. Let g = 3 - 1. Let z(n) = -2*n**4 + 4*n**2 - 2. Let d(o) = c*z(o) + g*s(o). Solve d(q) = 0.
-1, 0, 1
Let j(i) = -i**3 - 8*i**2 + 9*i + 12. Let y be j(-9). Factor -25*o**4 + 16*o**4 + 12*o**2 + 12*o**4 - y*o**3.
3*o**2*(o - 2)**2
Let t(n) be the first derivative of 16/15*n**3 - 9 + 8/5*n + 1/5*n**4 + 2*n**2. Factor t(f).
4*(f + 1)**2*(f + 2)/5
Let l(x) be the first derivative of x**3/3 + x**2/2 - x + 24. Let d(n) = 6*n**2 - 9*n - 3. Let q(h) = d(h) - 3*l(h). Solve q(a) = 0 for a.
0, 4
Let y = -10625/2 + 5184. Let j = 129 + y. Factor j*l**3 + 0 + 0*l**2 - 1/2*l.
l*(l - 1)*(l + 1)/2
Let a(l) be the third derivative of l**9/30240 + l**8/13440 - 17*l**4/2