- l**5/330 + l**4/132 + l**3/33 + 13*l**2/2 + 3. Let r(h) be the second derivative of p(h). Factor r(w).
-2*(w - 1)*(w + 1)**2/11
Let v = -76 - -384/5. Factor -3/5 - v*w**2 - 7/5*w.
-(w + 1)*(4*w + 3)/5
Let o(w) = w**4. Let k(s) = -3*s**4 - 4*s**3 - 6*s**2 + 16*s - 8. Let z(n) = k(n) + 5*o(n). Factor z(q).
2*(q - 2)*(q - 1)**2*(q + 2)
Let g be (-348)/((2/3)/1). Let i = g - -5746/11. Factor 2/11 - i*f - 6/11*f**2.
-2*(f + 1)*(3*f - 1)/11
Let s(k) be the second derivative of 49*k**6/50 + 21*k**5/100 - 69*k**4/10 - 64*k**3/5 - 48*k**2/5 - 196*k. Find d such that s(d) = 0.
-1, -4/7, 2
Let k be (11/(-22))/(2/(-16)). Suppose f + f = k. Factor c**2 + 6*c - 3 + c**2 - 5*c**f.
-3*(c - 1)**2
Let d(p) = -14*p - 1. Let i be d(-1). Let k = i + -11. Let 7/2*u**3 + 0 + 9/2*u**k + u = 0. Calculate u.
-1, -2/7, 0
Suppose 0 = 4*s - d + 209 - 206, -12 = -4*d. Solve 0 + s*r - 1/2*r**2 - 1/6*r**3 = 0.
-3, 0
Factor 58/23*v - 2/23*v**2 + 0.
-2*v*(v - 29)/23
Solve 22/5*x + 0 - 4/5*x**3 + 18/5*x**2 = 0 for x.
-1, 0, 11/2
Let b(m) be the second derivative of -16*m**7/63 + 8*m**6/9 - 11*m**5/10 + 5*m**4/9 - m**3/9 - m - 59. Let b(a) = 0. Calculate a.
0, 1/4, 1
Let q(c) = c**2 - 4*c - 11. Let d be q(6). Let m be (4 - 1) + -2 - d. Determine a so that -8/5 + m*a + 2/5*a**2 = 0.
-2, 2
Let y(w) be the third derivative of 2*w**7/105 - 4*w**5/15 - 325*w**2. Factor y(x).
4*x**2*(x - 2)*(x + 2)
Factor 415*c**2 - 832*c**2 - 9408 + 336*c + 414*c**2.
-3*(c - 56)**2
Let m(d) be the first derivative of 2*d**3/9 - 8*d**2/3 + 85. Find n such that m(n) = 0.
0, 8
Let p(y) be the second derivative of 0*y**2 - 1/60*y**6 + 15*y + 0 - 1/40*y**5 + 0*y**3 + 0*y**4. Find c, given that p(c) = 0.
-1, 0
Let d be 416/(-520) + (-8)/(-10). Let v(l) be the third derivative of 3/8*l**3 + d*l - l**2 + 5/32*l**4 + 1/480*l**6 + 0 + 7/240*l**5. Factor v(m).
(m + 1)*(m + 3)**2/4
Suppose 45 = -r - 5*j, 8*j - 165 = 2*r + 3*j. Let w = r + 492/7. Solve -2/7*v + w*v**3 + 2/7 - 2/7*v**2 = 0.
-1, 1
Let w(c) be the first derivative of -4*c**3/3 - 20*c**2 + 87. Factor w(l).
-4*l*(l + 10)
Let z(f) = -f**2 - 3*f. Let g(r) = -4*r**2 - 23*r + 32. Let m(t) = g(t) - 3*z(t). Factor m(v).
-(v - 2)*(v + 16)
Let v = -3004 + 3004. Let f be 4/6*6/8. Factor -1/2*y**4 + v*y - f*y**5 + 0 + 1/2*y**3 + 1/2*y**2.
-y**2*(y - 1)*(y + 1)**2/2
Let b = -77057/5 - -15413. Factor 2/5*g**4 - 2/5 - 2/5*g**3 - 7/5*g - b*g**2 + 1/5*g**5.
(g - 2)*(g + 1)**4/5
Let i(j) = j**3 - 43*j**2 - 89*j - 51. Let p(t) = 4*t**3 - 128*t**2 - 268*t - 152. Let x(b) = 8*i(b) - 3*p(b). Factor x(h).
-4*(h - 12)*(h + 1)**2
Let l(b) = b**2 - 5*b + 2. Suppose -9 = -2*j + 2*d + 3, -5 = 5*d. Let z be l(j). Solve 3/2*o + 1/2*o**3 + 3/2*o**z + 1/2 = 0.
-1
Let u = 26 - 155/6. Let t(s) be the first derivative of -1/3*s**3 + 3 + 0*s - 1/4*s**4 + 0*s**2 + 1/5*s**5 + u*s**6. Factor t(r).
r**2*(r - 1)*(r + 1)**2
Let y(o) be the first derivative of -12 + 1/3*o**2 + 0*o + 2/27*o**3. Suppose y(k) = 0. Calculate k.
-3, 0
Let x be (608/1764 - 16/72)/(5/35). Factor -x*z + 2/7*z**2 - 8/7.
2*(z - 4)*(z + 1)/7
Suppose -52*m**2 + 36*m**4 + 128*m + 2*m**5 - 18*m**4 - 10*m**4 - 22*m**3 - 64 = 0. Calculate m.
-4, 1, 2
Let l be -1 + 15*4/20. Let u(r) be the first derivative of 1/5*r**l - 2/15*r**3 + 1 + 4/5*r. Let u(c) = 0. What is c?
-1, 2
Let r be (-319)/145*1/(-14). Let b(n) be the second derivative of -r*n**5 + 2/7*n**2 + 5/14*n**4 + 1/35*n**6 + 6*n + 0 - 3/7*n**3. Let b(q) = 0. Calculate q.
2/3, 1
Let t = 82/5 - 487/30. Factor -1/6*m**2 + 0*m + 0 + 0*m**3 + t*m**4.
m**2*(m - 1)*(m + 1)/6
Let v be (2 - (9 + -3))*(-44)/242. Find r such that -v + 10/11*r**2 + 16/11*r = 0.
-2, 2/5
Let x(q) be the second derivative of q**7/1365 + q**6/156 + 2*q**5/195 - q**2 - 10*q. Let a(r) be the first derivative of x(r). Solve a(u) = 0 for u.
-4, -1, 0
Let k(x) be the third derivative of x**7/2415 - x**5/690 - 72*x**2. Factor k(i).
2*i**2*(i - 1)*(i + 1)/23
Let v(w) be the first derivative of -w**5/20 + 9*w**4/16 - 7*w**3/4 + 19*w**2/8 - 3*w/2 + 84. Determine j, given that v(j) = 0.
1, 6
Suppose 4*l = 12, 3*n + 4 = -2*l + 7. Let d(o) = o**2 - 1. Let g(v) = -v**3 - 4*v**2 - 7*v - 4. Let k(h) = n*g(h) + d(h). Suppose k(z) = 0. What is z?
-3, -1
Suppose -3*f + 4*i = -5*f + 16, -4*f = 4*i - 24. Suppose -57*z + 4 = -56*z. Factor -m**z + m**4 - m + 2*m**5 - f*m**4 - m + 4*m**2.
2*m*(m - 1)**3*(m + 1)
Let c(t) = 2*t**3 + t**2 - t - 1. Let u(g) = 7*g**3 + 4*g**2 + 12*g - 4. Let a(n) = 12*c(n) - 3*u(n). Suppose a(p) = 0. Calculate p.
-4, 0, 4
Let a(z) be the third derivative of 50/3*z**3 + 1/15*z**5 + 0*z + 13*z**2 - 5/3*z**4 + 0. Factor a(g).
4*(g - 5)**2
Let s(t) be the third derivative of 1/120*t**6 + 0*t + 1/8*t**4 + 2*t**2 + 0 - 1/20*t**5 - 1/6*t**3. Factor s(n).
(n - 1)**3
Let g be (-36)/10*(-40)/84. Suppose -3*j - 2 = -4*j. Factor 2/7*h**j + 18/7 - g*h.
2*(h - 3)**2/7
Let i(p) be the first derivative of 11*p + 27/8*p**2 - 3/4*p**3 + 1/16*p**4 + 8. Let t(v) be the first derivative of i(v). Factor t(o).
3*(o - 3)**2/4
Let w(f) be the second derivative of 2/9*f**3 - 13*f + 1/9*f**4 + 1/60*f**5 + 0 + 0*f**2. What is c in w(c) = 0?
-2, 0
Let o(t) be the third derivative of -t**6/20 - 3*t**5/4 - 3*t**4/4 + 7*t**3/2 - 40*t**2 - 5. Solve o(c) = 0 for c.
-7, -1, 1/2
Let v be 537/(-90) + 6 - 0. Let d(m) be the third derivative of 0*m**3 + 0*m + 0 + 0*m**4 + 1/120*m**6 + v*m**5 - 7*m**2. Factor d(t).
t**2*(t + 2)
Let g(x) be the first derivative of 3/14*x**4 + 9 + 0*x + 0*x**2 + 2/35*x**5 + 4/21*x**3. Factor g(d).
2*d**2*(d + 1)*(d + 2)/7
Suppose n + 24 = 2*n. Factor 8*j**2 - j + 7*j + 17*j + 4*j**3 - n - 43*j.
4*(j - 2)*(j + 1)*(j + 3)
Let d(q) be the third derivative of -q**6/780 + 23*q**5/390 - 40*q**4/39 + 100*q**3/13 - q**2 + 1. Determine c, given that d(c) = 0.
3, 10
Suppose -2/3*u**5 + 6*u**3 - 16/3*u + 4/3*u**4 + 0 - 4/3*u**2 = 0. What is u?
-2, -1, 0, 1, 4
Let p be 12/18 - 4/6. Let h = -3 - -3. Factor 1/2*n**2 + h*n - n**3 + 1/2*n**4 + p.
n**2*(n - 1)**2/2
Let g(l) be the third derivative of -l**6/40 + 3*l**5/4 - 75*l**4/8 + 125*l**3/2 - l**2 - 17*l. Determine j, given that g(j) = 0.
5
Let a be ((-6)/15)/(3/(-30)). Suppose -2*n + a*n = 0. Find g, given that n*g**2 + g**4 - 2*g**3 - g**2 - 2*g**4 = 0.
-1, 0
Let y = 14 + -10. Suppose -14 = -4*z + z - p, -y*p + 6 = 2*z. Let 12*g**2 + 14 + 0*g**4 - 6*g**z - 17 + 6*g**3 - 9*g**4 = 0. What is g?
-1, 1/2, 1
Let f(s) be the third derivative of -s**6/600 + 2*s**5/75 + 23*s**4/120 - s**3 + 105*s**2 - s. Factor f(p).
-(p - 10)*(p - 1)*(p + 3)/5
Let t(q) be the first derivative of -5*q**3 - 31 + 7*q**3 + 3*q**3 - 10*q**4 + 10 + 5*q**2 + 3*q**5. Solve t(u) = 0 for u.
-1/3, 0, 1, 2
Let m(f) = f**3 - f**2 - f. Let v be m(0). Let t(r) be the second derivative of 3*r**2 + 2/3*r**3 - 1/6*r**4 + v - 6*r. What is w in t(w) = 0?
-1, 3
Let z = -76 + 79. Factor 15*n + 44*n**2 - 6 + n**3 + 2*n**z - 56*n**2.
3*(n - 2)*(n - 1)**2
Let b = -128 - -130. Let s be ((-4)/14)/(18/(-14)). Suppose -28/9*k**b - s - 2*k**5 + 10/3*k**4 + 14/9*k + 4/9*k**3 = 0. What is k?
-1, 1/3, 1
Let m(q) be the third derivative of 5*q**5/6 - 55*q**4/24 - 25*q**3/6 - 2*q**2. Let r(y) = y**2 - y - 1. Let v(i) = m(i) - 30*r(i). Factor v(g).
5*(g - 1)*(4*g - 1)
Let s(n) be the first derivative of 3 - 1/6*n**3 - 1/32*n**4 - 1/4*n - 5/16*n**2. Determine t so that s(t) = 0.
-2, -1
Factor 2/9*v**3 + 8/3 - 10/9*v**2 - 16/9*v.
2*(v - 6)*(v - 1)*(v + 2)/9
Let d = -172 - -178. Let x(y) be the first derivative of -3/2*y**4 + 5 + 70/13*y**5 - 326/39*y**3 - 49/39*y**d + 88/13*y**2 - 24/13*y. Solve x(o) = 0 for o.
-1, 2/7, 1, 3
Suppose 236 = 12*r + 224. Let z(y) = -y**3 + 3*y**2 + 4*y + 2. Let m be z(4). Solve 14*u**m + 8*u + 1 - 10*u**2 - r = 0.
-2, 0
Let o(p) be the third derivative of -1/180*p**5 - 1/2016*p**8 + 1/36*p**3 + 0 + 1/360*p**6 - 1/144*p**4 + 1/1260*p**7 - 14*p**2 + 0*p. What is q in o(q) = 0?
-1, 1
Let c(x) be the third derivative of x**6/420 + x**5/210 - x**4/84 - x**3/21 - 608*x**2. Let c(i) = 0. What is i?
-1, 1
Let i be (-30)/(-2) + (10 - 11). Let t be (32/10)/(i/35). Solve -2*c**2 + 3*c + c**3 + t*c**2 + 2*c**3 = 0.
-1, 0
Let f be (10/5 - 3)*99. Let z be -12*(6/2)/f. Let -z*k - 2/11*k**3 - 6/11*k**2 + 0 = 0. What is k?
-2, -1, 0
Let c(a) be the third derivative of a**6/960 + 33*a**5/160 + 1089*a**4/6