- 3*m**4 - 4*m**4 + 4*m**5 + 3*m**4 = 0.
-1, 0, 1
Let o(r) be the first derivative of -100*r**5 + 175*r**4 + 55*r**3/3 - 105*r**2 - 45*r - 183. Find m such that o(m) = 0.
-3/10, 1
Let i(z) = -z**3 - z**2 + 3. Let l(a) = -a**3 + 151*a**2 + 2028*a + 8803. Let p(h) = -5*i(h) + l(h). Determine x so that p(x) = 0.
-13
Factor -8*w - 175616*w**2 + 8*w - 9018*w**3 - w**5 - 390*w**3 - 168*w**4.
-w**2*(w + 56)**3
Let u(b) be the third derivative of 3*b**2 - 25/2*b**4 - 539/40*b**6 + 0 - 4*b**3 - 203/10*b**5 + 0*b. Find i such that u(i) = 0.
-2/7, -2/11
Let j(u) be the second derivative of 39/10*u**5 - 4*u**3 + 7/10*u**6 + 5*u + 5*u**4 + 0*u**2 + 0. Let j(a) = 0. What is a?
-2, 0, 2/7
Suppose -2 = -l - 0*l. Find n, given that 7*n**3 - 2*n**3 - 6*n**l - 19*n**2 + 30*n = 0.
0, 2, 3
Let r be ((1593/30)/3)/(15/20). Let j = 24 - r. Solve -j*g**2 - 18/5 - 12/5*g = 0.
-3
Let b(c) be the second derivative of -c**4/42 - c**3/3 - 6*c**2/7 - 31*c. Solve b(f) = 0.
-6, -1
Let g(d) be the third derivative of -d**9/70560 - d**8/47040 + d**7/11760 + d**5/12 - 7*d**2. Let b(w) be the third derivative of g(w). Factor b(u).
-3*u*(u + 1)*(2*u - 1)/7
Let h be (-435)/33 - -13 - 103/(-22). Let l(t) be the first derivative of 0*t + h*t**3 - 1/12*t**6 - 2 + 9/10*t**5 - 27/8*t**4 + 0*t**2. Solve l(w) = 0.
0, 3
Let f(t) be the first derivative of -t**9/1008 - 9*t**8/280 - 27*t**7/70 - 9*t**6/5 - t**3 + 4. Let z(y) be the third derivative of f(y). Factor z(b).
-3*b**2*(b + 6)**3
Let m be 3/(-2)*(-12 - -10). Suppose -4*x + 37 = -m*g - 2*g, -5*g = -5*x + 45. Factor -3*y**2 - 4 - 4*y**2 + x*y - y**2 + 4*y**2.
-4*(y - 1)**2
Let t = 2161/306 - 125/18. Factor t*k**2 - 10/17*k**3 - 2/17*k**4 + 8/17 + 16/17*k + 2/17*k**5.
2*(k - 2)**2*(k + 1)**3/17
Let n be (-5)/10*-8 + -10. Let k = -2 - n. Factor 0 + 1/4*g**k + 1/4*g + 3/4*g**2 + 3/4*g**3.
g*(g + 1)**3/4
Let o(q) be the first derivative of -99*q**5/35 + 381*q**4/28 - 88*q**3/7 + 18*q**2/7 - 269. Find n, given that o(n) = 0.
0, 2/11, 2/3, 3
Suppose 2 + 2 = -2*m, -3*s + 21 = -3*m. Let o(q) = -8*q**2 - 21*q + 29. Let r(w) = 12*w**2 + 32*w - 44. Let z(f) = s*r(f) + 8*o(f). Factor z(p).
-4*(p - 1)*(p + 3)
Factor -3*r + 5*r - 5 - 31 + r**2 + 9*r + 5*r.
(r - 2)*(r + 18)
Let o(t) = -2 + t + t - 3 - t. Let c be o(5). Solve -7*n**3 + c*n**2 - 3*n - 2*n**2 + 5*n**3 + 7*n = 0 for n.
-2, 0, 1
Let j(r) = -7*r**2 - 16*r + 20. Let b(d) = -2*d**2 - 32*d - 13*d**2 + 2*d**2 + 20 + 20. Let n(l) = -3*b(l) + 5*j(l). Solve n(c) = 0 for c.
-5, 1
Let b(s) = -2*s**2 + 1. Let x(f) = 9*f**2 - 30*f + 45. Let m(i) = 3*b(i) + x(i). What is p in m(p) = 0?
2, 8
Let a(l) be the third derivative of 5/24*l**6 + 0*l - 1/6*l**5 + 7*l**2 + 5/3*l**3 - 25/24*l**4 + 0. Factor a(i).
5*(i - 1)*(i + 1)*(5*i - 2)
Let -15*x**3 - 9*x - 12*x**2 + 12*x**2 + 18*x**3 - 6 = 0. Calculate x.
-1, 2
Let j(b) = -b. Let n(w) = -5*w**2 + 3*w - 2. Let k = -28 - -23. Let m(p) = k*n(p) + 20*j(p). Factor m(h).
5*(h - 1)*(5*h - 2)
Let 1/4*v**4 - 67/4*v**2 + 17/2*v + 8*v**3 + 0 = 0. What is v?
-34, 0, 1
Let t(r) = 0*r**3 - r + 3 - 2*r - r**3 + 4*r**2. Let a be t(3). Factor 3/2 + 3/2*l**2 + a*l.
3*(l + 1)**2/2
Let x(m) = m**4 + m**3 + 23*m**2 - 16*m - 29. Let b(s) = 2*s**4 + 2*s**3 + 22*s**2 - 20*s - 30. Let c(f) = -5*b(f) + 6*x(f). Find r such that c(r) = 0.
-3, -1, 1, 2
Suppose -8*w = -40*w + 192. Let q(b) be the third derivative of -1/315*b**7 - w*b**2 + 0 + 0*b + 1/90*b**5 + 0*b**6 + 0*b**3 + 0*b**4. Factor q(x).
-2*x**2*(x - 1)*(x + 1)/3
Suppose -4*v = -2*j - 20, -8*j + 2*v - 10 = -6*j. Let b(u) be the third derivative of 0 + 7*u**2 + 0*u**3 + 1/96*u**4 + j*u - 1/240*u**5. Factor b(i).
-i*(i - 1)/4
Suppose -104 = -5*m - 2*k + 84, 2*m - 5*k - 52 = 0. Factor -49*u**4 + 14*u**3 + m*u - 39*u**2 - 70*u**2 - 2 - 2 + 112*u**3.
-(u - 1)**2*(7*u - 2)**2
Suppose -5*j + 0*k = -k - 2, -2*j - 4*k - 8 = 0. Let x(y) be the third derivative of 0*y + j*y**3 + y**2 + 0*y**5 + 0 - 1/480*y**6 + 1/96*y**4. Factor x(w).
-w*(w - 1)*(w + 1)/4
Let f be (532/228 - (-38)/(-15))/((-7)/15). Solve 0 - f*c**2 + 0*c = 0 for c.
0
Let y(k) = -k - 1. Let j be y(-19). Let c be -4 - (-17)/(-6)*j/(-12). Factor 1/4*z**5 + 0*z + c*z**2 - 1/4*z**4 - 1/4*z**3 + 0.
z**2*(z - 1)**2*(z + 1)/4
Let x = 32 - 28. Solve -4*w**3 - 3 + 3 + 2*w**x + 4*w**2 - w**4 = 0 for w.
0, 2
Let d(m) = 4*m**2 + 10*m + 3. Let q(f) = 7*f**2 + 18*f + 5. Let p(u) = -5*d(u) + 3*q(u). Let p(c) = 0. Calculate c.
-4, 0
Solve 24/5*p**2 - 13/5*p + 2/5 + 4/5*p**4 - 17/5*p**3 = 0.
1/4, 1, 2
Suppose 1 - 274 = -91*a. Factor -2/3*o**a - 8/3 + 2*o**2 + 0*o.
-2*(o - 2)**2*(o + 1)/3
Let w = -222 + 229. Let q be (18/27)/(w/6). Suppose -10/7*i + 2/7*i**5 + 8/7*i**4 + 8/7*i**3 - 4/7*i**2 - q = 0. Calculate i.
-2, -1, 1
Let d(c) be the third derivative of 2/21*c**4 - 1/84*c**6 + 0 - 3*c**2 - 1/735*c**7 + 1/210*c**5 + 1/1176*c**8 + 0*c + 4/21*c**3. Determine j so that d(j) = 0.
-1, 2
Factor 1/6*j**5 - 56/3*j**2 - 13/6*j**4 + 32/3*j + 10*j**3 + 0.
j*(j - 4)**3*(j - 1)/6
Let b(a) = -a**4 - 6*a**3 - 2*a**2 - 4*a + 3. Let f(d) = -d**3 - d**2 - d + 1. Let z(h) = 2*b(h) - 10*f(h). Let z(s) = 0. What is s?
-2, -1, 1
Let c(v) be the second derivative of -v**4/9 + 20*v**3/9 - 50*v**2/3 - 64*v. Factor c(s).
-4*(s - 5)**2/3
Let p(y) be the first derivative of -4*y**3/15 - 56*y**2/5 - 784*y/5 - 13. What is a in p(a) = 0?
-14
Let z(l) be the second derivative of l**7/360 - l**6/60 - l**5/30 - 7*l**4/3 + 9*l. Let u(p) be the third derivative of z(p). Determine j so that u(j) = 0.
-2/7, 2
Let u(l) be the third derivative of l**8/588 + 4*l**7/245 + l**6/42 - 198*l**2. Suppose u(a) = 0. What is a?
-5, -1, 0
Factor 5/2*i + 0 + 25/2*i**3 - 10*i**2 - 5*i**4.
-5*i*(i - 1)**2*(2*i - 1)/2
Let g = -11 - -13. Factor 10*z**3 + 36 + 44 + 26*z - 92 - 56*z**g + 32.
2*(z - 5)*(z - 1)*(5*z + 2)
Let d(b) = 60*b**2 - 1285*b + 7295. Let a(f) = -5*f**2 + 107*f - 608. Let h(r) = 35*a(r) + 3*d(r). Determine w, given that h(w) = 0.
11
Let t(q) = 2*q**2 - q - 1. Let x(j) = -55*j**2 + 10*j + 5. Let l(n) = 30*t(n) + x(n). Factor l(b).
5*(b - 5)*(b + 1)
Let g = 1517 + -700. Factor 30*w**2 + 892*w - 5*w**3 + 58 - 18 - g*w.
-5*(w - 8)*(w + 1)**2
Determine n, given that -2/7*n**4 + 2/7*n**2 + 0 + 4/7*n**3 - 4/7*n = 0.
-1, 0, 1, 2
Let y = 8 - -4. Factor 6 + 15 + 3 + y - 4*u**2.
-4*(u - 3)*(u + 3)
Let x(s) = -s**3 - 5*s**2 + s + 8. Let o be x(-5). Let g = -1 + 5. Factor 13*k**g + k**3 + 7*k**2 + k + k**o + 4*k**5 + 13*k**3.
k*(k + 1)**3*(4*k + 1)
Let w(f) = -f**2 + 4*f - 11. Let c be w(11). Let d = 93 + c. Solve 3/2*k**3 + 0 + 0*k + 3*k**4 + 3/2*k**d + 0*k**2 = 0 for k.
-1, 0
Factor 493 - 102*y - 21*y**2 - 3231 + 19*y**2 - 46*y.
-2*(y + 37)**2
Solve -33/4*l**4 - 45/4*l**3 + 81/4*l**2 + 0*l - 3/4*l**5 + 0 = 0.
-9, -3, 0, 1
Let l be ((-3)/33 + -1)*(-55)/10. Let n(i) be the third derivative of 1/15*i**5 + 0 + 0*i**3 + 0*i - 1/30*i**l + 0*i**4 - 7*i**2. Find m, given that n(m) = 0.
0, 1
Let v(w) be the first derivative of -w**6/10 - 3*w**5/20 + w**4/2 - 20*w + 22. Let d(p) be the first derivative of v(p). Factor d(a).
-3*a**2*(a - 1)*(a + 2)
Let r be -192*20/(-270) - (17 + -3). Suppose -2/9*x**2 - 2/9*x**5 + r*x**3 + 0*x + 2/9*x**4 + 0 = 0. Calculate x.
-1, 0, 1
Let y(u) be the second derivative of u**6/30 + 103*u**5/20 + 101*u**4/4 + 301*u**3/6 + 50*u**2 + u + 204. Find d such that y(d) = 0.
-100, -1
Let q(s) be the first derivative of 3*s**4/4 - 20*s**3 + 351*s**2/2 - 486*s - 3. Factor q(l).
3*(l - 9)**2*(l - 2)
Let k = 30/29 + 4841/58. Let p = k + -83. Suppose p*d**2 + 3/2*d**4 + 3*d**3 + 0 + 0*d = 0. What is d?
-1, 0
Let c(d) be the first derivative of 2*d**5/85 - 19*d**4/17 + 214*d**3/17 + 760*d**2/17 + 800*d/17 - 96. Factor c(y).
2*(y - 20)**2*(y + 1)**2/17
Let r(o) be the second derivative of -o**8/3360 - o**7/1890 + o**6/360 + o**5/90 + 3*o**4 - 3*o. Let a(j) be the third derivative of r(j). Factor a(c).
-2*(c - 1)*(c + 1)*(3*c + 2)/3
Let w(b) be the second derivative of -23/30*b**5 + 0 + 0*b**2 + 14*b - 25/18*b**3 - 1/126*b**7 - 2/15*b**6 - 5/3*b**4. Determine o so that w(o) = 0.
-5, -1, 0
Let r(w) be the first derivative of 2*w**5/85 - 93*w**4/34 - 190*w**3/17 - 287*w**2/17 - 192*w/17 - 410. Solve r(s) = 0 for s.
-1, 96
Let r(i) = -i**2 - 5*i + 26. Let h be r(-8). Let s(o) = 24*o**3 + 2*o**2 - 22. Let m(g) = g**3 - 1. Let