7, 3
Determine g, given that -9*g**2 - 26*g - 2*g**4 - 50*g + 44*g - 31*g**2 - 16*g**3 = 0.
-4, -2, 0
Let r(w) = -w**4 + w**3 - 1. Let f(y) = 0 - 6*y**3 + 8*y**4 + 9 - 2*y**3. Let b = -23 - -25. Let z(q) = b*f(q) + 18*r(q). Factor z(a).
-2*a**3*(a - 1)
Factor 12*c - 72*c + 4*c**4 - 16*c**4 + 28*c - 76*c**3 - 120*c**2.
-4*c*(c + 2)*(c + 4)*(3*c + 1)
Let z(i) be the third derivative of -i**5/60 - 3*i**4/4 + 11*i**3/3 + 7*i**2. Let f be z(-19). Suppose 0 + m**2 + 1/3*m + m**f + 1/3*m**4 = 0. Calculate m.
-1, 0
Let g = 123 + -115. Factor 8 + 177*o + g*o**2 - 327*o + 170*o - 16*o**3 - 4*o**5 - 16*o**4.
-4*(o - 1)*(o + 1)**3*(o + 2)
Factor 2*w**5 - 2*w**2 + 1 - 2*w**4 + 3 - 3*w**5 + 33*w - 40*w + 8*w**3.
-(w - 1)**3*(w + 1)*(w + 4)
Let a(b) be the third derivative of -31*b**5/60 + b**4/12 + 24*b**2 + 1. Determine w, given that a(w) = 0.
0, 2/31
Let j(q) = q**3 + 3*q**2 - 3*q. Let k be j(-4). Let n be (6 - (-34)/k)*4/(-5). Suppose 14/5*v - 14/5*v**3 - 4/5 + 4/5*v**n = 0. Calculate v.
-1, 2/7, 1
Let z(v) be the second derivative of v**5/70 + 19*v**4/42 + 104*v**3/21 + 176*v**2/7 - 144*v. Let z(t) = 0. What is t?
-11, -4
Let s(m) be the second derivative of 0*m**2 + 0 + 0*m**3 + 1/65*m**5 + 1/26*m**4 - 1/195*m**6 + 23*m. Factor s(t).
-2*t**2*(t - 3)*(t + 1)/13
Suppose -4*l + l = 4*t - 1362, 2*t - 4*l - 670 = 0. Suppose -337*o**3 - 7*o + 31*o + t*o**3 + 16 + 12*o**2 = 0. Calculate o.
-2
Let t(d) be the second derivative of -1/2*d**5 + 5/3*d**3 + 15/2*d**2 + 3*d + 0 + 1/6*d**6 - 5/3*d**4. Let t(j) = 0. Calculate j.
-1, 1, 3
Solve 20 + 5*h**2 + 29*h**3 - 40*h + 10*h**5 - 25*h**4 + 6*h**3 - 5*h**5 = 0.
-1, 1, 2
Let h = -542 - -542. Let q(f) be the third derivative of h*f**3 + 0 + 1/75*f**5 - 1/300*f**6 - 1/60*f**4 + 0*f + 6*f**2. What is j in q(j) = 0?
0, 1
Let p(x) be the first derivative of 1/36*x**4 + 6 + 0*x**2 + 3*x + 1/18*x**3. Let n(k) be the first derivative of p(k). Factor n(y).
y*(y + 1)/3
Factor -529/7 + 276/7*y - 36/7*y**2.
-(6*y - 23)**2/7
Let u(r) = 3*r**4 - 120*r**3 + 832*r**2 - 1322*r + 607. Let z(i) = 5*i**4 - 240*i**3 + 1665*i**2 - 2645*i + 1215. Let d(h) = 5*u(h) - 2*z(h). Factor d(v).
5*(v - 11)**2*(v - 1)**2
Let g(p) = p**2 + 2. Let v be g(2). Let k(j) = -j**2 - j - 1. Let h(a) = -2 - 2*a**2 - 3*a + 3 + 1 - 4. Let b(d) = v*h(d) - 14*k(d). Factor b(z).
2*(z - 1)**2
Let a(y) = 3*y - 3. Let f be a(2). Suppose s - 1 = f. Factor -t**5 + 0*t**5 + t**3 + 4*t**5 - s*t**5.
-t**3*(t - 1)*(t + 1)
Suppose 0*r - r + 5 = 0. Let v = -252 + 254. Factor 4*d**3 + 20*d**2 + 3*d**r - 20*d**v + 8*d**4 + d**5.
4*d**3*(d + 1)**2
Let v(n) = -5*n**3 - 3*n**2 - 3*n + 3. Let r(s) = 17*s + 10 - 22 + 29*s**3 - 5 + 18*s**2. Let w(x) = -6*r(x) - 34*v(x). Factor w(c).
-2*c**2*(2*c + 3)
Let x(w) be the first derivative of 5/2*w**2 - 1/3*w**3 - 3 + 1/6*w**4 - 1/30*w**5 + 0*w. Let g(k) be the second derivative of x(k). Factor g(j).
-2*(j - 1)**2
Factor -22*w**2 + 420*w - 206*w - 214*w - 24*w**2 - 2*w**3.
-2*w**2*(w + 23)
Let m(o) = -2*o**3 - 7*o**2 - 5*o. Let d be (36/15)/(3/(-30)). Let y(h) = -9*h**3 - 36*h**2 - 24*h. Let l(p) = d*m(p) + 5*y(p). Factor l(s).
3*s**2*(s - 4)
Determine z so that -64/11*z**2 + 4/11*z**4 + 30/11*z + 0 + 6/11*z**3 = 0.
-5, 0, 1/2, 3
Let j(f) = -f**3 - 20*f**2 - 99*f + 119. Let y(z) = z**2 - 2. Let a(t) = -2*j(t) + 2*y(t). Find n such that a(n) = 0.
-11, 1
Let x(r) be the third derivative of r**8/33600 - r**7/1800 + r**6/240 - 3*r**5/200 - 3*r**4/8 + 14*r**2. Let k(y) be the second derivative of x(y). Factor k(g).
(g - 3)**2*(g - 1)/5
Let s(p) = -32*p**2 + 161*p + 416. Let x(c) = 11*c**2 - 53*c - 138. Let o(v) = -6*s(v) - 17*x(v). Determine m so that o(m) = 0.
-2, 15
Let p(l) be the third derivative of 9*l**7/280 - l**6/60 + 3*l**3/2 - 12*l**2. Let n(a) be the first derivative of p(a). Factor n(m).
3*m**2*(9*m - 2)
Let f(q) be the second derivative of 0 + 2/5*q**5 - 8*q**2 + q**4 - 2/15*q**6 - 8/3*q**3 - 3*q. Factor f(g).
-4*(g - 2)**2*(g + 1)**2
Let r(f) be the second derivative of -f**4/54 + f**3/3 - 8*f**2/9 - 14*f + 2. Factor r(y).
-2*(y - 8)*(y - 1)/9
Let p be (-2268)/114 + 6 + 14. Factor p*j**2 - 6/19 - 4/19*j.
2*(j - 3)*(j + 1)/19
Let c(s) be the third derivative of 2/15*s**5 + 0 - 1/10*s**6 - 16/105*s**7 + 0*s**3 - 4*s**2 + 0*s**4 - 1/28*s**8 + 0*s. Find g, given that c(g) = 0.
-2, -1, 0, 1/3
Let z(f) = -f**2 - 6*f. Let n(v) = -6*v**2 - 27*v - 2. Let q(g) = n(g) - 5*z(g). Solve q(b) = 0 for b.
1, 2
Let g(j) be the third derivative of -28*j**2 + 0*j - 1/720*j**6 + 0 - 1/360*j**5 + 5/144*j**4 - 1/12*j**3. Factor g(z).
-(z - 1)**2*(z + 3)/6
Factor -5/2*m**2 - 35 + 45/2*m.
-5*(m - 7)*(m - 2)/2
Factor 19*d**2 - 44*d**2 + 49*d - 39*d.
-5*d*(5*d - 2)
Let h = 9/535 + 472/3745. Factor 0 - 1/7*g**2 - h*g**3 + 2/7*g.
-g*(g - 1)*(g + 2)/7
Suppose -2/5 + 4/15*h**2 - 8/15*h**3 + 2/15*h**4 + 8/15*h = 0. What is h?
-1, 1, 3
Let w(g) be the second derivative of g**10/50400 + g**9/25200 - g**8/11200 - g**7/4200 - g**4/12 - 4*g. Let p(z) be the third derivative of w(z). Factor p(v).
3*v**2*(v - 1)*(v + 1)**2/5
Let x(d) be the second derivative of -2*d**6/15 + 7*d**5/5 - 7*d**4/3 - 10*d**3 + 17*d - 2. Factor x(p).
-4*p*(p - 5)*(p - 3)*(p + 1)
Let x be (2/8)/((-33)/(-88)). Let q(a) be the first derivative of -1/2*a**2 + x*a**3 + 0*a - 4 - 1/4*a**4. Factor q(f).
-f*(f - 1)**2
Let n = 6929 + -6926. Factor 0 - 4/3*c - 5/3*c**2 - 1/3*c**n.
-c*(c + 1)*(c + 4)/3
Suppose -3*i + 17 = 2. Suppose 6 + 3*o**2 + i*o**2 - 6 + 4*o**3 + 4*o = 0. What is o?
-1, 0
Let p(v) be the second derivative of 9*v**7/56 + 9*v**6/20 + 9*v**5/20 + v**4/6 - 22*v + 3. Determine j, given that p(j) = 0.
-2/3, 0
Let l(w) = w**3 + 8*w**2 + 10*w + 11. Let q be l(-5). Factor q*m**3 - 48*m**2 - 140*m - 32 + 14*m**4 + 12*m - 4*m**3.
2*(m - 2)*(m + 2)**2*(7*m + 2)
Let v(i) = -i**3 - 66*i**2 + 51*i - 1072. Let z be v(-67). Suppose z*n**2 + 1/3*n**5 + 0*n**4 - 1/3*n**3 + 0*n + 0 = 0. What is n?
-1, 0, 1
Suppose -42*r - 14 = -52 - 46. Factor -4*s**3 - 42/13*s + 10/13 - 2/13*s**5 + 68/13*s**r + 18/13*s**4.
-2*(s - 5)*(s - 1)**4/13
Let -35220*u**2 - 5 + 15*u + 35221*u**2 + 19 = 0. Calculate u.
-14, -1
What is f in -35631 - 54*f**3 + 5550*f - 1674*f**2 - 23951 - 22848*f = 0?
-31/3
Suppose 0 = 5*w - 5*k + 15, w - k = 4*w - 3. Suppose w*p = p. Factor p + 2/5*b**2 + 2/5*b.
2*b*(b + 1)/5
Suppose 0 = -6*h + 3 - 81. Let o(b) = b**3 + 13*b**2. Let q be o(h). Factor 1/2*t + 1/2*t**3 + q + t**2.
t*(t + 1)**2/2
Suppose -3*v + 2 = 2*x - v, 0 = -2*x - 5*v - 1. Determine c, given that c**x + c**3 - 6*c + 0*c**3 - c**4 + 5*c = 0.
-1, 0, 1
Suppose -16 = -66*i + 182. Let 80/3 - 20*o**2 + 4/3*o**4 + 16/3*o + 8/3*o**i = 0. What is o?
-5, -1, 2
Let v(f) be the third derivative of -f**5/20 - 15*f**4/8 - 7*f**3 - 276*f**2. Determine x so that v(x) = 0.
-14, -1
Let b(w) be the first derivative of 2*w - 8 + 9/11*w**2 - 8/11*w**3 + 8/33*w**4. Let s(h) be the first derivative of b(h). Suppose s(f) = 0. What is f?
3/4
Let h(t) be the third derivative of t**7/7140 - t**6/1020 + t**5/510 + 13*t**3/3 - 24*t**2. Let x(n) be the first derivative of h(n). Factor x(g).
2*g*(g - 2)*(g - 1)/17
Let y(f) be the first derivative of -98*f**6/15 - 28*f**5/5 - 4*f**4/3 + 4*f - 15. Let r(b) be the first derivative of y(b). Factor r(j).
-4*j**2*(7*j + 2)**2
Factor -30*n + 0*n**2 + 55*n + 5*n**2.
5*n*(n + 5)
Let w(h) = -2*h**3 - 6*h**2 - 4*h + 5. Let x(j) = -j**2 - j - 1. Let u(r) = -w(r) + 2*x(r). Let v(t) be the first derivative of u(t). Factor v(s).
2*(s + 1)*(3*s + 1)
Let n = 12 + -16. Let z(h) = -h + 2. Let v be z(n). Factor 0 - 10*u**3 + 8*u**2 - 4*u + v*u**3 + 0.
-4*u*(u - 1)**2
Suppose 18/7*y**3 + 6/7*y**4 + 2/7*y**2 + 0 - 6/7*y - 4/7*y**5 = 0. Calculate y.
-1, 0, 1/2, 3
Let x(i) be the first derivative of 3*i**5/10 + 15*i**4/4 - 3*i**3/2 - 21*i**2 + 30*i + 456. Solve x(p) = 0 for p.
-10, -2, 1
Let j(m) be the third derivative of 1/40*m**6 + 0*m**3 - 4*m**2 + 0 - 1/16*m**4 + 0*m - 1/80*m**5 + 3/280*m**7. Suppose j(s) = 0. Calculate s.
-1, 0, 2/3
Let q = 122 + -119. Let h(k) be the second derivative of -1/24*k**4 + 1/40*k**5 - 1/84*k**7 + 0*k**q + 0*k**2 + 1/60*k**6 + 5*k + 0. Solve h(v) = 0 for v.
-1, 0, 1
Let b(l) be the second derivative of l**5/30 - l**4/12 + 7*l**2 - 18*l. Let t(o) be the first derivative of b(o). Let t(i) = 0.