- 9/20*f**5 - f**3 + 1/8*f**6 + 0*f - r*f**2 + 7/8*f**4 + 0. Solve o(p) = 0 for p.
1, 2
Let q(a) be the third derivative of a**6/160 + 19*a**5/20 + 361*a**4/8 - 32*a**2 - a. Determine k so that q(k) = 0.
-38, 0
Let f(c) be the third derivative of -c**7/630 - 13*c**6/2160 - c**5/120 - 3*c**4/8 + 18*c**2. Let j(s) be the second derivative of f(s). Factor j(x).
-(3*x + 1)*(4*x + 3)/3
Suppose l + 33 = -177. Let v = -1042/5 - l. Let -v*g**2 + 0 - 6/5*g - 2/5*g**3 = 0. What is g?
-3, -1, 0
Let r = -175 - -178. Let i(k) be the third derivative of -1/9*k**r + 0 + 0*k - k**2 - 1/36*k**4 + 1/45*k**5. What is u in i(u) = 0?
-1/2, 1
Let -60 + 45*b**3 - 39476*b - 3*b**5 - 5*b**4 + 25*b**2 + 39396*b - 2*b**5 = 0. What is b?
-3, -1, 2
Let g = 142 - 122. Let y be (3/(-4))/((-30)/g). Factor y*v + 3/4 - 1/4*v**2.
-(v - 3)*(v + 1)/4
Let u(n) = n**3 - 12*n**2 - 12*n - 9. Let b be u(13). Let q(x) be the first derivative of 7 - 1/4*x**b + 1/2*x**2 - 3*x + x**3. Find s, given that q(s) = 0.
-1, 1, 3
Let r = -116 + 144. Factor 20*j**2 + 32 - 17 - r*j - 7.
4*(j - 1)*(5*j - 2)
Let l(x) be the first derivative of -x**6/6 + x**5/4 + 5*x**4/4 - 25*x**3/6 + 5*x**2 - 44*x + 24. Let u(w) be the first derivative of l(w). Factor u(t).
-5*(t - 1)**3*(t + 2)
Let h(q) be the first derivative of q**4 + 20/21*q**3 + 10 - 32/7*q**2 + 16/7*q. Factor h(r).
4*(r - 1)*(r + 2)*(7*r - 2)/7
Let a(h) be the third derivative of -1/12*h**6 + 5/6*h**3 + 1/6*h**5 + 5/8*h**4 - 1/14*h**7 - 5/336*h**8 + 0 + 10*h**2 + 0*h. Factor a(z).
-5*(z - 1)*(z + 1)**4
Suppose 14*d + 2*d = 2*d. Let a(c) be the third derivative of d*c + 0*c**4 + 5*c**2 + 1/30*c**5 + 0 - 1/3*c**3. Determine b, given that a(b) = 0.
-1, 1
Let g(n) = 92*n**3 - 2292*n**2 - 3200*n - 744. Let b(q) = -18*q**3 + 458*q**2 + 640*q + 149. Let l(t) = -24*b(t) - 5*g(t). Let l(a) = 0. What is a?
-1, -2/7, 18
Let r = -2573 + 2573. Factor -k**3 + 2/3*k**2 + 0 + 1/3*k**4 + r*k.
k**2*(k - 2)*(k - 1)/3
Let m = 35/44 + 5/132. Let h(u) be the third derivative of 1/12*u**5 + 0*u + 5/12*u**4 + m*u**3 + 0 + 8*u**2. Factor h(r).
5*(r + 1)**2
Let s(k) be the first derivative of -8*k**3/27 + 17*k**2/3 + 26*k/9 + 35. What is j in s(j) = 0?
-1/4, 13
Let k(b) be the third derivative of 0*b + 5/336*b**8 + 0 + 7/24*b**6 + 5/42*b**7 + 1/4*b**5 + 0*b**4 - 4*b**2 + 0*b**3. Factor k(t).
5*t**2*(t + 1)**2*(t + 3)
Factor 25120 - 24*s + 3*s**2 - 412 + 588*s + 1800.
3*(s + 94)**2
Factor -332 - 252*c + 230 - 117*c**2 - c**3 + 151*c**2 - 546.
-(c - 18)**2*(c + 2)
Let u(z) be the third derivative of 27*z**6/32 - 15*z**5/4 + 185*z**4/96 - 5*z**3/12 - 145*z**2. Factor u(o).
5*(o - 2)*(9*o - 1)**2/4
Let n(z) be the third derivative of z**6/120 + z**5/15 - 7*z**4/24 - 4*z**3/3 + 3*z**2. Let i be n(-5). Factor 0*y**i - 32 + 31*y - 2*y**2 - 15*y.
-2*(y - 4)**2
Let y be 1/((-2)/(-2825))*4/4. Let b = y - 13999/10. Solve b*g**2 - 45*g**3 - 6/5*g + 312/5*g**4 - 144/5*g**5 + 0 = 0.
0, 1/4, 2/3, 1
Let a = -1030 - -23694/23. Let g = 74/161 - a. Factor -2/7 - 2/7*d + 4/7*d**2 + 4/7*d**3 - g*d**5 - 2/7*d**4.
-2*(d - 1)**2*(d + 1)**3/7
Let t(v) be the first derivative of 4*v**5 - 5*v**4/2 - 65*v**3/4 - 85*v**2/8 - 5*v/2 + 26. Let t(w) = 0. Calculate w.
-1, -1/4, 2
Factor -2*g**2 - 135*g - 2*g**2 + 28*g - 177*g.
-4*g*(g + 71)
Let s = 102 - 97. Find y, given that 2*y - 9 + 3*y**5 - s*y**3 - 623*y**4 + 614*y**4 - y**3 + 18*y**2 + y = 0.
-1, 1, 3
Let o be (-200)/(-90) + 4/(-18). Suppose 0 = -q + o. Find w, given that w**5 - 8*w + 24*w**3 - q*w**4 - 14*w**2 - 41*w**5 + 46*w**4 - 6*w**2 = 0.
-1/2, -2/5, 0, 1
Suppose 6*o + 5*d - 240 = o, 2*o = d + 99. Factor -20 - o*t**3 - 60*t + 49*t**3 + 45*t**2 + 35*t**3.
5*(t - 1)*(t + 2)*(7*t + 2)
Let g(i) = -2*i**5 - 3*i**4 + 14*i**3 + 3*i**2 - 37*i - 5. Let b(o) = o**5 + o**4 - 8*o**3 - 2*o**2 + 18*o + 2. Let y(h) = -5*b(h) - 2*g(h). Factor y(p).
-p*(p - 4)*(p - 1)*(p + 2)**2
Let q(x) = -12*x**2 - 44*x + 103. Let t(m) = -6*m**2 - 23*m + 52. Let y(a) = -2*q(a) + 5*t(a). Let y(z) = 0. What is z?
-6, 3/2
Let h(g) be the second derivative of -5*g**7/42 + g**6 - 5*g**5/2 + 55*g**3/6 - 15*g**2 - 443*g. Solve h(p) = 0.
-1, 1, 2, 3
Let z(r) be the third derivative of -r**7/42 + 5*r**6/24 + r**5/2 + 2*r**2 - 307*r. Factor z(h).
-5*h**2*(h - 6)*(h + 1)
Factor 46875/2 + 3/2*x**3 + 5625/2*x + 225/2*x**2.
3*(x + 25)**3/2
Let x be 6 - 4 - (0 + 1 + -1). Factor 20*k + 9*k**x - 11 + 19 - 5*k**2 + 16.
4*(k + 2)*(k + 3)
Factor -36/5 + 126/5*l + 6/5*l**3 - 56/5*l**2.
2*(l - 6)*(l - 3)*(3*l - 1)/5
Let z(d) be the second derivative of -d**7/336 - d**6/60 - 3*d**5/80 - d**4/24 - d**3/48 - 15*d - 4. What is j in z(j) = 0?
-1, 0
Let c = -11 + 15. Suppose c + 2 = 2*d. Factor 4 + 3*p**2 - 3*p**d - 3 - 4 + 3*p.
-3*(p - 1)**2*(p + 1)
Let n(o) = -o**3 - 8*o**2 - 9*o + 4. Let w be n(-7). Let g = 27 - w. Factor 5*t**4 + 3*t**2 - t**4 - g*t**3 + 5*t**4 - 3*t**5 + 0*t**5.
-3*t**2*(t - 1)**3
Let s(b) = 17*b**2 - 1244*b + 599. Let k(o) = 8*o**2 - 617*o + 299. Let p(c) = -5*k(c) + 2*s(c). Factor p(g).
-3*(g - 99)*(2*g - 1)
Let d(c) be the first derivative of 0*c + 0*c**2 - 12 - 4/3*c**3. Factor d(f).
-4*f**2
Let k be ((-476)/(-8))/(-17)*42/(-35). Let -18/5 - 3/5*b**2 - k*b = 0. Calculate b.
-6, -1
Let k(u) be the first derivative of 2/3*u**3 - 29 + 0*u - 2*u**2 + u**4 - 2/5*u**5. Factor k(l).
-2*l*(l - 2)*(l - 1)*(l + 1)
Let y(o) = -6*o**2 + 3*o**2 + 6*o - 5 + 1. Let k(x) = 24*x**2 + 7*x - 22*x**2 - 6*x**2 - 4. Let a(r) = -2*k(r) + 3*y(r). Let a(d) = 0. What is d?
2
Let h(s) be the first derivative of -16/27*s**3 + 1/9*s**4 + 7 + 7/9*s**2 - 1/27*s**6 - 4/9*s + 4/45*s**5. Factor h(a).
-2*(a - 1)**4*(a + 2)/9
Let j = 35 + -26. Let s = j + -9. Factor 2/7*o**2 - 2/7*o**4 + s + 2/7*o**3 - 2/7*o.
-2*o*(o - 1)**2*(o + 1)/7
Let x(q) = 17*q - 11. Let p be x(1). Solve 0 + 4*m**2 + 0 - 2*m**4 + p*m**2 - 8 = 0.
-2, -1, 1, 2
Let r be (2/60)/(-9 - (-4039)/448). Let z be (-36)/(-9)*2/4. Factor -2/15*c**z - r + 16/15*c.
-2*(c - 4)**2/15
Factor -60*g**2 + 1 + 35*g**3 + 3 - 67*g**3 - 24*g.
-4*(g + 1)**2*(8*g - 1)
Let u be 5/((-45)/(-3)) + 35/(-15) + 5. Factor -216/7 + 1/7*k**u + 108/7*k - 18/7*k**2.
(k - 6)**3/7
Determine j, given that 71*j - 40*j - 11*j**2 - 42 + 12*j**2 + 10 = 0.
-32, 1
Let h(f) be the first derivative of -f**5/5 - 9*f**4/4 + 7*f**3 - 11*f**2/2 + 27. Factor h(z).
-z*(z - 1)**2*(z + 11)
Let l(t) be the second derivative of t**8/84 + 2*t**7/105 + 10*t**2 + 4*t. Let n(y) be the first derivative of l(y). Factor n(r).
4*r**4*(r + 1)
Suppose 2*r - 1 - 5 = 0. Find t such that 5*t + r*t**3 - 5*t**3 - 2*t - t = 0.
-1, 0, 1
Let i(z) = -z**3 + 12*z**2 - 12*z + 15. Let o be i(11). Determine f, given that 2*f**3 - o*f + 10*f + 2*f**2 - 8*f - 2*f**4 + 0*f**2 = 0.
-1, 0, 1
Find x, given that 36 + 30*x + 7*x**2 + 0*x**2 - 69*x - 4*x**2 = 0.
1, 12
Let r(g) be the first derivative of 0*g - 3/4*g**4 + 0*g**3 - 11 + 0*g**2. Suppose r(j) = 0. What is j?
0
Let o(q) = -q**2 + 4. Let w be o(0). Factor -4*c**w - 19*c**2 + 1 + 17*c**2 + 5*c**4.
(c - 1)**2*(c + 1)**2
Let j(v) = 180*v - 4135. Let q be j(23). Factor 2*w**3 + 0 + 26*w**4 + 0*w**2 + 0*w + 169/2*w**q.
w**3*(13*w + 2)**2/2
Let z(x) be the second derivative of -x**7/210 + x**5/10 - x**4/3 - 19*x**3/6 - 8*x. Let f(t) be the second derivative of z(t). Find c, given that f(c) = 0.
-2, 1
Let u(d) be the third derivative of d**6/40 - d**5/10 - 5*d**4/8 + 3*d**3 - 75*d**2. Factor u(n).
3*(n - 3)*(n - 1)*(n + 2)
Suppose -o + 28 = 3*o. Let s(u) = -u**3 + 9*u**2 - 13*u - 1. Let c be s(o). Factor -3/4*r**3 - 3 - c*r - 15/4*r**2.
-3*(r + 1)*(r + 2)**2/4
Let x(y) = -8*y**2 + 168*y - 202. Let t(q) = -3*q**2 + 58*q - 67. Let z(d) = -7*t(d) + 2*x(d). Let z(f) = 0. What is f?
1, 13
Let h be (12/90)/(63/20 + (43 - 46)). Solve h + 2/9*u**3 + 4/9*u**2 - 14/9*u = 0 for u.
-4, 1
Factor -26/3*s**4 + 2/3*s**5 + 0 - 30*s**3 - 32/3*s - 94/3*s**2.
2*s*(s - 16)*(s + 1)**3/3
Let p be 258/172 - 1*-13*7. Let l = -2027/22 + p. Factor l*k + 0 + 2/11*k**2.
2*k*(k + 2)/11
Suppose 280 = s + 278. Let i(c) be the third derivative of -1/100*c**5 - 1/300*c**6 - 4*c**s + 2/15*c**3 + 1/30*c**4 + 0 + 1/1050*c**7 + 0*c. Factor i(g).
(g - 2)**2*(g + 1)**2/5
Factor 2*t**3 - 2*t**3 + 970*t**2 - t**3 - 969*t**2 + 8 + 10*t.
-(t - 4)*(t + 1)*(t + 2)
Let g = -5 + 7. Solve 6*k**3 - 6*k**g + 0*k**2 + 