nd derivative of -d**4/36 - 23*d**3/18 + 187*d**2/3 + 1854*d - 2. Find w such that i(w) = 0.
-34, 11
Let x(g) be the second derivative of -2/45*g**5 + 0*g**3 + 0 + 1/135*g**6 + 0*g**2 + 74*g + 2/27*g**4. Determine v, given that x(v) = 0.
0, 2
Let n be (-4)/(-48)*6*(-12)/(-2). Factor -11*s**2 - 49*s**2 - 18*s + n*s + 15*s + 12*s - 33*s**3.
-3*s*(s + 2)*(11*s - 2)
Let k(a) be the second derivative of -3/50*a**5 + 40*a + 1/10*a**3 + 2/5*a**4 - 6/5*a**2 - 2/25*a**6 + 0 + 1/70*a**7. Suppose k(n) = 0. What is n?
-1, 1, 4
Let g = -1431/5 - -287. Let m(r) be the first derivative of -5/4*r**4 - 1/6*r**6 + 0*r + 0*r**2 - 2/3*r**3 - g*r**5 - 2. Let m(o) = 0. Calculate o.
-2, -1, 0
Let j be -1 + (-1 + -30 - (-7)/(-7)). Let t be (-3)/(-1) - j/(-99). What is w in 4/9*w**2 - t*w + 4 = 0?
3
Suppose 5*s + 64 = -31. Let o be -1 + 5 - (s - -5). Factor 2*t**3 + 2*t**3 - 12*t**2 + 22 - 26 + o*t - 6*t.
4*(t - 1)**3
Factor 763 + 405*d + 14 + 87*d + 3*d**2 + 288*d.
3*(d + 1)*(d + 259)
Let o(x) = 4*x**3 + 3*x**2 - 9*x + 5. Let z be o(1). Solve -144/5 - 52/5*j**2 - 676/5*j**z + 96*j = 0.
-1, 6/13
Let g(j) be the second derivative of 18*j**2 + 0 - 1/140*j**5 - 1/28*j**4 + 0*j**3 + 3/280*j**6 + 16*j. Let x(z) be the first derivative of g(z). Factor x(o).
3*o*(o - 1)*(3*o + 2)/7
Let n = 300689/28 - 75146/7. Suppose -9*t**2 + 33/4*t + 9/2 - n*t**3 = 0. What is t?
-3, -2/5, 1
Let k(y) = 3*y**2 - 64*y + 180. Let m be ((-182)/(-78))/((-14)/(-12)). Let r(g) = 20*g**2 - 450*g + 1260. Let x(t) = m*r(t) - 15*k(t). Factor x(j).
-5*(j - 6)**2
Let u(m) be the first derivative of -m**5/30 - 2*m**4/3 - 4*m**3 - 92*m**2 + 50. Let j(p) be the second derivative of u(p). Factor j(q).
-2*(q + 2)*(q + 6)
Let l(s) be the first derivative of s**6/120 - s**5/30 - 5*s**4/24 + s**3 - 25*s**2/2 + 64. Let u(m) be the second derivative of l(m). Solve u(q) = 0.
-2, 1, 3
Let z(q) be the third derivative of q**8/504 - q**7/315 - q**6/18 - 4*q**5/45 - 440*q**2. Let z(x) = 0. What is x?
-2, -1, 0, 4
Let b(m) be the first derivative of -m**4/18 - 3184*m**3/27 - 633616*m**2/9 - 3042. Factor b(v).
-2*v*(v + 796)**2/9
Factor 288 + 3/2*o**3 + 57/2*o**2 + 168*o.
3*(o + 3)*(o + 8)**2/2
Let j(q) = 36*q**2 - 1140*q - 2292. Let c(a) = 5*a**2 - 163*a - 328. Let o(d) = -44*c(d) + 6*j(d). Factor o(v).
-4*(v - 85)*(v + 2)
Let c = -214361 - -214361. Factor c*i + 16/5*i**4 + 0 + 2/5*i**5 + 0*i**2 + 24/5*i**3.
2*i**3*(i + 2)*(i + 6)/5
Factor -26/3*l - 1/6*l**2 + 55/2.
-(l - 3)*(l + 55)/6
Let u(q) be the second derivative of -43/12*q**4 + 0 - 34/3*q**3 - 10*q**2 + 175*q + 1/4*q**5. Factor u(y).
(y - 10)*(y + 1)*(5*y + 2)
Suppose 12*y - 63*y + 3309127 = -2896043. Factor -y*i + 7935*i**2 - 230*i**3 + 5/2*i**4 + 1399205/2.
5*(i - 23)**4/2
Let f(i) = i**3 - 6*i**2 - 12*i + 51. Let b be f(7). Suppose 33*k + 16 = b. Determine y, given that 1/4*y**3 + 0*y + k + 1/2*y**2 = 0.
-2, 0
Let q(s) = -29*s**2 + 2*s - 1. Let r(j) = 56*j**2 - 3868*j - 1866310. Let h(p) = 4*q(p) + 2*r(p). Determine n so that h(n) = 0.
-966
Factor 43808/3 + 1776*o + 54*o**2.
2*(9*o + 148)**2/3
Let n be ((-68)/12 - 190/114) + (-1 - -9). Factor 0*u + n*u**2 + 0 - 2/3*u**3 + 1/6*u**4.
u**2*(u - 2)**2/6
Let f(o) = -3*o**2 - 93*o. Let q(w) = -2*w**2 + 3*w. Let h(m) = -f(m) + 4*q(m). Factor h(v).
-5*v*(v - 21)
Let u(r) = r**2 - 2*r + 3. Let v(b) = b**2 - 13*b + 14. Let k be v(12). Let g be u(k). Factor 7*h**2 - 7*h**2 - 3*h**2 - 6*h - g.
-3*(h + 1)**2
Let o(g) be the second derivative of -64*g**3 + 260*g - 40*g**2 + 0 - 95/3*g**4 - 12/5*g**5 + 14/15*g**6. Find p such that o(p) = 0.
-2, -1, -2/7, 5
Let n(t) = 12*t**4 + 40*t**3 - 4*t**2 - 16*t. Let r(k) = 4*k**4 + 13*k**3 - 2*k**2 - 5*k. Let s(v) = 5*n(v) - 16*r(v). Factor s(o).
-4*o**2*(o - 1)*(o + 3)
Let s be (39/3)/(285467/9411). Factor s*q**3 + 52/7*q + 4/7*q**4 - 34/7*q**2 - 24/7 - 1/7*q**5.
-(q - 2)**3*(q - 1)*(q + 3)/7
Let j(y) = -y - 4. Let u be j(-4). Let i = -71589 - -71591. Suppose -2/5*q**3 - 4/5*q - 6/5*q**i + u = 0. What is q?
-2, -1, 0
Let r(c) be the third derivative of c**7/1470 + 8*c**6/105 + 253*c**5/70 + 1976*c**4/21 + 61009*c**3/42 - 25*c**2 - 6. Solve r(x) = 0 for x.
-19, -13
Let u(y) = -27*y + 471. Let j be u(18). Let w be (-324)/(-8) - j/(-5). Solve -1/2*l**3 - 15/2*l**2 - w*l - 125/2 = 0.
-5
Let t(g) be the first derivative of 2/45*g**3 + 28 + 0*g**2 - 8/15*g. Factor t(k).
2*(k - 2)*(k + 2)/15
Determine a so that 4*a**2 + 10*a**2 - 909*a + 18*a**3 + 10*a**4 + 2*a**5 + 459*a + 454*a = 0.
-2, -1, 0
Suppose -115 = 9*p - 14*p. Factor -34*a**2 - 32*a**2 + p*a - 4*a**3 + 2*a**2 + 45*a.
-4*a*(a - 1)*(a + 17)
Factor -28*v**2 + 4050 + 495*v + 1/3*v**3.
(v - 45)**2*(v + 6)/3
Let r be 3108/(-370)*5/(-14). Suppose 140/3*u**2 + 5/3*u**5 + 10*u**r - 30 - 35/3*u - 50/3*u**4 = 0. What is u?
-1, 1, 2, 9
Let a(s) be the second derivative of 67/16*s**3 + 33/16*s**4 + 0*s**2 - 3/160*s**5 - 15 - 2*s. Factor a(u).
-3*u*(u - 67)*(u + 1)/8
Let q(t) be the second derivative of t**6/10 + 15*t**5/4 + 87*t**4/4 - 253*t**3/2 + 210*t**2 + 323*t. Factor q(m).
3*(m - 1)**2*(m + 7)*(m + 20)
Suppose -147 = -4*a + 57. Let q = -49 + a. Let -7*l**q - 1 + 6*l**2 + 6*l + 3 - 7*l = 0. What is l?
-2, 1
Suppose 12 = -4*x + 7*x. Suppose -j - 2*u = 6, 0 = -4*j - 4*u - x - 4. Factor -23*q**j - 10*q + 8*q**3 + 20*q**2 - 12*q**4 + 2*q + 15*q**2.
-4*q*(q - 1)*(q + 1)*(3*q - 2)
Factor -498*a - 82668 - 3/4*a**2.
-3*(a + 332)**2/4
Let j = 6 + -2. Suppose j*n + 10 = 9*n. Factor 3*m**n - 2*m + m**2 - 3*m**2 + 3*m**2.
2*m*(2*m - 1)
Suppose 0 = 72*w - 50*w - 132. Factor 125*n + 75*n + 160*n**2 - 12*n**4 + 5*n**4 - 38*n**3 + 3*n**4 + w*n**4.
2*n*(n - 10)**2*(n + 1)
Let r(p) be the second derivative of -p**4/6 - 17*p**3 - 308*p**2 + 2*p + 3044. Factor r(i).
-2*(i + 7)*(i + 44)
Let x(b) be the second derivative of -b**10/7560 - b**9/540 + b**8/210 - 13*b**4/4 + 124*b. Let p(h) be the third derivative of x(h). Factor p(c).
-4*c**3*(c - 1)*(c + 8)
Let u(f) be the second derivative of -5*f**9/12096 - f**8/448 + f**6/72 - 28*f**3/3 + 63*f - 2. Let c(r) be the second derivative of u(r). Factor c(d).
-5*d**2*(d - 1)*(d + 2)**2/4
Let m = -1249/10 + 27259/110. Solve m + 104/11*n + 2/11*n**2 = 0 for n.
-26
Let u(l) be the second derivative of -3*l**5/34 - 929*l**4/51 - 57412*l**3/51 + 7688*l**2/17 - 20*l - 4. Determine k so that u(k) = 0.
-62, 2/15
Let i(w) = 10*w**3 - 915*w**2 - 1660*w - 5. Let x(g) = -5*g**3 + 468*g**2 + 830*g + 3. Let j(o) = -3*i(o) - 5*x(o). Solve j(r) = 0 for r.
-2, 0, 83
Suppose -3*n + 8 = 3*a - 19, a = -3*n + 29. Suppose -n - 20 = -3*k. Factor 4*z - k + 6 - 2*z**2 + 2*z.
-2*(z - 2)*(z - 1)
Let t(x) be the third derivative of -2*x**7/105 - 23*x**6/30 - 22*x**5/15 - 1038*x**2. Factor t(a).
-4*a**2*(a + 1)*(a + 22)
Let v(d) = -11*d**4 - 96*d**3 - 113*d**2 + 219*d + 10. Let q(j) = j**4 + j**3 + 2*j**2 + j - 2. Let l(r) = -3*q(r) + v(r). Suppose l(k) = 0. Calculate k.
-4, -1/14, 1
Factor -78*z**2 - 1/4*z**4 - 79/2*z**3 + 0 + 0*z.
-z**2*(z + 2)*(z + 156)/4
Let b(r) be the first derivative of -r**6/60 + 11*r**5/30 + 7*r**4/6 - 8*r**3 + r**2/2 + 18*r + 243. Let s(i) be the second derivative of b(i). Factor s(z).
-2*(z - 12)*(z - 1)*(z + 2)
Find k such that 9/2*k + 30 + 1/6*k**2 = 0.
-15, -12
Factor 2543 - 2543 + 109*d + 27*d + 4*d**2.
4*d*(d + 34)
Let c(j) be the third derivative of -j**5/210 - 5*j**4/3 - 18*j**2 + 5. Suppose c(f) = 0. Calculate f.
-140, 0
Let z(x) be the first derivative of 5 + 676*x + 1/3*x**3 - 26*x**2. Factor z(h).
(h - 26)**2
Factor p**2 + 2*p - 2*p**2 + 10*p**2 + 2*p - 7*p**2 - 16.
2*(p - 2)*(p + 4)
Let g(t) = 32*t**2 + 34*t + 144*t + 99*t + 63 + 16*t**2. Let b(d) = 6 - 14 - 54 + 3*d**2 - 50*d**2 - 278*d. Let s(h) = 3*b(h) + 2*g(h). Factor s(q).
-5*(q + 6)*(9*q + 2)
Let a(z) be the first derivative of -2*z**5/5 + 3*z**4/10 + 464*z**3/15 + 492*z**2/5 + 64*z - 12864. Suppose a(u) = 0. Calculate u.
-5, -2, -2/5, 8
Let k(n) = 2*n**2 + 2*n - 4. Suppose -3*c + 15 = 33. Let z(p) = 3*p**2 - p - 6. Let q(i) = c*k(i) + 5*z(i). Suppose q(r) = 0. What is r?
-1/3, 6
Let o(a) be the second derivative of 0*a**3 + 0 + 1/63*a**7 + 81*a + 0*a**2 + 1/15*a**6 + 0*a**4 + 1/15*a**5. Suppose o(y) = 0. What is y?
-2, -1, 0
Let h(c) = -c**2 + c + 1. Let k(p) = -53*p - 7 + 44*p + 3*p**2 - 2*p**2. Let d(q) = -3*h(q) - k(q). Find b, given t